Feb 23, 2024  
2020-2021 Undergraduate Academic Catalog 
    
2020-2021 Undergraduate Academic Catalog [ARCHIVED CATALOG]

Course Descriptions


 

Industrial Engineering

  
  • IE 3771 - Automation Technologies

    2 lecture hours 2 lab hours 3 credits
    Course Description
    This course deals with automation technologies utilized in manufacturing, logistics, and service environments. It compares manual and automated systems for material handling, storage systems, inspection, and product identification. It includes hands-on lab instruction in topics such as robotic programming, as well as flexible manufacturing systems, and culminates with a project that uses microcontrollers, PLCs and a CoBot to sort work product and simulate an assembly line. (prereq: IE 426  or ME 323 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Understand and perform basic calculations regarding analog-to-digital conversion and digital-to-analog conversion
    • Distinguish important capabilities and limitations related to automation technologies, particularly with respect to robotics, identification, inspection, material handling, and storage systems
    • Select and justify a material transport system and a storage system for a given scenario in a manufacturing or service industry
    • Perform calculations related to production rate, production capacity, and storage capacity
    • Distinguish important capabilities and limitations of robotic processes
    • Program a robot using a software interface as well as online programming methods
    • Understand the inverse and forward kinematics of robots and related coordinate systems
    • Understand flexible automated production systems through case studies
    • Understand how image processing and visual systems are used in manufacturing processes

    Prerequisites by Topic
    • General understanding of a variety of manufacturing processes (such as machining, sheet metal stamping and forming, and plastic injection molding)

    Course Topics
    • Analog and digital Introduction: ADC, DAC, microcontroller employment, basics of arrays, vectors, matrices, & systems of linear equations
    • Introduction to logic control & PLCs: Boolean algebra, logic gates, truth tables, ladder logic for use in automation
    • Introduction to robotics: applications, coordinate system frames, manipulator classification, forward & inverse kinematics
    • Robotics & industrial control systems, robot programming, safety
    • Product lifecycle management (PLM), digital manufacturing, flexible manufacturing systems, transfer lines
    • flexible manufacturing systems & transfer lines case studies
    • Image processing and visual systems
    • Course project: employment of microcontrollers, PLC, and a CoBot to sort work product (factory mockup)

    Laboratory Topics
    • Analog/digital introduction via microcontrollers
    • PLCs & layout of factory (Sim)
    • Forward/inverse kinematics (SolidWorks Robot Sim)
    • RobotStudio Sim of ABB robot
    • Online programming of ABB robot & UR3 CoBots
    • Visual systems investigation

    Coordinator
    Dr. Leah Newman
  
  • IE 3820 - Stochastic Processes

    4 lecture hours 0 lab hours 4 credits
    Course Description
    This course continues the modeling approach to problem solving by presenting techniques used to analyze and design systems affected by random variables. Queueing theory, Markov processes, and decision theory are examined. Case studies and computer algorithms are utilized. (prereq: MA 262  and (MA 2314  or MA 231 ))
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Identify and apply quantitative analysis techniques to engineering problems related to random processes
    • Use quantitative management technique results to analyze alternative solutions and assist in decision making
    • Have an understanding of how these methods impact business and industry
    • Demonstrate systematic problem-solving skills and be able to communicate the process effectively

    Prerequisites by Topic
    • Understanding of basic probabilistic principles and calculations
    • Familiarity with common discrete probability distributions
    • An ability to take complex derivatives and limits

    Course Topics
    • Introduction to quantitative management
    • Probability for stochastic processes
    • Fundamentals of decision theory
    • Decision theory and utility theory
    • Queueing theory
    • Markov analysis
    • Dynamic programming
    • Review
    • Examinations

    Coordinator
    Dr. Aaron Armstrong
  
  • IE 4001 - Industrial Engineering Cooperative Practicum 1

    1 lecture hours 0 lab hours 1 credits
    Course Description
    Students complete the first quarter of approved, supervised cooperative employment. A written report of the work performed is required, as well as a draft of a technical paper related to the work experience. (prereq: sophomore standing and consent of program director)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Gain professional work experience
    • Present a written summary of the work experience and a related technical topic

    Prerequisites by Topic
    • None

    Course Topics
    • Depends on the specific co-op assignment

    Coordinator
    Dr. Leah Newman
  
  • IE 4002 - Industrial Engineering Cooperative Practicum 2

    1 lecture hours 0 lab hours 1 credits
    Course Description
    Students complete the second quarter of approved, supervised cooperative employment. A written report of the work performed is required, as well as a draft of a technical paper related to the work experience. (prereq: IE 4001  and consent of program director)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Gain professional work experience
    • Present a written summary of the work experience and a related technical topic

    Prerequisites by Topic
    • None

    Course Topics
    • Depends on the specific co-op assignment

    Coordinator
    Dr. Leah Newman
  
  • IE 4003 - Industrial Engineering Cooperative Practicum 3

    1 lecture hours 0 lab hours 1 credits
    Course Description
    Students complete the third quarter of approved, supervised cooperative employment. A written report of the work performed is required, as well as a final technical paper related to the work experience. (prereq: IE 4002  and consent of program director)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Gain professional work experience
    • Present a written summary of the work experience and a related technical topic

    Prerequisites by Topic
    • None 

    Course Topics
    • Depends on the specific co-op assignment

    Coordinator
    Dr. Leah Newman
  
  • IE 4260 - Design for Manufacture and Assembly

    2 lecture hours 2 lab hours 3 credits
    Course Description
    Product design has become increasingly challenging with shorter design/development cycles and the need to address numerous competing concerns, including usability, maintainability, reliability, disposability, and more. This course covers design guidelines and analytical techniques that can be utilized to improve product designs with the primary goal of simplifying manufacturing and assembly processes, thus making the production operations more cost-effective across the product’s lifecycle. (prereq: IE 426  or ME 323 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Understand the benefits associated with designing components and products with the entire product life cycle in mind
    • Understand how early design decisions can influence manufacturing processes, product costs, inspection practices, and supply chains
    • Evaluate and compare alternative component and assembly designs for manufacturability and cost effectiveness
    • Know some of the specific design changes and design guidelines that enable a component or product to have greater manufacturability, usability, maintainability, reliability, and disposability
    • Make and justify trade-offs between competing design objectives

    Prerequisites by Topic
    • Knowledge of a variety of manufacturing processes

    Course Topics
    • Product life cycle and design objectives
    • DFA
    • DFM for various manufacturing processes
    • Design for other objectives
    • Project work

    Laboratory Topics
    • The 2-hour weekly lab will be used to evaluate current product and component designs and to create improved designs. Students will disassemble one or more products and practice using various analytical techniques, as well as documenting new designs using CAD software

    Coordinator
    Dr. Doug Grabenstetter
  
  • IE 4332 - Lean

    3 lecture hours 0 lab hours 3 credits
    Course Description
    Lean techniques can be used to improve any business process and make companies globally competitive. During this course students will learn to identify what is value-added and what is waste in any business process and to eliminate identified waste. Students will also learn the value of teamwork in a Lean Enterprise and will be introduced to the concepts of 5S, Value Stream Mapping and Kaizen. (prereq: junior standing)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Explain lean thinking and management methods
    • Follow a phased process for Lean Enterprise implementation
    • Describe the seven forms of waste in business
    • Explain the five principles of lean and how to implement them in business
    • Understand and be able to apply the concept of value add and non-value add activities
    • Explain and prepare a value stream map
    • Explain and calculate takt time
    • Explain the difference between “push” and “pull” and apply tools to accomplish pull
    • Explain and apply 5S, cellular layouts, and leveling
    • Explain kaizen
    • Explain and apply A3

    Prerequisites by Topic
    • None

    Course Topics
    • Toyota philosophy and culture, lean leadership, and lean wastes
    • People development and team building
    • Process stability, flow and value stream mapping
    • Standard work
    • 5S, cellular layouts, and level loading
    • Total productivity maintenance
    • Manufacturing cells and setup reduction
    • Push vs. pull and kanban systems
    • Kaizen and change management
    • Toyota problem solving technique

    Coordinator
    Dr. Doug Grabenstetter
  
  • IE 4336 - Quick Response Manufacturing

    3 lecture hours 0 lab hours 3 credits
    Course Description
    Producing products profitably in an increasingly competitive world market requires speed and agility. Companies and organizations that can get their products and services to customers quickly tend to do so more efficiently and reliably and with better quality than do slower companies. This course will develop students’ abilities to sustainably and efficiently reduce the amount of time processes take to complete. Special focus will be placed on process mapping, production modeling, product development, cellular manufacturing, and mass customization. (prereq: junior standing)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Analyze important issues and decisions related to quick response manufacturing
    • Understand manufacturing system dynamics (particularly how lot size and utilization influence lead time)
    • Measure Manufacturing Critical-path Time, the QRM metric, in a variety of manufacturing, service, and logistical applications
    • Discuss quick response manufacturing in the context of production and office operations
    • Demonstrate knowledge of quick response manufacturing by redesigning a system or process to reduce the process lead time
    • Demonstrate knowledge of MPX rapid modeling software by utilizing it for process/system analysis and QRM focused improvements

    Prerequisites by Topic
    • None

    Course Topics
    • Benefits of QRM
    • Performance and time measurement
    • System dynamics and response time spiral
    • Reorganizing functional production departments into manufacturing cells
    • Designing, implementing, and operating manufacturing cells
    • Making capacity and lot sizing determinations/decisions
    • Building models and analyzing results using MPX software
    • Production planning in a QRM environment
    • POLCA and ConWIP production control systems
    • Customer and supplier relations with QRM
    • Office and service cells
    • New product introduction and product lifecycle with QRM principles

    Coordinator
    Dr. Aaron Armstrong
  
  • IE 4501 - Healthcare Systems Engineering

    3 lecture hours 0 lab hours 3 credits
    Course Description
    Healthcare as an industry is becoming an increasingly large part of the national and world economies at the same time that healthcare costs are escalating at an unsustainable rate. The purpose of this class is to increase the student’s understanding of how to apply proven industrial engineering methods to healthcare-related problems. Potential topics include statistical process control for medical applications; process improvement in healthcare delivery; simulation of healthcare services; time-based patient flow enhancement; resource scheduling optimization; hospital and clinic layout and facilities design; healthcare financing and cost management; and quality and other metrics for healthcare. (prereq: junior standing)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Understand how industrial engineering principles and methods can be applied to healthcare services
    • Explain and describe major healthcare processes from an engineering-based perspective
    • Understand key performance metrics that are utilized to analyze the effectiveness of healthcare quality and delivery
    • Apply engineering concepts and methods, including human factors, quality tools, operations research/simulation modeling, and facilities design, to healthcare-related problems
    • Conduct cost-based comparisons and investment justifications in a healthcare environment

    Prerequisites by Topic
    • None

    Course Topics
    • Introduction to healthcare processes
    • Applying engineering methods to healthcare services
    • Information technology management in healthcare
    • Use of bar coding, RFID, and other tracking systems in healthcare
    • Human factors and medical errors
    • Quality assurance and statistical process control in healthcare
    • Mistake-proofing in healthcare
    • Modeling of healthcare processes and systems
    • Healthcare layouts and facilities design

    Coordinator
    Dr. Leah Newman
  
  • IE 4621 - Socio-Technical Systems

    3 lecture hours 0 lab hours 3 credits
    Course Description
    Socio-technical Systems (STS) is a method that might be used to analyze manufacturing and service jobs, as well as entire organizations through the study of classical theories and techniques of management and organizational behavior (i.e., Frederick Taylor’s Scientific Management, Elton Mayo’s Human Relations, etc.), as well as more recent developments related to quality of working life, change management, and the macro-ergonomic analysis and design process. This course includes analysis of both social and technical systems within an organization in an effort to improve the design and functionality of the entire system. (prereq: IE 3621  or SS 464 , junior standing)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Describe what engineering socio-technical systems means, what it covers, and what shaped it as a profession
    • Understand socio-technical systems engineering theory
    • Understand how to apply the socio-technical systems theory and analytical methods to design or assist in the redesign of an organization
    • Understand how to conduct a socio-technical systems analysis of a work process
    • Understand how different leadership skills impact team/group performance
    • Understand how organizational culture impacts employee morale and performance
    • Understand the impact of motivation and satisfaction on team/group performance

    Prerequisites by Topic
    • None

    Course Topics
    • Open and other systems
    • History of socio-technical systems
    • Socio-technical systems - The environment
    • Socio-technical systems - The social system
    • Socio-technical systems - The technical system
    • Socio-technical system design, redesign and analysis
    • Macro-ergonomics and organizational design and participation
    • Socio-technical applications and case studies

    Coordinator
    Dr. Leah Newman
  
  • IE 4622 - Organization and Job Design

    3 lecture hours 0 lab hours 3 credits
    Course Description
    Organizations are becoming increasingly more complex with regards to how business is accomplished when considering issues of cultural and emotional intelligence of employees, the impact of globalization as well as quality of working life issues. This course assists in the design, implementation, and diffusion of productive organizations and an individual’s role within the organization. (prereq: IE 3621  or SS 464 , junior standing)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Understand the theories associated with organization and job design
    • Understand how to apply the job design theories and analytical methods in an effort to redesign a job and/or an organization
    • Conduct a detailed job analysis
    • Understand how different leadership skills and other organizational management approaches impact team/group performance
    • Understand how organizational culture impacts employee morale and performance
    • Understand the impact of motivation and satisfaction on team/group performance

    Prerequisites by Topic
    • None

    Course Topics
    • Organizational management theories - overview
    • Job design theories
    • Job analysis data collection methods
    • Employee motivation
    • Teamwork and participation
    • Job redesign and case studies
    • Employer/employee ethics

    Coordinator
    Dr. Leah Newman
  
  • IE 4640 - Product Design and Development Processes

    3 lecture hours 0 lab hours 3 credits
    Course Description
    This course introduces students to the product design and development process from the lens of human factors engineering.  It includes a team project in which students are expected to propose an original design idea, conduct a needs analysis, develop and test a prototype, and create a financial analysis of the product of interest.  (prereq: junior standing)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Understand tools and methods used for product design and development from a human factors perspective
    • Possess more confidence in developing a new product
    • Be aware of the role of multiple functions in creating a new product (e.g. strategy, project management, finance, marketing, industrial design, human factors, engineering, production, supply chain, safety)
    • Coordinate necessary roles, functions, resources, tasks, etc. to achieve a common goal
    • Understand how to complete a needs analysis
    • Understand how to develop, complete, and test a design prototype

    Prerequisites by Topic
    • None

    Course Topics
    • Human factors overview
    • Design thinking
    • Customer needs analysis
    • Product specifications + scrum process
    • Creativity and concept generation
    • Product architecture
    • Prototyping and testing design
    • Concept selection
    • Industrial design
    • Experience and service design
    • Design for environmental sustainability
    • Product costing

    Coordinator
    Dr. Leah Newman
  
  • IE 4773 - Computer Aided Manufacturing/CNC Machining/Rapid Prototyping

    2 lecture hours 2 lab hours 3 credits
    Course Description
    This course teaches students the fundamentals of computer-aided manufacturing (CAM), computer numerical control (CNC) machining, and rapid prototyping (RP). Students will learn how to program a CNC machine using manual G/M code programming and computer-aided manufacturing software. The course also provides an overview of rapid prototyping (freeform fabrication/additive manufacturing) technologies, and students will compare part production via RP and CNC. (prereq: IE 426  or ME 323  or consent of instructor, ME 1601 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Distinguish important capabilities and limitations of CNC machining and RP processes
    • Manually write a CNC program for a CNC mill and a CNC lathe
    • Use CAD/CAM software to create and execute CNC programs to machine workpieces on a CNC mill (for student-generated designs: 2.5D milling, hole-making, and 3D contour milling)
    • Explain workholding concepts and their importance to CNC machining operations
    • Select cutting tools and cutting conditions for various types of machining operations (drilling, facing, pocketing, etc.)
    • Set up a CNC machining center, with oversight from a lab technician

    Prerequisites by Topic
    • Knowledge of machining processes (milling, drilling, turning, etc.).
    • Must know how to create a part design using 3-dimensional CAD software

    Course Topics
    • Review of machining processes
    • CNC machining and programming for mills
    • CAM software and project work
    • Workholding
    • Rapid prototyping
    • CNC machining and programming for lathes
    • Canned programs and quick code
    • Multi-axis machining

    Laboratory Topics
    • The 2-hour weekly lab, plus some additional lecture class periods are used for working with the CAM software package to create CNC programs. The programs are thoroughly simulated and tested before running them on a Haas VF-1 machining center. Students also learn how to set up and operate the Haas.

    Coordinator
    Dr. Leah Newman
  
  • IE 4810 - Engineering Accounting

    3 lecture hours 0 lab hours 3 credits
    Course Description
    An overview of basic topics in financial and managerial accounting as applied to manufacturing companies and engineering projects is presented with a focus on helping engineers understand the meaning of financial metrics and how they are used in business planning and decision making. The basics of financial and managerial accounting are taught along with inventory valuation and depreciation methods in the context of the engineering business environment. The focus of the course is on information for cost management, budgetary control, and short-term and long-term financial decision making. Students will work in teams to prepare an in-depth financial analysis of an engineering project. (prereq: BA 2510 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Understand the underlying concepts of financial and managerial accounting and the roles of profit, cash, and cost in decision making related to engineering projects
    • Allocate overhead in manufacturing, service, and other engineering-oriented organizations
    • Explain the underlying concepts of accounting as they apply to manufacturing enterprises and the specific roles that depreciation, inventory valuation, and time offsetting play in their operations
    • Knowledgeably use managerial accounting information for decision-making in manufacturing and engineering related businesses
    • Create cost estimates for engineering projects and properly price engineering services
    • Accumulate and record financial data in accordance with Generally Accepted Accounting Principles (GAAP) applied to engineering-related businesses and projects
    • Recognize and understand some of the ethical and legal issues related to the practice of accounting

    Prerequisites by Topic
    • Introduction to accounting

    Course Topics
    • Role of accounting in engineering
    • Ledgers and transactions
    • Equity, assets, and liabilities
    • Balance sheets, income statements
    • Project expensing, accounting cycle for projects
    • Adjusting financial statements, cash flow analysis
    • Engineering payroll considerations, managerial accounting
    • Revenue reporting, receivables and collections, operating income
    • Cost drivers and estimation, product costing and pricing
    • Inventory allocation, writing down inventory, inventory disclosures
    • Income taxes, operational and capital budgeting, earned value analysis
    • Planning, organizing, and control cycle
    • Ethical and corporate responsibility
    • Performance reporting and scorecards

    Coordinator
    Dr. Aaron Armstrong
  
  • IE 4823 - Financial Engineering

    3 lecture hours 0 lab hours 3 credits
    Course Description
    Finance and economic analysis is a growing area of employment for engineers. The purpose of this class is to increase the student’s ability to apply engineering methods to finance, insurance, economics, and risk management. This is a student-directed course, where the interests of the participating students will influence the content and objectives of the course. Student influenced course topics may include but are not necessarily limited to options pricing theory, futures contracts and other financial instruments, real options, risk management, and game theory. Industry applications and case studies illustrate concepts and challenges. (prereq: IE 423  and junior standing)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Understand how engineering methods apply to finance, insurance, and economics
    • Understand options, futures, and other financial instruments
    • Understand real options
    • Understand risk and how risk is evaluated and incorporated into financial models
    • Apply game theory concepts to financial analysis

    Prerequisites by Topic
    • None

    Course Topics
    • Introduction to financial engineering
    • Application of engineering methods to finance, insurance, and economics
    • Mathematical modeling for financial analysis and decision making
    • Options, futures, and other financial instruments
    • Real options
    • Evaluating risk and incorporating it into financial models
    • Game theory
    • Industry applications and case studies

    Coordinator
    Dr. Aaron Armstrong
  
  • IE 4880 - Supply Chain Engineering

    3 lecture hours 0 lab hours 3 credits
    Course Description
    Supply chain design and logistical planning and execution are critical areas for many businesses and industries. This class is intended to increase students’ understanding of how to apply engineering methods to supply chain related problems. Student influenced course topics may include but are not necessarily limited to: supply chain demand modeling, multi-tier forecasting and coordination, negotiation strategies, total acquisition cost calculation, make versus buy decision analysis, integration of supply chain with product development, dynamic lot sizing inventory models, and the bullwhip effect. Industry applications and case studies illustrate concepts and challenges. (prereq: junior standing)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Understand how engineering methods apply to supply chain problems
    • Model a dynamic supply chain
    • Forecast demand and incorporate this forecast across the supply chain model
    • Complete a capacity planning analysis
    • Understand negotiation strategies and where to apply them
    • Explain software tools and methods available for logistical network design and operation
    • Understand make versus buy decisions and the associated cost analysis
    • Understand the bullwhip effect and how it can be dampened

    Prerequisites by Topic
    • None

    Course Topics
    • Introduction to supply chain engineering
    • Operations research models for supply chain analysis
    • Forecasting
    • Capacity planning
    • Negotiation strategies
    • Software tools and methods for logistics network design
    • Make versus buy decisions
    • Bullwhip effect and other flow problems
    • Integration problems in supply chain management
    • Industry applications and case studies

    Coordinator
    Dr. Aaron Armstrong
  
  • IE 4901 - Industrial Engineering Senior Design Project I

    2 lecture hours 2 lab hours 3 credits
    Course Description
    This is the first of a two- (three-) course sequence in developing and executing a team capstone design project in Industrial Engineering. The purpose of this project is to demonstrate the student’s ability, working within a design team, to integrate the knowledge, skills, and experiences acquired in the Industrial Engineering program. Evaluation of user (client) needs, development of an engineering specification, appropriate evaluation criteria, and techniques for design in the presence of conflicting design constraints (quality, productivity, safety, cost) are reviewed. This course includes an external client-sponsored design project and a design proposal submitted to, and approved by, the client. (prereq: senior standing, GS 1003 , IE 391 , IE 440,  consent of instructor)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Understand the client’s situation and define the problem/opportunity with a clear and concise project purpose and scope
    • Utilize input from the client to establish performance improvement objectives
    • Define an appropriate solution methodology, collect relevant data and information, and identify relevant analytical methods and tools
    • Create a detailed and executable project schedule
    • Utilize agendas and minutes to plan for and document the results of client meetings
    • Communicate, verbally and in writing, the project proposal and project plan
    • Function as an effective team member in the context of a real-world project

    Prerequisites by Topic
    • Must have sufficient knowledge of specific industrial engineering techniques that are likely to relate to the course project (such as operations research, manufacturing systems analysis, lean manufacturing, production control, ergonomics, safety, etc.).
    • Must have successfully completed the junior project class, demonstrating the student’s ability to work successfully within a team on a client-sponsored industrial engineering project

    Course Topics
    • Project proposals
    • Teamwork, performance evaluations, peer feedback
    • Formal presentations
    • Project schedules
    • Literature review and library research
    • Data gathering and analysis
    • Formal technical reports

    Laboratory Topics
    • All laboratory work will be done at the sponsor site or in an MSOE lab, as needed by a particular project

    Coordinator
    Dr. Leah Newman
  
  • IE 4902 - Industrial Engineering Senior Design Project II

    1 lecture hours 3 lab hours 3 credits
    Course Description
    In this second of the senior design courses, the student teams execute the design proposal developed in IE 4901 . The design is documented in a written team report and orally defended before a faculty review panel. Typically, the project is also presented to the client in a separate presentation, often at the client facility. (prereq: IE 4901 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Utilize relevant industrial engineering methods and tools to collect and analyze data
    • Formulate creative alternatives, perform systematic comparisons of alternatives, and formulate recommendations based on quantitative and qualitative evaluations
    • Justify recommendations based on quantitative and qualitative performance metrics, taking the context of the client organization into consideration
    • Communicate, verbally and in writing, the project methodology, results, recommendations, and organizational impact
    • Write an abstract that is clear and concise, emphasizing the most important aspects of the project and its potential for impact at the client organization
    • Develop a poster that creates interest and clearly highlights key aspects of the project

    Prerequisites by Topic
    • Must have developed a client-approved project proposal in IE 4901  

    Course Topics
    • Topics are geared towards helping the students satisfactorily complete their projects
    • Topics may vary depending on the content of the projects and the specific strengths and weaknesses of the students enrolled in the course
    • Topics covered could include review of technical information or techniques, technical writing, and effective oral presentations

    Laboratory Topics
    • All laboratory work will be done at the sponsor site or in an MSOE lab, as needed by a particular project

    Coordinator
    Dr. Leah Newman
  
  • IE 4903 - Industrial Engineering Senior Design Project III

    1 lecture hours 3 lab hours 3 credits
    Course Description
    This course provides a mechanism for a design team, with approval received during IE 4901  from the course coordinator and faculty advisor, to undertake a larger scope project with correspondingly longer planned duration. A final project presentation and written report are submitted at the end of IE 4902 .  IE 4903 is subsequently handled in a similar fashion as an independent study course, with the deliverables and expectations set by the faculty advisor. The additional time may be used for building a prototype of the design, implementing changes within a company, or other means of expanding the project scope. A grade is given just for the IE 4903 deliverables; there is no carry-over from IE 4902 . This course satisfies the requirements of an Industrial Engineering elective. (prereq: IE 4902 , consent of instructor)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Depends on project objectives and scope

    Prerequisites by Topic
    • Must have developed a client-approved project proposal in IE 4901  and been given consent by the course coordinator and faculty advisor to undertake a larger scope project

    Course Topics
    • This course is administered similarly to an independent study course. Students meet weekly with their advisor to discuss project progress and concerns
    • Topics covered in weekly meetings are geared towards helping the students satisfactorily complete their projects
    • Topics may vary depending on the content of the projects and the specific strengths and weaknesses of the students enrolled in the course
    • Topics covered could include review of technical information or techniques, technical writing, and effective oral presentations

    Laboratory Topics
    • All laboratory work will be done at the sponsor site or in an MSOE lab, as needed by a particular project

    Coordinator
    Dr. Leah Newman

Mathematics

  
  • MA 120 - Precalculus Mathematics

    4 lecture hours 0 lab hours 4 credits
    Course Description
    This course provides a review of the aspects of algebra, trigonometry, and analytic geometry that are necessary for success in calculus for the benefit of students with slight deficiencies in any of these areas. It is not intended as a substitute for a rigorous course in any of these topics. (prereq: MA 125  or equivalent)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Be proficient with exponential expressions including the laws of exponents and negative and rational exponents
    • Factor simple polynomial expressions
    • Simplify rational expressions including products, sums, and complex rational expressions
    • Solve rational equations including consideration of the domain by means of linear approach and quadratic approach (solving by factoring and/or quadratric formula)
    • Be able simplify radical expressions including rationalizing the numerator or denominator
    • Solve radical equations (optional)
    • Understand the concept of a function, its range and domain, and its graph
    • Be proficient with linear functions and models including recognizing that the slope represents rate of change
    • Know the graphs of common equations
    • Transform the graphs of functions graphically and algebraically
    • Understand piecewise-defined functions
    • Use operations of functions including composition of functions on calculus concepts such as difference quotients
    • Understand exponential functions, their domain and range, and graphs
    • Understand logarithmic functions, their domain and range, and graphs
    • Be proficient with the properties of logarithms including solving exponential equations
    • Understand the measure of an angle including radians and degrees
    • Understand the definition of the six trigonometric functions including their relation to the geometry of the unit circle and right triangles
    • Evaluate the trigonometric functions both approximately, by using the calculator, and exactly, by using reference angles of common angles
    • Apply trigonometric properties to applications
    • Know the graphs of the three of sine, cosine and tangent. Recognize the remaining three trigonometric graphs
    • Be proficient with basic trigonometric identities including reciprocal identities, ratio identities and Pythagorean identities
    • Be familiar with other trigonometric identities (double angle and reduction or half-angle identities)
    • Understand the definition of the inverse trigonometric functions and be able to evaluate to find common angles
    • Solve basic trigonometric equations

    Prerequisites by Topic

    Course Topics
    • Inequalities and absolute value
    • Factoring and completing the square
    • General functions
    • Rational functions
    • Trigonometric functions
    • Exponential and log functions
    • Complex numbers
    • Systems of equations

    Coordinator
    Dr. Anthony van Groningen
  
  • MA 120A - Precalculus Mathematics

    4 lecture hours 1 lab hours 4 credits
    Course Description
    This course is the same as MA 120 . The ‘A’ designation after the course number indicates this is a special section taught with extra math lab hours built in as a requirement for successful completion of the course. (prereq: MA 125  or equivalent and consent of instructor)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Be proficient with exponential expressions including the laws of exponents and negative and rational exponents
    • Factor simple polynomial expressions
    • Simplify rational expressions including products, sums, and complex rational expressions
    • Solve rational equations including consideration of the domain by means of linear approach and quadratic approach (solving by factoring and/or quadratric formula)
    • Be able simplify radical expressions including rationalizing the numerator or denominator
    • Solve radical equations (optional)
    • Understand the concept of a function, its range and domain, and its graph
    • Be proficient with linear functions and models including recognizing that the slope represents rate of change
    • Know the graphs of common equations
    • Transform the graphs of functions graphically and algebraically
    • Understand piecewise-defined functions
    • Use operations of functions including composition of functions on calculus concepts such as difference quotients
    • Understand exponential functions, their domain and range, and graphs
    • Understand logarithmic functions, their domain and range, and graphs
    • Be proficient with the properties of logarithms including solving exponential equations
    • Understand the measure of an angle including radians and degrees
    • Understand the definition of the six trigonometric functions including their relation to the geometry of the unit circle and right triangles
    • Evaluate the trigonometric functions both approximately, by using the calculator, and exactly, by using reference angles of common angles
    • Apply trigonometric properties to applications
    • Know the graphs of the three of sine, cosine and tangent. Recognize the remaining three trigonometric graphs
    • Be proficient with basic trigonometric identities including reciprocal identities, ratio identities and Pythagorean identities
    • Be familiar with other trigonometric identities (double angle and reduction or half-angle identities)
    • Understand the definition of the inverse trigonometric functions and be able to evaluate to find common angles
    • Solve basic trigonometric equations

    Prerequisites by Topic

    Course Topics
    • Properties of exponents
    • Factoring and simplifying polynomials, rational and radical expressions
    • Solving quadratics and trigonometric functions
    • General functions and their properties: linear, basic graphs, piece-wise
    • Trigonometric functions and their properties
    • Exponential and log functions

    Coordinator
    Dr. Anthony van Groningen
  
  • MA 125 - College Algebra I

    4 lecture hours 0 lab hours 4 credits
    Course Description
    This course provides a review of basic algebra. Topics covered include fundamental algebraic operations; equations, ratio and proportion, variation; systems of linear equations; factoring and fractions; quadratic equations. (prereq: none)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Perform the four fundamental operations with signed numbers and polynomials
    • Remove and insert symbols of grouping
    • Perform basic operations with exponents and radicals
    • Solve systems of two equations in two unknowns
    • Find special products
    • Factor polynomials
    • Reduce a given fraction to lowest terms
    • Perform the four fundamental operations with fractions
    • Simplify complex fractions
    • Solve fractional equations
    • Solve quadratic equations
    • Solve word problems leading to algebraic equations

    Prerequisites by Topic
    • None

    Course Topics
    • Fundamental operations
    • Equations and applications
    • Systems of equations
    • Special products and factoring
    • Operations with algebraic fractions
    • Quadratic equations

    Coordinator
    Dr. Anthony van Groningen
  
  • MA 125A - College Algebra I

    4 lecture hours 1 lab hours 4 credits
    Course Description
    This course is the same as MA 125. The ‘A’ designation after the course number indicates this is a special section taught with extra math lab hours built in as a requirement for successful completion if the course. (prereq: consent of instructor) 
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Perform the four fundamental operations with signed numbers and polynomials
    • Remove and insert symbols of grouping
    • Perform basic operations with exponents and radicals
    • Solve systems of two equations in two unknowns
    • Find special products
    • Factor polynomials
    • Reduce a given fraction to lowest terms
    • Perform the four fundamental operations with fractions
    • Simplify complex fractions
    • Solve fractional equations
    • Solve quadratic equations
    • Solve word problems leading to algebraic equations

    Prerequisites by Topic
    • None

    Course Topics
    • Fundamental operations
    • Equations and applications
    • Systems of equations
    • Special products and factoring
    • Operations with algebraic fractions
    • Quadratic equations

    Coordinator
    Dr. Anthony van Groningen
  
  • MA 126 - Trigonometry

    4 lecture hours 0 lab hours 4 credits
    Course Description
    Topics include trigonometric functions, special angles, solution of triangles, radian measure, graphs, inverse trigonometric functions, solution of trigonometric equations, basic identities and the sum, difference, double angle and half angle formulas. An introduction to exponents and logarithms is included. (prereq: MA 125  or equivalent)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Define the six trigonometric functions
    • Determine the smallest positive angle coterminal with a given angle
    • Use a calculator to find the values of trigonometric functions and inverse trigonometric functions
    • Determine the values of trigonometric functions of quadrantal and special angles
    • Solve triangles
    • Convert from degree measure to radian measure and vice versa
    • Find the length of a circular arc and the area of a circular sector
    • Graph sine and cosine functions
    • Evaluate inverse trigonometric functions
    • Prove trigonometric identities using fundamental relationships
    • Prove trigonometric identities using sum, difference, double-angle, and half-angle formulas
    • Solve trigonometric equations
    • Use properties of logarithms
    • Solve exponential equations by means of logarithms

    Prerequisites by Topic
    • Fundamental algebraic operations
    • Equations and systems of equations
    • Special products and factoring
    • Operations with algebraic fractions
    • Quadratic equations

    Course Topics
    • Trigonometric functions and right triangle applications
    • Laws of sines and cosines
    • The unit circle
    • Trigonometric functions and real numbers
    • Addition and subtraction formulas
    • Double and half angles formulas
    • Trigonometric graphs
    • Basic trigonometric identities
    • Inverse trigonometric functions
    • Trigonometric equations
    • Exponential functions
    • Logarithmic functions
    • Laws of logarithms
    • Exponential and logarithmic equations
    • Applications of exponential and logarithmic equations

    Coordinator
    Dr. Kseniya Fuhrman
  
  • MA 127 - College Algebra II

    4 lecture hours 0 lab hours 4 credits
    Course Description
    This course provides a review or introduction to more advanced algebra. Topics covered include exponents and radicals; solving linear, quadratic and selected radical and polynomial equations; an introduction to analytic geometry; the function concept and terminology; determinants, matrices and systems of linear equations; the binomial theorem. (prereq: MA 125  or equivalent)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Simplify expressions containing exponents and radicals
    • Perform the four fundamental operations with radicals
    • Represent complex numbers as vectors
    • Perform the four fundamental operations with complex numbers in rectangular form
    • Solve linear and quadratic equations
    • Convert a given complex number from rectangular to polar form and vice versa
    • Multiply and divide complex numbers in polar form
    • Use De Moivre’s formula to find powers and roots of complex numbers
    • Solve systems of quadratic equations algebraically
    • Solve radical equations and equations in quadratic form
    • Use synthetic division to find roots of polynomial equations
    • Use the properties of determinants to evaluate a determinant of arbitrary order
    • Solve linear systems by Cramer’s Rule
    • Perform algebraic operations with matrices
    • Use row operations to find the inverse of a given matrix and solve a given system of equations
    • Use the binomial theorem to expand a given binomial
    • Use the distance and midpoint formulas
    • Find equations of lines

    Prerequisites by Topic
    • Fundamental algebraic operations
    • Special products and factoring
    • Operations with algebraic functions
    • Quadratic equations
    • Basic concepts of trigonometry

    Course Topics
    • Exponents and radicals 
    • Algebraic expressions
    • Factoring
    • Linear equations and applications
    • Quadratic equations
    • Other equations
    • Coordinate plane
    • Functions
    • Systems of linear equations
    • Matrices
    • Determinants
    • Binomial Theorem

    Coordinator
    Dr. Kseniya Fuhrman
  
  • MA 129 - Business Calculus

    4 lecture hours 0 lab hours 4 credits


    Course Description
    This course covers functions, the derivative with applications, techniques of differentiation, the exponential and logarithmic functions with applications, and an introduction to the definite integral.

    Note: this course is only open to students in the Rader School of Business. (prereq: MA 120  or equivalent)


    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Use functional notation in business applications
    • Develop small business models
    • Determine break-even points and optimal profit using algebraic methods
    • Calculate the derivative of an algebraic function
    • Apply the first derivative as a marginal function
    • Use the first derivative for optimization
    • Solve the exponential and logarithmic equations
    • Use the compound interest model to calculate Future Value and Present Value
    • Calculate the derivative of an exponential function
    • Calculate the antiderivative of a polynomial function
    • Interpret the definite integral as area
    • Use the integral to calculate revenue and profit

    Prerequisites by Topic
    • Properties of exponents
    • Operations with polynomials
    • Functions and graphs
    • Solving first degree equations
    • Solving second degree equations by factoring
    • Solving second degree equations using the quadratic formula

    Course Topics
    • Algebra review, functions, graphs, etc.
    • Business and economic models 
    • Vertical asymptotes and limits 
    • Derivative computations 
    • Applications of the derivative 
    • Exponential, log, compound interest
    • Integrals
    • Reviews
    • Exams 

    Coordinator
    Edward Griggs

  
  • MA 136 - Calculus I

    4 lecture hours 0 lab hours 4 credits
    Course Description
    This course begins with a short review of topics in algebra and trigonometry before introducing the student to differential calculus. Topics include algebra of functions, limits, continuity, differentiation of algebraic, trigonometric, exponential and logarithmic functions and application of the derivative to curve sketching and optimization problems. (prereq: MA 120  or equivalent)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Understand the Mean Value Theorem
    • Evaluate the limits of algebraic, trigonometric, exponential and logarithmic functions
    • Identify removable and non-removable discontinuities
    • Evaluate the derivative of algebraic, trigonometric, exponential and logarithmic functions
    • Find the equation of a tangent line to a curve
    • Find the position, velocity and acceleration of a moving object
    • Use derivatives to find relative extrema and points of inflection on a curve
    • Set up and solve optimization problems
    • Set up and solve related rate problems

    Prerequisites by Topic
    • Simplification of algebraic expressions containing complex fractions, exponents, and radicals
    • Factoring
    • Linear, fractional, and quadratic equations
    • Cartesian coordinate system
    • Systems of equations
    • Trigonometric functions
    • Trigonometric identities

    Course Topics
    • Algebra and trigonometry review
    • Functions
    • Limits and continuity
    • Rates of change, tangent lines, and definition of derivative
    • Derivatives of algebraic and trigonometric functions
    • Derivatives of exponential and logarithmic and inverse trig functions
    • First and second derivative tests for extrema, curve sketching
    • Applied optimization problems
    • Related rates problems
    • Mean Value Theorem

    Coordinator
    Dr. Anthony van Groningen
  
  • MA 136A - Calculus I

    4 lecture hours 1 lab hours 4 credits
    Course Description
    This course is the same as MA 136 . The ‘A’ designation after the course number indicates there are extra math lab hours built in as a requirement for successful completion of the course. (prereq: MA 120  or equivalent and consent of instructor)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Understand the Mean Value Theorem
    • Evaluate the limits of algebraic, trigonometric, exponential and logarithmic functions
    • Identify removable and non-removable discontinuities
    • Evaluate the derivative of algebraic, trigonometric, exponential and logarithmic functions
    • Find the equation of a tangent line to a curve
    • Find the position, velocity and acceleration of a moving object
    • Use derivatives to find relative extrema and points of inflection on a curve
    • Set up and solve optimization problems
    • Set up and solve related rate problems

    Prerequisites by Topic
    • Simplification of algebraic expressions containing complex fractions, exponents, and radicals
    • Factoring
    • Linear, fractional, and quadratic equations
    • Cartesian coordinate system
    • Systems of equations
    • Trigonometric functions
    • Trigonometric identities

    Course Topics
    • Algebra and trigonometry review
    • Functions
    • Limits and continuity
    • Rates of change, tangent lines, and definition of derivative
    • Derivatives of algebraic and trigonometric functions
    • Derivatives of exponential and logarithmic and inverse trig functions
    • First and second derivative tests for extrema, curve sketching
    • Applied optimization problems
    • Related rates problems
    • Mean Value Theorem

    Coordinator
    Dr. Anthony van Groningen
  
  • MA 136C - Calculus I

    4 lecture hours 0 lab hours 4 credits
    Course Description
    This course is the same as MA 136. The ‘C’ designation after the course number indicates enrollment in Carter Academy. (prereq: enrollment in Carter Academy and consent of instructor)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Understand the Mean Value Theorem
    • Evaluate the limits of algebraic, trigonometric, exponential and logarithmic functions
    • Identify removable and non-removable discontinuities
    • Evaluate the derivative of algebraic, trigonometric, exponential and logarithmic functions
    • Find the equation of a tangent line to a curve
    • Find the position, velocity and acceleration of a moving object
    • Use derivatives to find relative extrema and points of inflection on a curve
    • Set up and solve optimization problems
    • Set up and solve related rate problems

    Prerequisites by Topic
    • Simplification of algebraic expressions containing complex fractions, exponents, and radicals
    • Factoring
    • Linear, fractional, and quadratic equations
    • Cartesian coordinate system
    • Systems of equations
    • Trigonometric functions
    • Trigonometric identities

    Course Topics
    • Algebra and trigonometry review
    • Functions
    • Limits and continuity
    • Rates of change, tangent lines, and definition of derivative
    • Derivatives of algebraic and trigonometric functions
    • Derivatives of exponential and logarithmic and inverse trig functions
    • First and second derivative tests for extrema, curve sketching
    • Applied optimization problems
    • Related rates problems
    • Mean Value Theorem

    Coordinator
    Dr. Anthony van Groningen
  
  • MA 137 - Calculus II

    4 lecture hours 0 lab hours 4 credits
    Course Description
    This course is a continuation of MA 136 and an introduction to integral calculus. Topics include Newton’s method, differentials, basic integrals involving algebraic, trigonometric, exponential, logarithmic, and inverse trig functions. Topics also include rectilinear motion, work, areas and volumes of revolution, integration techniques such as integration by parts and partial fractions, and numerical integration methods.  (prereq: MA 136)  
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Use Newton’s method to approximate the zeros of a function
    • Find the differential of a function and use it to approximate error
    • Integrate algebraic, exponential, trigonometric, logarithmic and inverse trigonometric functions
    • Evaluate a definite integral by the limit of Riemann sums
    • Evaluate a definite integral by Fundamental Theorem of Calculus
    • Use method of substitution to find indefinite and definite integrals
    • Use method of integration by parts
    • Integrate products and powers of trigonometric functions
    • Integrate functions using partial fractions
    • Find areas between curves
    • Find volumes of solids of revolution using disk and washer methods
    • Use integration to solve work problems

    Prerequisites by Topic
    • Graphing of functions
    • Derivatives of algebraic, exponential, trigonometric, inverse trig and logarithmic functions
    • Limits of algebraic and trigonometric functions
    • Implicit derivatives
    • Graphing using relative extrema

    Course Topics
    • Newton’s method of approximating zeros of a function
    • Differentials
    • Area problem and indefinite integrals 
    • The definite integral as the limit of Riemann sums and the Fundamental Theorem of Calculus
    • Integration by substitution 
    • Areas between curves
    • Rectilinear motion
    • Volumes by disk and washers
    • Work
    • Integration by parts
    • Integration of products and powers of trig functions
    • Integration using partial fractions
    • Integration using trigonometric substitutions (optional)
    • Numerical integration

    Coordinator
    Dr. Kseniya Fuhrman
  
  • MA 137A - Calculus II

    4 lecture hours 1 lab hours 4 credits
    Course Description
    This course is the same as MA 137 . The ‘A’ designation after the course number indicates there are extra math lab hours built in as a requirement for successful completion of the course. (prereq: MA 136  and consent of instructor)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Use Newton’s method to approximate the zeros of a function
    • Find the differential of a function and use it to approximate error
    • Integrate algebraic, exponential, trigonometric, logarithmic, and inverse trigonometric functions
    • Evaluate a definite integral by the limit of Riemann sums
    • Evaluate a definite integral by Fundamental Theorem of Calculus
    • Use method of substitution to find indefinite and definite integrals
    • Use method of integration by parts
    • Integrate products and powers of trigonometric functions
    • Integrate functions using partial fractions
    • Find areas between curves
    • Find volumes of solids of revolution using disk and washer methods
    • Use integration to solve work problems

    Prerequisites by Topic
    • Graphing of functions
    • Derivatives of algebraic, exponential, trigonometric, inverse trig, and logarithmic functions
    • Limits of algebraic and trigonometric functions
    • Implicit derivatives
    • Graphing using relative extrema

    Course Topics
    • Newton’s method of approximating zeros of a function
    • Differentials
    • Area problem and indefinite integrals 
    • The definite integral as the limit of Riemann sums and the Fundamental Theorem of Calculus
    • Integration by substitution 
    • Areas between curves
    • Rectilinear motion
    • Volumes by disk and washers
    • Work
    • Integration by parts
    • Integration of products and powers of trig functions
    • Integration using partial fractions
    • Integration using trigonometric substitutions (optional)
    • Numerical integration

    Coordinator
    Dr. Kseniya Fuhrman
  
  • MA 231 - Calculus III

    4 lecture hours 0 lab hours 4 credits
    Course Description
    This course is a continuation of MA 137  and an introduction to multivariable calculus. Topics include L’Hȏpital’s rule, improper integrals, applications of integrals to physics, parametric equations, polar coordinates, vector algebra, surfaces in three dimensions, and partial derivatives with applications. (prereq: MA 137 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Use L’Hȏpital’s Rule to evaluate a limit
    • Evaluate improper integrals
    • Find the length of the arc of a curve
    • Find work, fluid pressure, and force
    • Eliminate the parameter from parametric equations
    • Draw graphs of parametric equations and determine the direction of travel for an increasing parameter
    • Find first and second derivatives of parametric functions
    • Find the arc length for parametric curves
    • Convert between rectangular and polar coordinates
    • Draw graphs of polar curves
    • Find area and arc length in polar coordinates
    • Perform operations using vector algebra
    • Find dot products, cross products, and equations of lines and planes in three dimensions
    • Sketch surfaces in three dimensions
    • Find first and second partial derivatives
    • Find the total differential of a function of more than one variable and use it to approximate error
    • Use chain rules to find derivatives and partial derivatives
    • Find implicit partial derivatives
    • Determine the maximum, minimum, and saddle points on a surface

    Prerequisites by Topic
    • The basic principles of algebra
    • The basic principles of trigonometry
    • Differentiation and integration of algebraic and transcendental functions
    • Limits
    • Understanding of the definition of the definite integral

    Course Topics
    • L’Hȏpital’s Rule 
    • Improper integrals
    • Arc length 
    • Work 
    • Fluid pressure and force 
    • Parametric equations 
    • Polar coordinates and graphs 
    • Vectors, lines, and planes 
    • Surfaces in three dimensions 
    • Functions of several variables 
    • Partial derivatives 
    • Extrema of functions of two variables 

    Coordinator
    Dr. Chunping Xie
  
  • MA 232 - Calculus IV

    3 lecture hours 0 lab hours 3 credits
    Course Description
    This course is a continuation of MA 231  and an introduction to multiple integration and infinite series. Topics include double and triple integrals with applications to areas, volumes and moments, infinite series with tests for convergence, power series, Taylor and Maclaurin series, and operations with series. (prereq: MA 231 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Set up and evaluate double integrals using rectangular and polar coordinates
    • Find areas, volumes, and moments using double integrals
    • Set up and evaluate triple integrals
    • Use triple integrals to find volumes and moments of solids
    • Use integrals in cylindrical or spherical coordinates to find volumes and moments
    • Test sequences for convergence and divergence
    • Test infinite series for convergence and divergence
    • Find the interval of convergence for a power series
    • Perform algebraic and calculus operations on power series
    • Use Taylor and Maclaurin series to approximate functions

    Prerequisites by Topic
    • The basic principles of algebra
    • The basic principles of trigonometry
    • Differentiation and integration of algebraic and transcendental functions
    • Applications of integration
    • Integration techniques
    • L’Hȏpital’s Rule
    • Functions of several variables
    • Partial derivatives
    • Limits and improper integrals
    • Parametric equations
    • Polar coordinates

    Course Topics
    • Double integrals, area, volume, and moments
    • Triple integrals, volume, moments, cylindrical and spherical coordinates
    • Sequences
    • Infinite series and tests for convergence
    • Power series and intervals of convergence
    • Taylor and Maclaurin series

    Coordinator
    Edward Griggs
  
  • MA 235 - Differential Equations

    4 lecture hours 0 lab hours 4 credits
    Course Description
    This course discusses the solution of first-order differential equations, the solution of higher-order differential equations with constant coefficients, applications of differential equations, and an introduction to the method of Laplace transforms applied to the solution of certain differential equations. (prereq: MA 231  or MA 2314 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Determine the solution of first-order differential equations by the method of separation of variables
    • Determine the solution of first-order differential equations having homogeneous coefficients
    • Determine the solution of exact first-order differential equations
    • Determine appropriate integrating factors for first-order linear differential equations
    • Apply and solve first-order differential equations of selected physical situations
    • Determine the general and particular solutions of higher-order linear homogeneous differential equations with constant coefficients
    • Determine the general and particular solutions of certain nonlinear second-order homogeneous differential equations with constant coefficients using the methods of Undetermined Coefficients and Variation of Parameters
    • Apply and solve second-order differential equations of selected physical situations
    • Determine the Laplace transform of selected elementary functions (such as polynomials and exponential and trigonometric functions having linear arguments)
    • Determine a function having a given Laplace transform; that is, determine the inverse Laplace transform of a function
    • Solve linear differential equation of various orders using the method of Laplace transforms

    Prerequisites by Topic
    • Determinants
    • Solution of algebraic equations
    • Limits including L’Hopital’s rule
    • Differentiation of algebraic and transcendental functions
    • Integration (especially improper and the method of partial fractions)
    • Factoring of polynomials

    Course Topics
    • Basic concepts
    • Solution of first-order differential equations by separation of variables
    • Solution of exact equations
    • Solution of first-order linear differential equations
    • Solution of first-order differential equations using numerical methods
    • Solution of physical situations that can be modeled by first-order differential equations
    • Solution of higher order homogeneous differential equations with constant coefficients
    • Solution of non-homogeneous higher-order differential equations using the method of Undetermined Coefficients
    • Solution of non-homogeneous higher-order differential equations using the method of Variation of Parameters
    • Solution of physical situations that can be modeled by higher-order differential equations
    • Introduction of Laplace transforms
    • Laplace transforms of elementary functions
    • Inverse Laplace transforms
    • Solution of linear differential equations with constant coefficients using Laplace transforms
    • Applications of Laplace transforms

    Coordinator
    Dr. Chunping Xie
  
  • MA 262 - Probability and Statistics

    3 lecture hours 0 lab hours 3 credits
    Course Description
    This course provides a basic introduction to the laws of probability needed to perform statistical analyses. Both descriptive and inferential statistics are considered. Probability distributions, the Central Limit Theorem, confidence intervals, hypothesis testing, and analysis of variance are considered in depth. Note: students cannot receive credit for both MA 262 and MA 3611 . (prereq: MA 137 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Be familiar with the terminology and nomenclature of both probability and statistics
    • Know the difference between a parameter and a statistic
    • Know the difference between a population and a sample
    • Understand the basic concepts and properties of probability
    • Understand the meaning and significance of the standard deviation
    • Calculate the mean and variance of probability distributions
    • Be familiar with, and able to calculate probabilities of, the binomial, Poisson, Normal, Student-t, Chi-square, and F distributions
    • Construct appropriate confidence intervals for population parameters
    • Have a basic familiarity with the Central Limit Theorem and realize that it affects the calculations of test values and confidence intervals
    • Perform hypothesis tests concerning the means, variances, and proportions of one or two populations
    • Perform hypothesis tests concerning the comparison of means of more than two populations

    Prerequisites by Topic
    • Algebra
    • Trigonometry
    • Differentiation of algebraic and transcendental functions
    • Integration of algebraic and transcendental functions

    Course Topics
    • Measures of central tendency and dispersion
    • Introduction to probability and the laws of probability
    • Discrete probability distributions: binomial and Poisson
    • Introduction to the Central Limit Theorem
    • Continuous probability distributions: normal, t, chi-square, and F
    • One-sample hypothesis testing and statistical inference
    • One-sample confidence intervals and statistical inference
    • Two-sample confidence intervals and statistical inference
    • Two-sample hypothesis testing and statistical inference
    • Analysis of variance

    Coordinator
    Dr. Won Chul Song
  
  • MA 315 - Nursing Statistics

    3 lecture hours 0 lab hours 3 credits
    Course Description
    This course considers both visual and calculational aspects of statistics. The major portion of the course deals with the analysis of data, including medical data. Calculational topics include the estimation of population parameters, tests of hypotheses, and tests for goodness of fit. Note: this course is open only to students in the School of Nursing. (prereq: MA 125  or MA 1204  or equivalent)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Understand basic statistical terminology
    • Produce data through sampling and experimental design
    • Classify data by type
    • Produce several methods of visually displaying data
    • Compute measures of central tendency and measures of dispersion
    • Understand the meaning, calculation, and interpretation of linear regression and correlation results
    • Have a basic understanding of the normal distribution and its application to appropriate statistical situations
    • Have a basic understanding of the concepts of sampling error and sampling distributions
    • Have an understanding as to the construction of confidence intervals for the population mean and the importance of the Student-t distribution to the construction of such confidence intervals
    • Have an understanding concerning the performance of hypothesis tests for the mean of a single population
    • Have an understanding relating to inferences for the comparison of two population means
    • Have a basic understanding with respect to the use of the chi-square distribution in goodness-of-fit and tests for independence calculations

    Prerequisites by Topic
    • Simplification of algebraic expressions containing fractions, exponents and radicals
    • Factoring
    • Linear and quadratic equations
    • Cartesian coordinate system
    • Systems of equations

    Course Topics
    • Descriptive and inferential statistics introduction and discussion
    • Linear regression
    • The normal distribution and its use in statistics
    • The central limit theorem and its importance to statistics
    • Confidence intervals for the population mean
    • Types of statistical errors 
    • Hypothesis testing 
    • Chi-square situations
    • Analysis of variance

    Coordinator
    Edward Griggs
  
  • MA 327 - Mathematical Modeling

    4 lecture hours 0 lab hours 4 credits
    Course Description
    The construction of a mathematical model requires the modeler to describe physical characteristics and processes of behavior in physical and natural systems by invoking mathematical language, using mathematical laws and concepts. Then the model is used to verify known results of the past and present, and to hopefully be able to extrapolate the future events. Topics of the course might include, depending upon instructor and student interest, statistical models, differential equations models, difference equations, Markov processes, optimization, etc. (prereq: MA 235 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • None

    Prerequisites by Topic
    • Calculus (single and multivariable)
    • Differential equations
    • Probability and statistics

    Coordinator
    Dr. Chunping Xie
  
  • MA 330 - Vector Analysis

    3 lecture hours 0 lab hours 3 credits
    Course Description
    This course provides a brief study of vector algebra and vector calculus, including velocity and acceleration, space curves, gradient, divergence and curl using the del operator, line, surface and volume integrals, conservative fields, curvilinear coordinates, Green’s theorem, the divergence theorem, and Stokes’ theorem. (prereq: MA 232  or MA 2323 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Perform elementary vector operations
    • Find the equations of lines and planes
    • Differentiate vector functions of one variable
    • Analyze three-dimensional curves
    • Calculate the divergence and curl of a vector field
    • Calculate line, surface, and volume integrals
    • Use the divergence and Stokes’ theorems to facilitate integral calculation

    Prerequisites by Topic
    • Basic vector algebra
    • Three dimensional analytic geometry
    • Differential and integral calculus

    Course Topics
    • Vector valued functions
    • Vector fields
    • Line integrals
    • Green, Gauss and Stokes’ theorems

    Coordinator
    Dr. Anthony van Groningen
  
  • MA 340 - Business Statistics

    4 lecture hours 0 lab hours 4 credits
    Course Description
    Almost all managerial decisions involve some amount of uncertainty. This course is designed to acquaint the student with some of the statistical methods that can be used to help make these decisions. Topics covered are probability, probability models, estimation, tests of hypotheses, analysis of variance, and regression. Note: This course is open only to students in the Rader School of Business. (prereq: MA 120  or equivalent)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Set up a frequency distribution
    • Compute the mean and standard deviation of a set of numbers
    • Determine probabilities of specific events
    • Recognize and use the binomial and normal probability distributions
    • Test a hypothesis about means and the binomial parameter ‘p’
    • Estimate the mean of a population and the parameter ‘p’
    • Understand analysis of variance and be able to calculate linear and multiple regression using Microsoft® Excel*. *Microsoft is a registered trademark of Microsoft Corporation in the United States and/or other countries

    Prerequisites by Topic
    • Algebra

    Course Topics
    • Introduction
    • Probability
    • Discrete probability distributions
    • Binomial distribution
    • Poisson distribution
    • Hypergeometric distribution
    • Continuous probability distributions
    • Normal distribution
    • Exponential distribution
    • Sampling
    • Hypothesis testing
    • Estimating mean and variance
    • Estimating proportion
    • Analysis of variance
    • Regression

    Coordinator
    Edward Griggs
  
  • MA 343 - Linear Programming

    3 lecture hours 0 lab hours 3 credits
    Course Description
    This course introduces the fundamentals of linear programming methods. Topics include formulating real-life problems (such as production planning, inventory, shortest path, and assignment problems) as linear programs, the simplex algorithm, geometry of feasible regions and optimal solutions, duality theory, and complementary slackness conditions. Tools relating linear and integer programs such as Gomory cuts and branch-and-bound methods will also be introduced. (prereq: MA 2314  or MA 231 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Formulate various real-life problems as linear and integer programs
    • Solve linear programs using the simplex algorithm
    • Construct the dual problem of a general linear program
    • Understand the weak and strong duality relations for linear programs
    • Verify optimal solutions using duality theory and complementary slackness conditions
    • Execute the primal-dual algorithm to solve the shortest path problem
    • Tackle integer programs using linear programming tools such as Gomory cuts and branch-and-bound methods

    Prerequisites by Topic
    • College algebra including basic operations and concepts with real vectors and matrices

    Course Topics
    • Linear algebra review
    • Formulation of linear and integer programs
    • Outcomes of linear programs
    • Basic feasible solutions and the simplex method
    • The 2-phase method
    • Duality theory and complementary slackness
    • Primal-dual algorithm - shortest path problem
    • Gomory cuts and branch-and-bound

    Coordinator
    Edward Griggs
  
  • MA 344 - Nonlinear Programming

    3 lecture hours 0 lab hours 3 credits
    Course Description
    This course introduces the fundamentals of nonlinear optimization. Topics include convex sets and functions, necessary and sufficient optimality conditions, duality in convex optimization, and algorithms for unconstrained and constrained optimization problems. (prereq: MA 343 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Understand the differences between linear, integer and nonlinear programs, as well as their levels of computational complexities
    • Learn the basic properties of convex sets and functions and common operations that preserve convexity
    • Solve small constrained and unconstrained convex nonlinear programs by hand
    • Understand and be able to verify the Karush-Kuhn-Tucker optimality conditions
    • Understand the Lagrangian function, and the notion of duality in convex optimization

    Prerequisites by Topic
    • The basic principles of algebra
    • Differentiation of algebraic functions
    • Exposure to multivariate calculus and partial derivatives
    • Experience with formulating industrial and graph theoretical problems using integer and linear programs
    • Duality theory in linear programming
    • Exposure to vectors and matrices

    Course Topics
    • Introduction to nonlinear programs
    • Convex sets and functions
    • Karush-Kuhn-Tucker conditions, gradient version
    • Lagrangian duality
    • Algorithms for unconstrained optimization
    • Algorithms for constrained optimization

    Coordinator
    Edward Griggs
  
  • MA 380 - Advanced Differential Equations

    3 lecture hours 0 lab hours 3 credits
    Course Description
    This course presents the student with more powerful methods of solving differential equations. Topics include matrix methods for solution of systems of linear differential equations, open-form solutions of linear differential equations with variable coefficients using infinite series (including the method of Frobenius), and additional Laplace transform methods. (prereq: MA 235 , and MA 232  or MA 2323 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Solve some linear systems of ordinary differential equations by Laplace transforms and differential operator methods including the Heaviside function, convolutions, Gamma functions, and periodic functions
    • Solve some linear ordinary differential equations with variable coefficients near an ordinary point
    • Solve some linear ordinary differential equations with variable coefficients near a regular singular point
    • Solve systems of linear differential equations using matrix methods

    Prerequisites by Topic
    • Convergence status and interval of convergence of infinite series
    • Power series manipulations using differentiation and integration
    • Using Maclaurin and Taylor series to approximate functions
    • Solution of higher-order linear homogeneous differential equations having constant coefficients
    • Solution of non-homogeneous linear differential equations having constant coefficients using the methods of undetermined coefficients and variation of parameters
    • Solution of linear differential equations using Laplace transforms
    • Matrix operations such as row manipulations, matrix inversion, and solution of a system of equations using matrices

    Course Topics
    • Solution of differential equations using Laplace transforms
    • Solution of linear differential equations near ordinary points and regular singular points
    • Solution of systems of differential equations using matrix methods

    Coordinator
    Dr. Chunping Xie
  
  • MA 381 - Complex Variables

    3 lecture hours 0 lab hours 3 credits
    Course Description
    This course is an introduction to the theory of analytic functions of a complex variable. Topics covered include algebra of complex numbers, mapping by elementary functions, analytic functions, complex integrals, Cauchy’s Theorem, power series, Laurent series, residues and poles. (prereq: MA 235 , and MA 232  or MA 2323 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Determine if a complex-valued function is analytic
    • Apply the Cauchy-Riemann equations, Cauchy’s theorem, Cauchy’s integral formula, Cauchy’s inequality, Liouville’s theorem, and the maximum modulus principle to complex valued functions
    • Apply Taylor’s theorem, Laurent’s theorem, and residue theorem

    Prerequisites by Topic
    • Differential and integral calculus
    • Elementary differential equations

    Course Topics
    • Complex numbers and the complex plane 
    • Analytic functions 
    • The elementary functions 
    • Elementary transcendental functions over the complex numbers 
    • Integration of analytic functions
    • Infinite series expansions, residues, and poles

    Coordinator
    Edward Griggs
  
  • MA 382 - Laplace and Fourier Transforms

    3 lecture hours 0 lab hours 3 credits
    Course Description
    This course introduces the theoretical concepts and uses of the Laplace and Fourier transforms. It includes Laplace transform of special functions, properties, operations and using Laplace transforms to solve ordinary and partial differential equations. It also includes Fourier series, Fourier Integral representation and Fourier transform of special functions, properties, operations and using them in partial differential equations. (prereq: MA 232  or MA 2323 , and MA 235 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Find Laplace and inverse Laplace transforms using a table
    • Find Fourier transforms
    • Solve linear differential equations and systems of equations with input functions, such as: continuous, piecewise continuous, unit step, impulse and periodic
    • Solve certain types integral, and integro-differential equations
    • Solve certain classes of linear partial differential equations

    Prerequisites by Topic
    • Improper integrals
    • Infinite series
    • Linear differential equations

    Course Topics
    • Basic properties of Laplace transforms and transforms of special functions
    • Transforms of derivatives and integrals and derivatives of transform
    • Application to differential equations
    • The unit step function
    • The Dirac delta function
    • Applications of step and impulse functions
    • Periodic functions and their applications
    • Convolution and applications
    • Solving integral equations
    • Fourier series
    • Fourier integral representation
    • Fourier transforms and its properties
    • Fourier sine and cosine transforms
    • Application of Fourier transforms to partial differential equation

    Coordinator
    Dr. Yvonne Yaz
  
  • MA 383 - Linear Algebra

    3 lecture hours 0 lab hours 3 credits
    Course Description
    Topics include the use of elementary row operations to solve systems of linear equations, linear dependence, linear transformations, matrix operations, inverse of a matrix, determinants, subspaces, null spaces, column spaces, dimension and rank, eigenvalues and eigenvectors, diagonalization of matrices, and similarity. (prereq: MA 231  or MA 2314  or MA 3501 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Learn the basic theory of linear algebra
    • Apply the basic row operations to solve systems of linear equations
    • Solve a matrix equation and a vector equation
    • Understand the concept of linear dependence and independence
    • Understand matrix transformations and linear transformations and the relationship between them
    • Perform all matrix operations, be able to find the inverses and determinants of matrices
    • Understand the concept of a subspace and basis
    • Describe the column and null spaces of a matrix and find their basis and dimensions, and the rank of a matrix
    • Understand the concept of similarity
    • Find the eigenvalues and eigenvectors of a matrix

    Prerequisites by Topic
    • Differential and integral calculus
    • Basic vector mathematics

    Course Topics
    • Introduction to systems of linear equation and solving them using matrices, row operations
    • Vectors, vector and matrix equations
    • Matrix operations
    • Vector spaces including bases, dimension, rank and nullity
    • Linear independence
    • Matrix transformations, linear transformations and their relations
    • Similarity
    • Eigenvalues, eigenvectors and their applications
    • Diagonalization
    • Applications

    Coordinator
    Dr. Yvonne Yaz
  
  • MA 384 - Statistical Methods for Use in Research

    3 lecture hours 0 lab hours 3 credits
    Course Description
    This course is an introduction to the techniques and methods used in research and seen in published research papers. It assumes a knowledge of the statistical methods generally encountered in an introductory, calculus-based statistics course. Methods such as multiple and nonlinear regression, sequential models regression, two-way analysis of variance, contingency tables, and nonparametric statistical methods from the basis of this course. (prereq: MA 262  or MA 3611  or MA 2410 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Understand the underlying assumptions for the use of any statistical test and understand why those assumptions exist
    • Perform single- and multiple-variable regression analyses and be able to provide the correct interpretation of applied hypothesis tests
    • Perform and interpret the meaning of a lack-of-fit analysis
    • Perform and interpret analyses of categorical data
    • Perform and interpret the application of various normality tests
    • Perform and interpret stepwise regression techniques
    • Correctly assess nonparametric situations, including knowing which nonparametric statistic to apply, which nonparametric hypothesis test to apply, and how to interpret the results obtained using such statistics and performing such hypothesis tests
    • Correctly determine a statistical test’s power
    • Correctly determine the sample size necessary for a given statistical situation

    Prerequisites by Topic
    • Differentiation and partial differentiation
    • Integration and multiple integration
    • Basic inferential statistical knowledge
    • Knowledge of hypothesis testing

    Course Topics
    • Simple linear regression and correlation
    • Multiple and nonlinear regression, including sequential models
    • Contingency tables
    • Tests of normality
    • Two-way analysis of variance
    • Nonparametric statistics
    • Power and sample size

    Coordinator
    Dr. Won Chul Song
  
  • MA 385 - Modern Algebra with Applications

    3 lecture hours 0 lab hours 3 credits
    Course Description
    This course is an introduction to abstract algebra with a focus on elementary group theory and some of its applications. Topics include modular arithmetic, groups, subgroups, isomorphism, external direct products, rings, integral domains and fields. Applications include error checking/correction and the RSA encryption algorithm. (prereq: MA 383  or MA 2830  or MA 2310 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Perform modular arithmetic operations including powers and inverses of large numbers
    • Identify whether or not a set together with a binary operation is a group
    • Relate divisibility facts to properties of cyclic groups
    • Identify isomorphic groups
    • Perform arithmetic operations with external direct products of cyclic groups
    • Prove basic theorems involving groups
    • Perform error-checking and error-correction computations including the ISBN system
    • Use the RSA algorithm to encrypt and decrypt large numbers
    • Solve second-degree equations in various rings
    • Prove basic theorems involving rings

    Prerequisites by Topic
    • None 

    Course Topics
    • Division algorithm, Euclidean algorithm, modular arithmetic and error-checking
    • Binary operations and groups
    • Finite groups and subgroups
    • Cyclic groups
    • Mappings and isomorphisms
    • External direct products
    • RSA encryption and modular arithmetic with large numbers
    • Fundamental Theorem of Finite Abelian Groups
    • Rings
    • Impossible constructions
    • Reviews
    • Exams

    Coordinator
    Dr. Anthony van Groningen
  
  • MA 386 - Functions of a Real Variable

    3 lecture hours 0 lab hours 3 credits
    Course Description
    This course looks at the foundations of calculus with more rigor, using the concepts of sequences and limits to understand continuity, differentiation and integration in greater depth than is possible in the calculus sequence. (prereq: MA 232  or MA 2323 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Understand the basic topology of the real number line
    • Understand the basic definitions and theorems concerning limits of sequences
    • Determine the convergence of sequences
    • Understand the concept and know the basic properties of continuous functions
    • Understand the concept and know the basic properties of differentiable functions
    • Understand the Riemann integral and the Fundamental Theorem of Calculus

    Prerequisites by Topic
    • None

    Course Topics
    • Mathematical induction
    • Real number line
    • Sequences
    • Limits
    • Continuity
    • Differentiability
    • Integrability

    Coordinator
    Dr. Chunping Xie
  
  • MA 387 - Partial Differential Equations

    3 lecture hours 0 lab hours 3 credits
    Course Description
    This course provides a smooth transition from a course in elementary ordinary differential equations to more advanced topics in a first course in partial differential equations, with heavier emphasis on Fourier series and boundary value problems. Topics covered includes separation of variables, classification of second order equations and canonical form, Fourier series, the one-dimensional and two-dimensional wave equation and heat equation, and Laplace’s equation. It also covers some applications, such as vibrating string, vibrating membrane, vibration of beams, heat conduction in bars and rectangular regions, etc. (prereq: MA 235 , MA 232  or MA 2323 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Write Fourier series of functions with period 2p
    • Write Fourier series of functions with arbitrary periods
    • Be able to write Fourier series of non-periodic functions using half-range expansions
    • Write the complex form of Fourier series
    • Solve one-dimensional wave equation using method of separation of variables and apply it to vibrating strings
    • Solve one-dimensional heat equation using method of separation of variables and apply it to heat conduction in bars
    • Solve two-dimensional wave and heat equations using method of separation of variables
    • Solve two-dimensional Laplace’s equation in rectangular coordinates
    • Solve two-dimensional wave equation in polar coordinates and apply it to vibrating membranes
    • Solve two-dimensional Laplace’s equation in polar coordinates and use it in applications.

    Prerequisites by Topic
    • Infinite series
    • Ordinary differential equations

    Course Topics
    • What is a partial differential equation and interpreting a given partial differential equation
    • Periodic functions
    • Fourier series
    • Fourier series of functions with arbitrary periods
    • Half-range expansions: Fourier sine and cosine series
    • Complex form of Fourier series
    • Forced oscillations
    • Modeling: Vibrating string and one-dimensional wave equation 
    • Solution of one-dimensional wave equation using method of separation of variables
    • D’Lambert’s method of solving one-dimensional wave equation
    • Solution of one-dimensional heat equation using method of separation of variables
    • Heat conduction in bars: Varying the boundary conditions
    • The two-dimensional wave and two-dimensional heat equations
    • Laplace’s equation in rectangular coordinates
    • The Poisson’s Equation: The method of eigenfunction expansion
    • Neumann and Robin conditions
    • Laplacian in various coordinate systems
    • Two-dimensional wave equation in polar coordinates: Vibration of a circular membrane
    • Two-dimensional Laplace’s equation in polar coordinates

    Coordinator
    Dr. Yvonne Yaz
  
  • MA 388 - Introduction to Number Theory

    3 lecture hours 0 lab hours 3 credits
    Course Description
    Number theory is primarily concerned with the properties of the integers. While the subject has long been thought of as quintessentially “pure” mathematics, recent developments in fields such as cryptography have renewed interest in it. Topics include mathematical induction; divisibility and primes; the Euclidean algorithm; linear Diophantine equations; modular arithmetic; primality testing; and continued fractions. (prereq: MA 231  or MA 2314 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Write elementary proofs
    • Use the principle of mathematical induction
    • Apply the Euclidean algorithm and solve linear Diophantine equations
    • Perform modular arithmetic
    • Apply Fermat’s Little Theorem and Euler’s Theorem
    • Understand the distribution of the prime numbers
    • Test for primality of integers
    • Find continued fraction expressions for real numbers (optional)
    • Understand the RSA encryption algorithm
    • Use Quadratic Reciprocity to compute Legendre symbols

    Prerequisites by Topic
    • None 

    Course Topics
    • Introduction to number theory, mathematical proof, and induction
    • Euclidean algorithm, divisibility, the GCD, and linear Diophantine equations
    • Fundamental theorem of arithmetic
    • Congruences and Fermat’s little theorem
    • The phi function and Euler’s theorem
    • Chinese remainder theorem
    • Distribution of primes; primality testing
    • Successive squaring, k-th roots, and RSA
    • Primitive roots and discrete logarithms
    • Quadratic reciprocity

    Coordinator
    Dr. Anthony van Groningen
  
  • MA 390 - Financial Mathematics

    4 lecture hours 0 lab hours 4 credits
    Course Description
    This course will the last course which prepares students for the second actuarial exam, referred to as Exam FM by the SOA, and Exam 2 by the CAS. It will review and/or cover the topics such as time value of money, annuities, loans, bonds, cash flow, and portfolios, immunization, general derivatives, options, hedging, forwards and futures and swaps. (prereq: BA 2503 , AS student, or consent of the program director)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Demonstrate knowledge of the fundamental concepts of financial mathematics
    • Demonstrate an ability to apply these concepts in calculating present and accumulated values for various streams of cash flows as a basis for use in: reserving, valuation, pricing, asset/liability management, investment income, capital budgeting, and valuing contingent cash flows
    • Show introductory knowledge of financial instruments, including derivatives, and the concept of no-arbitrage as it relates to financial mathematics
    • Successfully complete the FM exam

    Prerequisites by Topic
    • Business finance and accounting knowledge 

    Course Topics
    • General cash flows and portfolios
    • Immunization
    • General derivatives
    • Options
    • Hedging and investment strategies
    • Forwards and futures
    • Swaps

    Coordinator
    Dr. Yvonne Yaz
  
  • MA 461 - Applied Probability Models

    4 lecture hours 0 lab hours 4 credits
    Course Description
    This is an advanced probability course which covers topics such as Poisson processes, Markov chains, Markov decision process, inventory theory, queueing theory and reliability theory. (prereq: MA 2630  and MA 2631 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • None

    Prerequisites by Topic
    • Fundamentals of probability

    Coordinator
    Dr. Yvonne Yaz
  
  • MA 499 - Independent Study

    3 lecture hours 0 lab hours 3 credits
    Course Description
    A student enrolled in this course is afforded the opportunity to pursue a specialized topic in his or her chosen field of study. After an approved area of study has been selected, weekly meetings with the course advisor are required. A final report, the format of which is left to the discretion of the advisor, is required at the end of the term. (prereq: none)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Vary

    Prerequisites by Topic
    • None

    Course Topics
    • Vary

    Coordinator
    Dr. Kseniya Fuhrman
  
  • MA 1204 - Quantitative Reasoning for Health Care Professionals

    4 lecture hours 0 lab hours 4 credits
    Course Description
    This course addresses mathematical concepts and calculations frequently encountered by health care professionals. Topics include fundamental operations; ratio, proportion and percentage; magnitude and scale; manipulation and conversion of units; rounding and scientific notation. Additional topics include solving equations involving ratio, proportion and rate; interpretation of graphs; evaluation of formulas, including formulas encountered in statistics. (prereq: only open to Nursing students)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Perform arithmetic operations involving ratio, proportion, percentage and rate
    • Use rounding principles and scientific notation to report results of calculations
    • Interpret numerical values as magnitude, quantity and scale
    • Interpret and convert units
    • Solve and interpret equations involving ratio, proportion, percentage and rate
    • Solve and interpret applied problems relating to concentrations and mixtures
    • Interpret graphs involving time relationships
    • Evaluate formulas encountered in pediatric medication and statistics

    Prerequisites by Topic
    • None

    Course Topics
    • Fundamental operations involving fractions, decimals and percents
    • Solving equations involving ratio, percentage and rate
    • Conversion of units between systems of measurement of magnitude, quantity and scale including temperature, angles and volume
    • Health care applications involving ratio, proportion, rate and percentage including dosage calculations, angle measurement and IV rates
    • Read and interpret time series graphs such as EKG
    • Evaluate formulas commonly encountered in statistics

    Coordinator
    Edward Griggs
  
  • MA 1830 - Transition to Advanced Topics in Mathematics

    4 lecture hours 0 lab hours 4 credits
    Course Description
    Introduction to proof techniques to be used in upper-level mathematics courses. Topics include logic and proofs, set theory, relations and partitions, functions, and cardinality of sets. (prereq: only open to AS students)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Demonstrate proficiency in elementary logic, including using truth tables to prove logical equivalence
    • Manipulate logical sentences symbolically and semantically: for example, apply DeMorgan’s Law to construct denials
    • Demonstrate familiarity with the natural numbers, integers, rational numbers, real numbers, and complex numbers
    • Demonstrate proficiency in interpreting and manipulating existential and universal quantifiers
    • Read and construct proofs using direct and indirect methods
    • Choose methods of proof appropriately
    • Read and construct proofs involving quantifiers
    • Demonstrate proficiency in elementary set theory including construction of sets, subsets, power sets, complements, unions, intersections, and Cartesian products
    • Interpret unions and intersections of indexed families of sets
    • Read and construct proofs involving set theoretic concepts
    • Apply the principle of mathematical induction and its equivalent forms
    • Manipulate summations in sigma notation
    • Read and construct proofs related to relations, equivalence relations, and partitions of sets
    • Demonstrate familiarity with functions as relations; injections, surjections, and bijections
    • Construct functions from other functions: for example, compositions, restrictions, and extensions
    • Read and construct proofs related to functions
    • Demonstrate familiarity with cardinality for finite, countable, and uncountable sets

    Prerequisites by Topic
    • None

    Course Topics
    • Elementary logic with truth tables
    • Quantifiers
    • Methods of proof
    • Elementary set theory
    • Operations with sets including indexed families of sets
    • Principle of mathematical induction and its equivalent forms
    • Cartesian products
    • Relations, equivalence relations, and partitions of sets
    • Functions, surjections, and injections
    • Cardinality of sets

    Coordinator
    Dr. Anthony van Groningen
  
  • MA 1840 - Computer Applications in Applied Mathematics

    4 lecture hours 0 lab hours 4 credits
    Course Description
    This course introduces students to computer applications used for solving mathematical problems. Emphasis is placed on learning advanced functions in Microsoft Excel and MATLAB. Topics include problem formulation, model development and implementation, data analysis, and the use of computer graphics in solutions of various problems. The course material is presented as a combination of lecture and hands-on exercises.  (prereq: none)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Apply a variety of computer tools to solve a wide range mathematical problems
    • Analyze and present data
    • Use computer tools to create professional presentations of solutions
    • Work with advanced formulas and functions in Microsoft Excel
    • Write macros in Microsoft Excel
    • Program scripts and functions using the MATLAB development environment
    • Implement selection and loop statements
    • Generate plots for use in reports and presentations
    • Fit curves to data 

    Prerequisites by Topic
    • None

    Course Topics
    • Working with data and Excel tables 
    • Performing calculations on data 
    • Formatting
    • Filters 
    • Formulas and functions
    • Charts and graphics
    • PivotTables and PivotCharts 
    • Macros and forms
    • MATLAB environment 
    • MATLAB scripts
    • Selection statements
    • Loop statements 
    • Plotting techniques
    • Fitting curves to data

    Coordinator
    Dr. Kseniya Fuhrman
  
  • MA 2310 - Discrete Mathematics I

    3 lecture hours 0 lab hours 3 credits
    Course Description
    This course provides an introduction to discrete mathematics as it applies to computer science. Topics include sets, logic, relations, functions, recursion, Boolean algebra, and graph theory. A student cannot receive credit for both MA 2310 and MA 1830 . (prereq: sophomore standing)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Illustrate by examples the basic terminology of functions, relations, and sets
    • Illustrate by examples, both discrete and continuous, the operations associated with sets, functions, and relations
    • Apply functions and relations to problems in computer science
    • Manipulate formal methods of symbolic propositional and predicate logic
    • Demonstrate knowledge of formal logic proofs and logical reasoning through solving problems
    • Illustrate by example the basic terminology of graph theory
    • Apply logic to determine the validity of a formal argument
    • Identify a relation; specifically, a partial order, equivalence relation, or total order
    • Identify a function; specifically, surjective, injective, and bijective functions
    • Illustrate by examples tracing Euler and Hamiltonian paths
    • Construct minimum spanning trees and adjacency matrices for graphs

    Prerequisites by Topic
    • Basic concepts of college algebra
    • Basic concepts of set theory

    Coordinator
    Dr. Chunping Xie
  
  • MA 2314 - Calculus III

    4 lecture hours 0 lab hours 4 credits
    Course Description
    This course is a continuation of MA 137. Topics include L’Hȏpital’s rule, improper integrals, parametric equations, polar coordinates, vector algebra, infinite series with tests for convergence, power series, Taylor and Maclaurin series, and operations with series. (prereq: MA 137 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Use L’Hȏpital’s rule to evaluate a limit
    • Evaluate improper integrals
    • Find the length of the arc of a curve
    • Eliminate the parameter from parametric equations
    • Draw graphs of parametric equations and determine the direction of travel for an increasing parameter
    • Find first and second derivatives of parametric functions
    • Find the arc length for parametric curves
    • Convert between rectangular and polar coordinates
    • Draw graphs of polar curves
    • Find area and arc length in polar coordinates
    • Perform operations using vector algebra
    • Find dot products, cross products, and equations of lines and planes in three dimensions
    • Test sequences for convergence and divergence
    • Test infinite series for convergence and divergence
    • Find the interval of convergence for a power series
    • Perform algebraic and calculus operations on power series
    • Use Taylor and Maclaurin series to approximate functions

    Prerequisites by Topic
    • The basic principles of algebra
    • The basic principles of trigonometry
    • Differentiation and integration of algebraic and transcendental functions
    • Limits
    • Understanding of the definition of the definite integral

    Course Topics
    • L’Hȏpital’s rule 
    • Improper integrals
    • Arc length
    • Parametric equations 
    • Polar coordinates and graphs 
    • Vectors, lines, and planes 
    • Sequences
    • Infinite series and tests for convergence
    • Power series and intervals of convergence
    • Taylor and Maclaurin series                               

    Coordinator
    Dr. Chunping Xie
  
  • MA 2320 - Introduction to Graph Theory

    3 lecture hours 0 lab hours 3 credits
    Course Description
    This course introduces a sampling of fundamental concepts and results in graph theory. Topics include graph isomorphisms, trees and connectivity, matching and covering, planarity and colouring, and Ramsey’s Theorem. Graph algorithms for solving the assignment problem and the max-flow problem will also be discussed. (prereq: MA 1830  or MA 2310 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Demonstrate knowledge of basic terminology associated with graphs, such as isomorphisms, trees, connectivity, planarity, colouring, and matchings
    • Demonstrate knowledge of fundamental results in graph theory, such as Konig’s Theorem, Hall’s Theorem, Kuratowski’s Theorem and the 4-Colour Theorem
    • Be able to apply various techniques (e.g. mathematical induction, proof by contradiction) to construct basic proofs for statements involving graphs
    • Model simple real world problems using graph theory
    • Be able to solve instances of the assignment problem and the max-flow problem using appropriate graph algorithms

    Prerequisites by Topic
    • Basic concepts of college algebra
    • Basic concepts of set theory
    • Basic concepts of logic and proofs 

    Course Topics
    • Basic definitions and notions for graphs
    • Matching and covering
    • Planarity and colouring
    • Graph algorithms
    • Ramsey Theory

    Coordinator
    Edward Griggs
  
  • MA 2323 - Calculus IV

    3 lecture hours 0 lab hours 3 credits
    Course Description
    This course is a continuation of MA 2314 and an introduction to multivariate calculus. Topics include surfaces in three dimensions, partial derivatives, double and triple integrals with applications to areas, volumes, and moments.  (prereq: MA 2314 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Sketch surfaces in three dimensions
    • Find first and second partial derivatives
    • Find the total differential of a function of more than one variable and use it to approximate error
    • Use chain rules to find derivatives and partial derivatives
    • Find implicit partial derivatives
    • Determine the maximum, minimum, and saddle points on a surface
    • Set up and evaluate double integrals using rectangular and polar coordinates
    • Find areas, volumes, and moments using double integrals
    • Set up and evaluate triple integrals
    • Use triple integrals to find volumes and moments of solids
    • Use integrals in cylindrical or spherical coordinates to find volumes and moments

    Prerequisites by Topic
    • The basic principles of algebra
    • The basic principles of trigonometry
    • Differentiation and integration of algebraic and transcendental functions
    • Applications of integration
    • Integration techniques
    • L’Hȏpital’s rule
    • Polar coordinates

    Course Topics
    • Surfaces in three dimensions 
    • Functions of several variables 
    • Partial derivatives 
    • Extrema of functions of two variables 
    • Double integrals, area, volume, and moments
    • Triple integrals, volume, moments, cylindrical and spherical coordinates

    Coordinator
    Edward Griggs
  
  • MA 2410 - Statistics for AS

    4 lecture hours 0 lab hours 4 credits
    Course Description
    The course is designed to expose actuarial science majors to the statistical tools needed to make decisions based on the computed probability of occurrence. Both descriptive and inferential statistics will be considered. This course is designed to satisfy all the required topics of SOA (Society of Actuaries) VEE Mathematical Statistics curriculum. (prereq: MA 2323 , AS student, or consent from AS program director)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Choose which probability distribution applies to a given statistical situation
    • Perform a complete hypothesis test
    • Correctly calculate and interpret a p-value
    • Recognize the similarities between the various hypothesis tests and the formulas used by these tests
    • Construct estimators using method of moments and maximum likelihood estimator
    • Demonstrate understanding of sampling distributions
    • Perform analysis of variance when appropriate and interpret the results
    • Describe properties of estimators, including mean squared errors and UMVUE
    • Apply Neyman-Pearson Lemma and likelihood ratio tests
    • Construct confidence intervals for mean, the difference of two means, the difference of proportions and variance 
    • Apply analysis of variance and chi-square goodness-of-fit tests

    Prerequisites by Topic
    • Differential and integral calculus (both single and multivariable)

    Course Topics
    • Major probability distributions used in hypothesis testing including normal, student-t, chi-square, and F
    • Sampling distribution and central limit theorem
    • Constructing estimators using such as the method of moments and maximum likelihood estimator 
    • Properties of estimators, including mean squared errors and UMVUE
    • Theory of hypothesis test, including Neyman-Pearson Lemma and likelihood ratio test
    • One-sample and two-sample hypothesis testing
    • Confidence intervals for mean, the difference of two means, the difference of proportions and variance
    • Analysis of variance and chi-square goodness-of-fit test

    Coordinator
    Dr. Won Chul Song
  
  • MA 2411 - Time Series Analysis

    4 lecture hours 0 lab hours 4 credits
    Course Description
    This course is designed for actuarial science majors taking the sequence of actuarial exams. A time series is a collection of measurements taken at different points in time. This course will introduce the theory and practice of analyzing time series, emphasizing practical skills. In particular, these skills will include providing compact descriptions of time series data, interpretation of time series data, forecasting future values based on known time series data, hypothesis testing with respect to time series analysis, and simulation using time series models. (prereq: MA 232  or MA 2323 MA 2630 , MA 2410  or consent of the AS program director)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • State the basic theory of time-series analysis and forecasting approaches
    • Synthesize the relevant statistical knowledge and techniques for forecasting
    • Identify, define, and formulate forecasting problems and use statistical software for the analysis of time series and forecasting
    • Interpret analysis results and make recommendations for the choice of forecasting methods
    • Produce and evaluate forecasts for a given time series
    • Present analysis results of forecasting problems
    • Be able to read published articles concerning time series

    Prerequisites by Topic
    • Calculus (single variable and multivariable)
    • Probability theory and application
    • Statistics including regression

    Course Topics
    • Simple linear regression
    • Multiple linear regression
    • Model building
    • Residual analysis
    • Time series regression
    • Exponential smoothing

    Coordinator
    Dr. Won Chul Song
  
  • MA 2630 - Probability I for AS

    4 lecture hours 0 lab hours 4 credits
    Course Description
    This course introduces elementary probability theory, which includes basic probability concepts such as counting, sets, axioms of probability, conditional probability and independence, Bayes’ theorem, discrete random variables, common discrete distributions, joint distributions, properties of expectation, moment generating functions, and limit theorems. (prereq: sophomore standing in AS program or consent of instructor)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Perform basic set theory operations including union, intersection, and apply them to probability situations
    • Understand the differences between mutually exclusive events and independent events and apply this knowledge to probability situations
    • Understand the differences and similarities of combinations and permutations and how combinations are used to evaluate probabilities
    • Understand the concept of conditional probability and how it extends to the Law of Total Probability and Bayes’ Rule
    • Use various discrete probability distributions to determine probabilities
    • Use, understand, derive and use discrete probability mass functions, distribution functions, and moment-generating functions
    • Understand, derive, and use discrete joint probability functions
    • Understand the meaning and relevance of variance and standard deviation and how it relates to probability calculations
    • Understand and use the results of the Central Limit Theorem
    • Use a transformation function to transform one probability mass function into another

    Prerequisites by Topic
    • Algebra
    • Calculus

    Course Topics
    • Union and intersection notation, theory, and examples
    • Mutually exclusive events and independent events
    • Addition and multiplication rules for probability
    • Combinatorics
    • Conditional Probability
    • Law of Total Probability
    • Bayes’ Rule
    • Discrete probability distributions such as the binomial, Poisson, negative binomial, uniform, geometric, hypergeometric, etc.
    • Discrete probability mass functions
    • Discrete cumulative distribution functions
    • Discrete moment-generating functions
    • Continuous probability distributions such as the Gaussian (normal) distribution, Student-t, chi-squared, F, exponential, gamma, beta, etc.
    • Continuous probability density functions
    • Continuous cumulative density functions
    • Continuous moment-generating functions
    • Measures of dispersion (including variance)
    • Transformations of random variables

    Coordinator
    Dr. Yvonne Yaz
  
  • MA 2631 - Probability II for AS

    4 lecture hours 0 lab hours 4 credits
    Course Description
    This course continues where MA 2630  ended.  In particular, topics of discussion will include continuous probability distributions such as the uniform, normal, exponential, gamma, beta, Cauchy, and Weibull distributions, both discrete and continuous joint probability distributions, and additional expectation results, such as moment-generating functions, that were not discussed in MA 2630 . (prereq: MA 2630 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Understand and apply continuous probability distributions to appropriate probability situations
    • Understand, derive, and use continuous probability density functions, conditional probability density functions, marginal functions, and moment-generating functions
    • Understand, derive, and use continuous joint probability functions
    • Understand the meaning and relevance of and use measures of dispersion for continuous multi-variable probability distributions
    • Understand, calculate, and use covariance
    • Understand, calculate, and apply to correlation coefficient appropriate situations
    • Perform transformations of continuous random variables
    • Form and use linear combination of random variables with respect to calculation of probabilities and moments

    Prerequisites by Topic
    • Multivariable calculus
    • Discrete random variables

    Course Topics
    • Continuous probability distributions such as the Gaussian (normal) distribution, Student-t, chi-squared, F, exponential, gamma, beta, etc.
    • Continuous probability density functions
    • Continuous cumulative density functions
    • Continuous moment-generating functions
    • Continuous joint probability functions, joint probability density functions, and joint cumulative density functions
    • Conditional and marginal distributions and densities
    • Moments for the discrete and continuous joint functions considered
    • Joint moment-generating functions
    • Measures of dispersion for multi-variable probability distributions
    • Covariance
    • Correlation coefficients
    • Transformations of continuous random variables
    • Linear combinations of random variables including probabilities and moments

    Coordinator
    Dr. Yvonne Yaz
  
  • MA 2830 - Linear Algebra for Math Majors

    4 lecture hours 0 lab hours 4 credits
    Course Description
    Topics include the use of elementary row operations to solve systems of linear equations, linear independence, matrix operations, inverse of a matrix, linear transformations, vector spaces and subspaces, coordinate systems and change of bases, determinants of matrices and their properties, eigenvalues, eigenvectors, diagonalization, inner product and orthogonality, the Gram-Schmidt Process, and the least-squares problem. Particular emphasis is given to proper mathematical reasoning and presentation of solutions. The students will use MATLAB to explore certain applications.  (prereq: MA 1830 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Understand the basic theory of linear algebra
    • Apply the basic row operations to solve systems of linear equations
    • Solve a matrix equation and a vector equation
    • Understand the concept of linear dependence and independence
    • Understand matrix transformations and linear transformations and the relationship between them
    • Perform all matrix operations, be able to find the inverses of matrices
    • Understand concepts of vector space, subspace and basis and be able to change bases
    • Describe the column and null spaces of a matrix and find their dimensions
    • Find the rank of a matrix
    • Be able to find the eigenvalues and corresponding eigenvectors of matrices 
    • Be able to identify a diagonalizable matrix and diagonalize it 
    • Understand the relationship between eigenvalues and linear transformations 
    • Understand the concepts of orthogonality and orthogonal projections 
    • Apply the Gram-Schmidt Process to produce orthogonal bases 
    • Find the least-squares solution to a system of linear equations 

    Coordinator
    Dr. Kseniya Fuhrman
  
  • MA 3320 - Discrete Mathematics II

    3 lecture hours 0 lab hours 3 credits
    Course Description
    This course continues the introduction of discrete mathematics begun in MA 2310. Emphasis is placed on concepts applied within the field of computer science. Topics include logic and proofs, number theory, counting, computational complexity, computability, and discrete probability.  A student cannot receive credit for both MA 3320 and MA 1830. (prereq: MA 2310 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Apply conditional probability to identify independent events
    • Apply Bayes’ rule and demonstrate an understanding of its implications
    • Be familiar with standard complexity classes
    • Derive closed-form and asymptotic expressions from series and recurrences for growth rates of processes
    • Identify a given set as countable or uncountable
    • Calculate the number of possible outcomes of elementary combinatorial processes such as permutations and combinations
    • Illustrate by examples the properties of primes
    • Apply the Chinese remainder theorem
    • Synthesize induction hypotheses and simple induction proofs
    • Illustrate by examples proof by contradiction

    Prerequisites by Topic
    • Predicate logic
    • Recurrence relations
    • Fundamental structures

    Coordinator
    Dr. Chunping Xie
  
  • MA 3501 - Engineering Mathematics I

    4 lecture hours 0 lab hours 4 credits
    Course Description
    This course provides topics to bridge the technical calculus sequence to the university’s calculus sequence. Topics include vector algebra; review of single variable calculus, including differentiation of elementary functions, the mean value theorem, antiderivatives, and definite integrals; selected methods of integration including partial fractions decomposition; functions of several variables including partial differentiation and multiple integration in cylindrical and spherical coordinates. (prereq: one year of technical calculus or equivalent)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Differentiate and integrate elementary functions
    • Evaluate improper integrals on an infinite interval
    • Integration by partial fractions decomposition
    • Evaluate partial derivatives of functions of multiple variables
    • Use the chain rule to find derivatives of functions of multiple variables
    • Evaluate the total differential to estimate change in a function of multiple variables
    • Evaluate double integrals in rectangular and polar coordinates
    • Evaluate triple integrals in rectangular, cylindrical, and spherical
    • Perform operations using vector algebra
    • Evaluate dot and cross products of vectors
    • Find equations of planes in three dimensions
    • Parameterize lines in three dimensions
    • Solve geometric problems involving lines and planes

    Prerequisites by Topic
    • Differentiation of trigonometric, inverse trigonometric, exponential and logarithmic functions.
    • Basic integration including substitution.

    Course Topics
    • Review of differentiation of elementary functions
    • The mean value theorem
    • Review of antiderivatives and basic integration techniques, definite integrals, and the fundamental theorem of calculus
    • Improper integrals on an infinite interval
    • Integration by partial fractions decomposition
    • Functions of two or more variables
    • Partial differentiation, the chain rule, and the total differential
    • Double integrals in rectangular and polar coordinates
    • Triple integrals in rectangular, cylindrical, and spherical
    • Three-dimensional coordinate systems
    • Vector algebra including dot and cross products of vectors
    • Lines and planes in three-dimensional space

    Coordinator
    Dr. Anthony van Groningen
  
  • MA 3502 - Engineering Mathematics II

    4 lecture hours 0 lab hours 4 credits
    Course Description
    Solution of first order equations, higher order linear equations and initial value problems, the methods of undetermined coefficients, variation of parameters, and Laplace transforms. (prereq: MA 225, MA 231 /MA 2314  or equivalent)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Determine the solution of a first order differential equations by the method of separation of variables
    • Solve exact equations
    • Determine appropriate integrating factors for first order linear equations
    • Determine the general solution of higher order linear homogeneous equations with constant coefficients
    • Determine the general and particular solutions of certain linear non-homogenous equations using the methods of undetermined coefficients and variation of parameters
    • Determine the Laplace transform and inverse Laplace transform of certain elementary functions
    • Solve certain linear differential equations using Laplace transforms

    Prerequisites by Topic
    • Differentiation of elementary functions for all topics
    • Integration techniques for solving differential separable and exact equations and for variation of parameters
    • Improper integrals for Laplace transforms

    Course Topics
    • Basic concepts of differential equations
    • Solution of first order equations by separation  of variables
    • Solution of exact equations
    • Solution of first order linear non-homogeneous equations
    • Solution of higher order linear homogeneous differential equations with constant coefficients
    • Solution of higher order linear non-homogeneous differential equations using the method of undetermined coefficients
    • Solution of higher order linear non-homogeneous differential equations using the method of variation of parameters
    • Introduction to Laplace transforms
    • Laplace transforms of elementary functions
    • Inverse Laplace transforms
    • Operational properties: Laplace transforms and inverse Laplace transforms involving transforms of derivatives, derivatives of transforms, exponential shift (translation on the s-axis) and Heaviside function (translation on the t-axis), Dirac delta function and periodic functions
    • Solution of linear differential equations using Laplace transforms

    Coordinator
    Dr. Anthony van Groningen
  
  • MA 3611 - Biostatistics

    3 lecture hours 0 lab hours 3 credits
    Course Description
    This course provides an introduction to biostatistics for biomedical engineering students. As a result of this course the students are expected to understand and prepare statistical analyses of data from physiological systems in the laboratory and clinical environment. Students learn basic probability theory that includes discrete and continuous probability distributions. They learn how to apply that theory to hypothesis testing and understand the difference between a z-test and t-test, one- and two-sample inference hypothesis testing, and Analysis of Variance. Additional concepts covered include hypothesis formulation and testing, both parametric and nonparametric. Either the statistical package SAS or the statistical package SPSS will be introduced to the students and will be used to perform statistical analyses.  Finally, journal articles from the New England Journal of Medicine (NEJM) containing significant statistical components will be considered in class. (prereq: MA 136 ) (coreq: MA 137 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Recognize and evaluate conditional probability situations such as Bayes’ Rule, specificity, sensitivity, predictive value positive, and predictive value negative
    • Set up and evaluate inferences using hypothesis tests and confidence intervals
    • Perform hypothesis tests for one- and two-sample situations
    • Recognize when analysis of variance (ANOVA) is applicable, and subsequently be able to apply and evaluate ANOVA calculations
    • Recognize when nonparametric situations are present and then be able to apply the correct nonparametric test, evaluate it, and interpret it
    • Use SAS (or SPSS if it is the statistical package being used) when appropriate
    • Read and interpret the statistical content of assigned articles in the NEJM

    Prerequisites by Topic
    • None

    Coordinator
    Dr. Won Chul Song
  
  • MA 3710 - Mathematical Biology

    3 lecture hours 0 lab hours 3 credits
    Course Description
    This course is an overview of several techniques used in the development and analysis of mathematical models that illustrate various biological processes. The topics covered involve applications of ordinary and partial differential equations, dynamical systems, and statistical analysis. Applications include population models, infectious disease and epidemic models, genetics, tumor growth, and DNA sequencing. (prereq: MA 235 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Interpret biological assumptions in terms of mathematical equations
    • Construct mathematical models to illustrate a biological processes
    • Write computer simulations for a biological model
    • Analyze a model numerically and graphically
    • Find equilibria of system of equations
    • Perform local stability analysis
    • Solve counting problems involving the addition and multiplication rules, permutations, and combinations
    • Calculate discrete probability

    Prerequisites by Topic
    • Know the techniques of limits, differentiation, and integration
    • Be able to determine the solution of first-order differential equations by the method of separation of variables
    • Be able to determine appropriate integrating factors for first-order linear differential equations

    Course Topics
    • Introduction to mathematical biology
    • Constructing a model
    • Exponential and logistic growth
    • Population-genetic models
    • Models of interaction among species
    • Epidemiological models of disease spread
    • MATLAB review
    • Numerical and graphical techniques
    • Finding equilibrium
    • Performing local stability analysis: one variable model
    • Finding an approximate equilibrium
    • Matrices, Eigenvalues, Eigenvectors
    • Performing local stability analysis: non-linear models with multiple variables
    • Counting principles: addition and multiplication rules
    • Permutations
    • Combinations
    • Arrangements with repetitions
    • Probability
    • Conditional probability and independence of events

    Coordinator
    Dr. Kseniya Fuhrman
  
  • MA 4980 - Topics in Mathematics

    0-4 lecture hours 0 lab hours 0-4 credits
    Course Description
    This course gives an opportunity to the students to take a course in a topic that is not covered in other mathematics courses offered. Topics covered can be determined by the faculty and the students based on their mutual interest. (prereq: instructor consent)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Vary by topic

    Prerequisites by Topic
    • Depend on the topic of choice.

    Coordinator
    Dr. Yvonne Yaz

Mechanical Engineering

  
  • ME 190 - Computer Applications in Engineering I

    2 lecture hours 2 lab hours 3 credits
    Course Description
    The purpose of this course is to familiarize students with the modern computer tools required for engineering practice and teach them how to apply these tools to solve practical engineering problems. Topics include problem formulation, model development, algorithm development, and the use of numerical methods and computer graphics in the solution of engineering problems. Laboratory exercises will involve the use of various numerical and graphical software packages. (prereq: MA 127  or equivalent)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Apply problem-solving skills to engineering problems
    • Present formal solutions to engineering problems
    • Apply modern computational tools to solve mechanical and industrial engineering problems

    Prerequisites by Topic
    • College trigonometry and algebra

    Course Topics
    • Problem solving methodologies; introduction to algorithm development
    • Working with arrays, plotting
    • Programming - loops, logic, and functions
    • Flowcharts
    • Curve fitting and the least-squares method
    • Solving system of equations
    • Matrix methods
    • Importing and exporting data
    • Numerical integration and differentiation
    • Optimization

    Laboratory Topics
    • Problem solving
    • Plotting data
    • Roots of equations
    • Numerical integration
    • Solution of simultaneous equations
    • Optimization

    Coordinator
    Dr. Michael Cook
  
  • ME 205 - Engineering Statics

    4 lecture hours 0 lab hours 4 credits
    Course Description
    This is a study of force systems acting on bodies that are not in motion. The course includes analysis of forces in trusses, frames and machine components; additional topics include friction, location of centroids, and evaluation of area and mass moments of inertia. Not for credit for students who have credit in AE 200 . (prereq: MA 137 , high school physics)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Draw free body diagrams for static systems
    • Perform 2-D equilibrium analysis using scalar analysis
    • Perform 3-D equilibrium analysis using vector analysis
    • Determine internal forces in trusses, frames and machines
    • Analyze the effect of friction in static systems
    • Compute area and mass moments of inertia of shapes and bodies

    Prerequisites by Topic
    • Vector mathematics
    • Physics of mechanics
    • Integral calculus

    Course Topics
    • Introduction to mechanics (unit systems, forces, vector mathematics) (2 classes)
    • 2-D and 3-D particle equilibrium (4 classes)
    • Moments, force/couple systems (5 classes)
    • 2-D and 3-D rigid body equilibrium (7 classes)
    • Analysis of trusses, frames, and machines (5 classes)
    • Friction (3 classes)
    • First area moments, centroids (by composite shapes and direct integration) (3 classes)
    • Area moment of inertia (by composite shapes and direct integration) (3 classes)
    • Mass moment of inertia (by composite shapes and direct integration) (3 classes)
    • Testing and review (5 classes)

    Coordinator
    Dr. Joseph Musto
  
  • ME 206 - Engineering Dynamics

    4 lecture hours 0 lab hours 4 credits
    Course Description
    This is the study of motion and the forces which affect the motion. This course includes the study of rectilinear motion, curvilinear motion, plane motion, dynamic force analysis, work and energy, and impulse and momentum. (prereq: ME 205 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Determine the position, velocity, and acceleration of particles subjected to rectilinear translation
    • Determine the trajectory of projectiles given initial conditions
    • Determine the position, velocity and acceleration of given points of a properly constrained kinematic linkage
    • Determine the acceleration or force causing acceleration using Newton’s Second Law of Motion
    • Determine the motion of kinetic systems using the principle of work and energy
    • Determine the motion of particles using the principle of impulse and momentum
    • Determine the forces acting on rigid bodies in motion

    Prerequisites by Topic
    • None

    Course Topics
    • Rectilinear motion of particles
    • Relative and dependent motion of particles
    • Curvilinear motion of particles
    • Plane kinematics of rigid bodies-velocities
    • Plane kinematics of rigid bodies-accelerations
    • Kinematics of particles-Newton’s 2nd Law
    • Work and energy
    • Conservation of energy
    • Impulse and momentum
    • Kinetics of rigid bodies

    Coordinator
    Dr. Joseph Musto
  
  • ME 207 - Mechanics of Materials

    3 lecture hours 2 lab hours 4 credits
    Course Description
    This is the first course in the mechanics of deformable bodies. Topics include stresses and strains produced by axial loading, torsion, and bending; elastic deflections of beams; effects of combined loading; and buckling of slender columns. Laboratory topics will reinforce lecture material. Not for credit for students who have credit in either AE 201 or AE 2011 . (prereq: ME 205  or ME 255, MA 231  or MA 2314  or MA 226)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Determine stresses resulting from axial, bending, torsion, and transverse loading
    • Apply Hooke’s Law for materials with linear stress-strain behavior
    • Construct shear and bending moment diagrams for statically indeterminate structures
    • Determine the stress state in a member resulting from combinations of loads
    • Know how to find principal stresses for a state of plane stress
    • Determine beam deflections by integrating the moment equation
    • Be familiar with the Euler buckling load for columns of various end conditions

    Prerequisites by Topic
    • Statics
    • Integral and differential calculus

    Course Topics
    • Review of statics, reactions, internal loads
    • Concept of stress and strain
    • Mechanical properties of materials
    • Axial loading
    • Stress concentrations
    • Torsion
    • Shear and moment diagrams
    • Bending stresses
    • Transverse shear
    • Combined loads
    • Stress and strain transformations, including Mohr’s circle and strain rosettes
    • Principal stresses
    • Beam deflections

    Laboratory Topics
    • Specimen in tension or compression
    • Uniaxial loading in a truss
    • Shear of joined sections
    • Combined stresses
    • Stresses in beams
    • Beam deflection
    • Stress-strain curve

    Coordinator
    Dr. Robert Rizza
  
  • ME 230 - Dynamics of Systems

    4 lecture hours 0 lab hours 4 credits
    Course Description
    This course introduces the modeling of electrical, mechanical, fluid and thermal engineering systems and the various methods for solving their corresponding differential equations. A systems approach is employed to represent dynamical systems and quantify their response characteristics. (prereq: EE 201 MA 235 , ME 190 , and (ME 206  or ME 2002 ))
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Understand basic system components of mechanical, electrical, thermal, and fluid systems and combine components into systems
    • Formulate mechanical, electrical, thermal, fluid and mixed discipline systems into appropriate differential equation models
    • Analyze linear systems for dynamic response - both time and frequency response
    • Recognize the similarity of the response characteristics of various physically dissimilar systems
    • Solve systems using classical methods and MATLAB/Simulink

    Prerequisites by Topic
    • Electrical circuits
    • Differential equations
    • Dynamics

    Course Topics
    • Introduction to dynamic systems
    • Review of time domain solutions for 1st and 2nd order systems
    • Free and constant force responses (step input)
    • Determine system dynamic response characteristics
    • Laplace domain analysis and pole-zero plots
    • Block diagram model representation and transfer functions
    • Simulation of block diagrams systems using Simulink
    • Modeling mechanical systems (M-S-D)
    • Modeling of mechanical systems (Torsional Systems)
    • Linearization of differential equations
    • Modeling electrical systems (RC and RLC circuits)
    • Modeling of operational amplifiers
    • Modeling of electromechanical systems (DC motor)
    • Modeling of other analogous systems
    • State-space representation
    • Numerical integration with Euler and ODE45
    • Frequency response function
    • Bode plots and 1st and 2nd order system characteristics

    Coordinator
    Dr. Daniel Williams
  
  • ME 300 - Modeling and Numerical Analysis

    3 lecture hours 2 lab hours 4 credits
    Course Description
    This course is a study of mathematical techniques used to model engineering systems. It involves the development of mathematical models and the application of the computer to solve engineering problems using the following computational techniques: Taylor Series approximation, numerical differentiation, root finding using bracketing and open methods, linear and polynomial curve fitting, solution methods for matrix equations, numerical integration, and the solution of differential equations. Laboratory sessions involve the application of numerical analysis to physical systems involving statics, dynamics, fluid dynamics, heat transfer, electrical circuits, and vibratory systems. (prereq: ME 230 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Model engineering systems using first and second order differential equations, and solve the equations both analytically and numerically
    • Employ the Taylor Series for approximation and error analysis
    • Formulate and apply numerical techniques for root finding, curve fitting, differentiation, and integration
    • Write computer programs to solve engineering problems

    Prerequisites by Topic
    • Programming
    • Differential equations
    • Differential and integral calculus

    Course Topics
    • Introduction to modeling
    • Error analysis/Taylor Series
    • Root finding
    • Curve fitting
    • Matrix applications
    • Numerical differentiation
    • Numerical integration
    • Differential equations
    • Partial differential equations & boundary value problems

    Laboratory Topics
    • Programming/computing techniques
    • Matrix solution methods
    • Solution of simultaneous equations
    • Modeling and numerical simulation of first and second order mechanical/electrical/thermal systems
    • Applications of root-finding to vehicle dynamics & thermal insulation
    • Applications of curve-fitting to experimental data
    • Applications of numerical integration to evaluate moments of inertia, friction work, volumetric fluid flow, and/or thermal heat flow

    Coordinator
    Dr. Nebojsa Sebastijanovic
  
  • ME 314 - Principles of Thermodynamics II

    4 lecture hours 0 lab hours 4 credits
    Course Description
    This is a continuation of introductory thermodynamic concepts for mechanical engineering students. The course begins with energy balances for unsteady processes, followed by a detailed treatment of entropy and the second law of thermodynamics. Isentropic efficiency, irreversibility and exergy are covered. Thermodynamic principles are applied to the study of gas power cycles, vapor power cycles, and refrigeration cycles. Thermodynamic performance parameters are used to characterize the cycles, including a discussion of energy use and environmental impacts. (prereq: ME 311)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Write the energy balance for unsteady flow, and use it to evaluate processes, including determination of work and heat transfer
    • Apply a Second Law analysis (entropy or energy) to processes involving both closed and open systems
    • Evaluate the performance of Rankine and Brayton cycles, with their modifications
    • Analyze refrigeration cycles

    Prerequisites by Topic
    • First Law of Thermodynamics
    • Ideal gas, equation of state, steam tables, property diagrams
    • Energy balances for closed and open systems

    Course Topics
    • Unsteady flow processes
    • Second Law, entropy, reversible and irreversible processes, performance parameters of real and ideal devices, isentropic efficiency, exergy
    • Rankine cycle with modifications
    • Brayton cycle with modifications
    • Refrigeration cycles

    Coordinator
    Dr. Prabhakar Venkateswaran
  
  • ME 318 - Heat Transfer

    4 lecture hours 0 lab hours 4 credits
    Course Description
    This course covers the three fundamental mechanisms of heat transfer: conduction, convection, and radiation. The course includes steady state and transient conduction, free and forced convention, as well as heat exchanger design. (prereq: ME 2101 , ME 3103 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Demonstrate the ability to model physical systems subject to heat transfer, using calculus and differential equations
    • Demonstrate the ability to solve the related differential equations, and concretely relate the results to observable heat transfer processes
    • Apply models of conduction, convection and radiation heat transfer, and to solve practical engineering heat transfer problems

    Prerequisites by Topic
    • Fluid mechanics
    • Differential equations
    • 1st Law of Thermodynamics

    Course Topics
    • Introduction to heat transfer (rate laws for the three heat transfer mechanisms)
    • The heat diffusion equations
    • One-dimensional steady-state conduction for planar, cylindrical, and spherical geometry
    • Electrical circuit analogy to heat transfer analysis
    • Fins
    • Transient lumped capacitance method
    • Physical significance of dimensionless parameters
    • Forced convection (external flow)
    • Forced convection (internal flow)
    • Free convection
    • Heat exchangers
    • Radiation overview

    Coordinator
    Dr. Christopher Damm
  
  • ME 321 - Materials Science

    3 lecture hours 0 lab hours 3 credits
    Course Description
    Atomic, crystal and defect structure fundamentals are studied to lay the foundation for understanding the structure-property-processing relationship. Material properties (with particular focus on mechanical properties) are described along with common test methods. (prereq: CH 201 ) (coreq: ME 2004  or ME 207 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Classify materials based on structure and bonding
    • Be familiar with common mechanical properties of materials and testing methods
    • Be familiar with the fundamental crystal structures and important crystallographic defects of various materials
    • Be familiar with the fundamentals of atomic movement in solids, including how it occurs and the mathematical models
    • Be familiar with typical properties and common engineering applications of broad categories of materials (metals, polymers, ceramics, composites)
    • Be familiar with engineering literature/resources for material property information

    Prerequisites by Topic
    • Introductory solid state chemistry
    • Introductory strength of materials
    • Differential/integral calculus

    Course Topics
    • Types of materials (metals, ceramics and polymers) and the structure-property-processing relationship
    • Properties of materials, sources of material property data, standards for testing, relative property values for the major classes of materials
    • Mechanical and physical properties of materials (metals, ceramics and polymers)
    • Bonding and structure in materials (metals, ceramics and polymers), including defects and imperfections
    • Atomic movement (diffusion) in crystalling solids
    • Ceramics and ceramic-matrix composites
    • Polymers and polymer-matrix composites

    Coordinator
    Dr. Cynthia Barnicki
  
  • ME 322 - Engineering Materials

    3 lecture hours 2 lab hours 4 credits
    Course Description
    The course covers the relationship between structure, properties, and processing in engineering material. The primary emphasis is on metals. Basic concepts of solidification and heat treatment are presented. Alloy phase diagrams and lever rule calculations are shown as a means to understanding both solidification and heat treatment. The relationship between processing/heat treatment and the underlying related strengthening mechanisms are presented. Material selection in terms of mechanical strength service stability, cost, and environmental impact are discussed. (prereq: ME 321 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Utilize binary alloy phase diagrams in microstructure determination and heat treating
    • Apply knowledge of the structure- processing-property relationships to specify basic heat treatment, solidification, and deformation processes to obtain desired properties
    • Identify important microstructural features in various alloy systems
    • Be familiar with typical mechanical properties and applications of common alloys
    • Be familiar with basic materials lab equipment and conduct experiments
    • Correctly analyze and interpret data from lab experiments

    Prerequisites by Topic
    • Atomic, crystal and defect structure in solids
    • Atomic movement in solids, diffusion
    • Structure and general properties of metals
    • Strength of materials
    • Introductory thermodynamics

    Course Topics
    • Review of mechanical properties
    • Overview of strengthening mechanisms in metals and alloys
    • Deformation of metals and strain hardening
    • Principles of solidification
    • Isomorphous phase diagrams and phase rule
    • Eutectic phase diagrams and solidification in eutectic systems
    • Precipitation hardening
    • Microstructure and heat treatment of steels
    • Martensite transformation, tempering
    • Effect of alloy elements in steels
    • Stainless steels
    • Cast iron

    Laboratory Topics
    • Hardness testing
    • Metallographic methods
    • Recrystallization of brass
    • Impact testing
    • Cooling curves/Pb-Sn phase diagram
    • Precipitation strengthening of aluminum
    • Heat treatment of steel
    • Jominy test/hardenability of steel
    • Tensile testing

    Coordinator
    Dr. Cynthia Barnicki
  
  • ME 323 - Manufacturing Processes

    3 lecture hours 2 lab hours 4 credits
    Course Description
    This course covers the basic manufacturing processes commonly used in the production of metal, plastic, and composite parts. Process description, product/process characteristics are covered along with design and economic and environmental considerations. Topics include casting, forging, powder metallurgy, traditional machining, laser/waterjet/EDM, welding, additive manufacturing, and various processes for producing polymer parts. The course introduces several topics in manufacturing systems including computer simulation of the casting process, design for manufacturing, quality control, and sustainable manufacturing. (prereq: ME 322 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Describe the attributes of common manufacturing processes
    • Understand the advantages and limitations of common manufacturing processes
    • Recommend a manufacturing process based on characteristics of a part and required production quantities
    • Design components for ease of manufacture

    Prerequisites by Topic
    • None

    Course Topics
    • Attributes of manufacturing systems
    • Casting processes
    • Powder metallurgy
    • Deformation processing
    • Machining - traditional metal cutting
    • Non-traditional machining - EDM, laser and waterjet
    • Welding
    • Design for manufacturing and assembly
    • Sustainable manufacturing & recycling
    • Polymer part processing
    • Additive manufacturing

    Laboratory Topics
    • Measurement and statistical process control
    • Introduction to SolidCast© - simulating the sand casting process
    • Using SolidCast© to design a sand cast mold
    • Foundry practice and sand casting
    • CNC machining
    • Product reverse engineering to determine manufacturing process
    • Surface roughness measurement

    Coordinator
    Dr. Matt Schaefer
  
  • ME 354 - Thermodynamics and Heat Transfer

    3 lecture hours 0 lab hours 3 credits
    Course Description
    A study of the fundamental concepts and laws of heat transfer, with supporting foundation in thermodynamics. Application of principles of heat transfer to problems encountered in electrical and computer equipment. Not for ME majors. (prereq: MA 226 or MA 231  or MA 2314  and PH 2030 or PH 2031  or  )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Apply mass and energy balances to simple thermodynamic systems
    • Apply heat transfer equations to solve problems in cooling of electronic and electrical components or other applicable problems

    Prerequisites by Topic
    • Introductory thermal physics

    Course Topics
    • Introduction to thermodynamic analysis: system, property, process
    • Mass and energy balance equations
    • Ideal gas equations of state
    • Energy balance for closed and open systems
    • Heat transfer mechanisms: introduction
    • Conduction
    • Convection: forced and natural
    • Radiation or heat exchangers (instructor’s choice)

    Coordinator
    Dr. Christopher Damm
  
  • ME 362 - Design of Machinery

    3 lecture hours 0 lab hours 3 credits
    Course Description
    This course is an application of principles of machine dynamics to the design of machinery. Topics include synthesis of mechanisms, machine balancing, design of flywheels, actuator selection and computer-aided design of mechanisms. (prereq: ME 2003 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Synthesize four bar linkages
    • Apply computer-aided engineering packages to machinery design
    • Determine the actuation force or torque required for a mechanism, and select an appropriate actuator
    • Determine shaking forces due to dynamic unbalance, and perform static and dynamic balancing
    • Design flywheels
    • Perform dynamic analysis of cam/follower systems

    Prerequisites by Topic
    • Rigid body motion

    Course Topics
    • Fundamentals of dynamics
    • Practical considerations, actuators and motors
    • Computer-aided engineering
    • Linkage synthesis
    • Machine balancing
    • Design of flywheels
    • Dynamics of cams
    • Project presentations

    Laboratory Topics
    • Design of a mechanism

    Coordinator
    Dr. William Farrow
  
  • ME 363 - Design of Machine Components

    4 lecture hours 0 lab hours 4 credits
    Course Description
    This course applies mechanics of materials concepts to the design of machine components. Static and fatigue failure criteria are introduced and applied to shafts, bearings, gears, threaded fasteners, and helical springs. (prereq: ME 3005 
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Calculate factors of safety for ductile and brittle components subjected to static and cyclic loading
    • Be familiar with terminology associated with various machine components
    • Design or select shafts, journal and rolling-element bearings, spur and helical gears, threaded fasteners, and helical springs

    Prerequisites by Topic
    • Mechanics of materials
    • Dynamics of machinery

    Course Topics
    • Static design
    • Traditional tolerances
    • Review of static and fatigue failure criteria
    • Shafts, including keys and keyways
    • Rolling-element bearings
    • Spur gears
    • Helical gears
    • Threaded fasteners
    • Helical springs

    Coordinator
    Dr. Robert Rizza
  
  • ME 401 - Vibration Control

    3 lecture hours 0 lab hours 3 credits
    Course Description
    This is an introduction to mechanical vibrations, to free and forced vibrations of single-degree of freedom systems, and to two-degree of freedom of systems. Various types of forcing functions are considered for both damped and undamped systems. (prereq: MA 232  or MA 2323 , ME 230 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Model simple vibratory systems and determine equations of motion
    • Solve equations of motion for single degree of freedom systems subject to harmonic, general periodic and arbitrary forcing functions
    • Write equations of motion for idealized multi-degree of freedom systems
    • Determine natural frequencies and mode shapes for systems with two and three degrees of freedom
    • Develop appropriate analytical models for simulation using MATLAB w/ Simulink
    • Perform measurements and conduct modal tests on simple systems

    Prerequisites by Topic
    • Dynamics
    • Calculus
    • Differential equations
    • Computer programming

    Course Topics
    • Review: Modeling mechanical systems
    • Review: Solving differential equations - analytical, numerical methods
    • Free vibration
    • Harmonically excited vibration
    • Fourier series, periodic functions
    • Transient vibration
    • Systems with two or more degrees of freedom
    • Lagrange’s equation
    • Vibration control
    • Vibration measurement and applications

    Laboratory Topics
    • Free and forced vibration demonstration and measurement on 1 and 2 DOF systems

    Coordinator
    Dr. Subha Kumpaty
  
  • ME 402 - Vehicle Dynamics

    3 lecture hours 0 lab hours 3 credits
    Course Description
    This course covers the application of engineering mechanics to the design of road vehicles. Topics include pneumatic tires, load transfer, performance limits, suspension and steering, and handling and response. (prereq: ME 230 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Simulate acceleration and braking performance of common vehicles
    • Model the normal road loads acting on vehicles
    • Model and simulate suspension forces due to road inputs and steady state cornering forces
    • Design and simulate common suspension and steering geometries
    • Apply tire properties to vehicle performance

    Prerequisites by Topic
    • Kinematics
    • Dynamics of systems

    Course Topics
    • Introduction to modeling and dynamic loads
    • Power and traction limited acceleration models
    • Braking performance, forces, and systems
    • Road loads, aerodynamic drag, and rolling resistance
    • Ride and suspension models
    • Steady state cornering, forces, and suspension effects
    • Analysis of common suspensions
    • Analysis of common steering systems
    • Properties and construction of tires
    • Safety ratings and roll-over propensity

    Coordinator
    Dr. Nebojsa Sebastijanovic
  
  • ME 409 - Experimental Stress Analysis

    2 lecture hours 2 lab hours 3 credits
    Course Description
    In this course, students learn to apply modern experimental stress analysis techniques to measure strains and stresses in engineering components and structures. The course includes strain gage measurements and analysis, design of strain gage-based transducers, photoelasticity, and stress analysis. (prereq: ME 3005 
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Understand concept of stress and strain
    • Understand underlying principles in using strain gages
    • Mount strain gages, take measurements, and analyze the obtained data
    • Design strain gage-based transducers for measuring specific loads
    • Understand basic principles of photoelasticity and use it as an analysis tool
    • Use sources outside the class notes and text

    Prerequisites by Topic
    • Intermediate Mechanics of Materials

    Course Topics
    • Review of states of stress
    • State of strain at a point
    • Principal strains and Mohr’s circle
    • Electrical Resistance strain gages
    • Strain gage circuits
    • Transducer design
    • Photoelasticity

    Laboratory Topics
    • Strain measurement on a cylindrical pressure vessel
    • Strain gage mounting practive
    • Strain gage mounting and soldering
    • Strain measurements of lab projects
    • Photoelasticity demonstration
    • Photoelastic measurement

    Coordinator
    Dr. Mohammad Mahinfalah
  
  • ME 411 - Advanced Topics in Fluid Mechanics

    3 lecture hours 0 lab hours 3 credits
    Course Description
    This course focuses on differential relations for treating fluid flow problems. The theory developed will allow students to pursue advanced practice in fluid dynamics (e.g. computational fluid dynamics). In addition to differential relations and potential flow theory, this course covers dimensional analysis/similitude, and external flow. The Navier-Stokes equations are applied to fluid mechanics problems both analytically and numerically. (prereq: ME 3104 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Characterize potential flow fields
    • Analyze certain types of flows using Navier-Stokes equations
    • Use numerical analysis to solve potential flow problems

    Prerequisites by Topic
    • Introductory fluid mechanics
    • Vector calculus
    • Differential equations
    • Partial derivatives

    Course Topics
    • Differential analysis of fluid flow
    • Fluid element kinematics
    • Differential forms of conservation of mass, momentum, and energy equations
    • Potential flow
    • Stress-deformation relationships for viscous flow
    • The Navier-Stokes equations

    Coordinator
    Dr. Christopher Damm
  
  • ME 419 - Internal Combustion Engines

    2 lecture hours 2 lab hours 3 credits
    Course Description
    This course covers the basic theory of internal combustion reciprocating engines. Course topics include engine performance parameters, combustion, engine cycles, fuels, and emissions. (prereq: ME 3105 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Understand the general engineering operation and design compromises involved in spark and compression ignition engines
    • Be familiar with common I.C. engine terminology such as knock, detonation, auto ignition, surface to volume ratio, and compression ratio
    • Apply thermodynamics to I.C. engine processes and cycles
    • Analyze the engine parameters of friction, torque, MEP, IHP, and bsfc
    • Understand the mechanisms of combustion and the effect of air-fuel ratio on performance
    • Understand the variables which influence the production of undesirable emissions
    • Understand the importance of air flow and how it is affected by valves and by forced induction (turbocharging and supercharging)

    Prerequisites by Topic
    • Thermodynamic cycles and processes
    • Combustion chemistry

    Course Topics
    • Engine types and operation
    • Engine parameters
    • Engine power cycles
    • Inlet and exhaust gas flow
    • Combustion - SI engines
    • Combustion - CI engines
    • Emissions and control

    Coordinator
    Dr. Christopher Damm
  
  • ME 423 - Materials Selection

    3 lecture hours 0 lab hours 3 credits
    Course Description
    This course provides students with an understanding of materials as grouped systems, as well as familiarization with enough specific engineering materials to allow their effective use in daily assignments. The course also illustrates guidelines for screening candidate materials and arriving at reasonable choices. (prereq: ME 323 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Optimize material and shape selection factors
    • Screen candidate materials and select suitable choices to fit given application requirements

    Prerequisites by Topic
    • Mechanical properties
    • Strength and materials
    • Heat treatment and properties of ferrous alloys
    • Heat treatment and properties of aluminum alloys
    • Polymer basics
    • Manufacturing processing for metals, polymers, & composites

    Course Topics
    • Categorization of materials and processes 
    • Design process and materials selection
    • Identification of design functions constraints and objectives
    • Screening selection with multiple constraints
    • Influence of shape
    • Product characteristics

    Coordinator
    Dr. Matt Schaefer
  
  • ME 424 - Engineering with Plastics

    3 lecture hours 0 lab hours 3 credits
    Course Description
    This course provides students with knowledge of polymers that are commonly used and of how the physical and mechanical properties of these materials influence their selection. Also, the relation between fabrication processes and material selections in design is presented. (prereq: ME 321  or equivalent)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Know fundamentals of redesigning a metal part using a polymer
    • Know the fundamental mechanical properties of polymers
    • Interpret resin manufacturer’s data sheets
    • Analyze components and structures fabricated from polymers from a mechanical design viewpoint
    • Predict the mechanical performance of parts fabricated from polymers and composites
    • Select the most desirable manufacturing process and a suitable polymer for producing a given component
    • Be familiar with ASTM test standards

    Prerequisites by Topic
    • Mechanical & physical properties of materials
    • Basic mechanics of materials

    Course Topics
    • Classification and description of polymers
    • Properties of polymers
    • Processing of polymers
    • Polymer design criteria and considerations
    • Applications of polymers (such as creep, wear, friction, damping, etc.)
    • Fiber-reinforced composites, macroscopic composites
    • Structural and component analysis

    Coordinator
    Dr. Cynthia Barnicki
  
  • ME 429 - Composite Materials

    3 lecture hours 0 lab hours 3 credits
    Course Description
    This course introduces the student to the mechanical behavior of fiber-reinforced composite materials. Topics to be covered include anisotropic stress-strain relationships, failure theories, and stress analysis of plates and shells. Different manufacturing methods and applications will be presented. (prereq: ME 2004 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Be familiar with indicial notation
    • Transform tensor quantities from one coordinate system to another
    • Compute stresses and strains for a composite lamina subjected to in-plane, bending, and thermal loads
    • Apply different failure criteria to predict laminate failures
    • Be familiar with the most commonly-used manufacturing processes of composite structures
    • Be familiar with aerospace, automotive, recreational, and industrial applications of composite materials
    • Be familiar with several standard test methods of composites

    Prerequisites by Topic
    • Mechanics of materials

    Course Topics
    • Introduction to composite materials
    • Indicial notation, matrices, and tensors
    • Mechanics of a composite lamina
    • Extensional behavior of a symmetric laminate
    • Failure criteria
    • Composite schedules
    • Macro mechanical models
    • Micro mechanical models
    • Mechanical behavior of a general lamina
    • Manufacturing processes
    • Test methods
    • Testing lab demonstration

    Coordinator
    Dr. Robert Rizza
  
  • ME 431 - Automatic Control Systems

    3 lecture hours 2 lab hours 4 credits
    Course Description
    This course provides an introduction to automatic controls used in mechanical engineering applications, including fluid power. Differential equations are used to model and analyze basic feedback control systems. Laboratory experiments are done using fluid power and electronic equipment. (prereq: ME 230 ) (coreq: ME 300 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Use Laplace transformation and selected linearization techniques
    • Develop mathematical models of selected systems
    • Determine system stability using the Routh and root locus techniques
    • Determine steady state errors due to reference and disturbance inputs
    • Make root locus plots and use them as appropriate to evaluate system transient response characteristics
    • Construct and analyze Bode plots

    Prerequisites by Topic
    • Differential equations
    • System dynamics

    Course Topics
    • Introduction
    • Mathematical models of systems
    • State variable models
    • Feedback control systems characteristics
    • The performance of feedback control systems
    • The stability of linear feedback systems
    • The root locus method
    • Frequency response methods
    • Stability in the frequency domain

    Laboratory Topics
    • Laboratory orientation
    • RLC step input modeling
    • RLC dynamic measurements
    • Valve steady state PQ characteristics
    • Dynamic valve characteristics
    • Rotary speed control simulation
    • Rotary speed control
    • Position control

    Coordinator
    Dr. Daniel Williams
  
  • ME 433 - Electromechanical Systems

    3 lecture hours 2 lab hours 4 credits
    Course Description
    This course extends the concepts of feedback control to the design and realization of electromechanical systems. Topics will include modeling, simulation, and implementation of digital control algorithms. The course includes an electromechanical systems design project. (prereq: ME 431 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Develop mathematical models of electromechnical components and systems
    • Evaluate and select sensors and electrical circuit components
    • Formulate and evaluate analog and digital controllers
    • Specify and evaluate state feedback algorithms
    • Design an electromechanical system to achieve specified performance objective
    • Determine component and system-wide frequency response characteristics
    • Develop frequency response design tools

    Prerequisites by Topic
    • Laplace transforms
    • Feedback control systems
    • Numerical methods

    Course Topics
    • DC motor modeling
    • Analog component selection
    • Z-transforms
    • Difference equations
    • State feedback
    • Digital system effects

    Laboratory Topics
    • Electric motor characteristics
    • Discrete equivalent PID controller implementation
    • Electromechanical design and simulation

    Coordinator
    Dr. Daniel Williams
  
  • ME 460 - Finite Element Methods

    3 lecture hours 2 lab hours 4 credits
    Course Description
    This course serves as an introduction to finite element analysis (FEA) for structural and steady-state thermal problems. In the lecture portion of the course, finite element equations are developed for several element types from equilibrium and energy approaches and used to solve simple problems. In the laboratory portion, students use a commercial, general-purpose finite element computer program to solve more complex problems and learn several guidelines for use of FEA in practice. A project introduces the use of FEA in the iterative design process. (prereq: ME 309 or ME 3005 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Understand steps involved in FEA analysis
    • Understand how finite element equations are developed from both equilibrium and energy methods
    • Solve simple FE problems by hand
    • Understand why certain element types are used for different types of analyses
    • Be familiar with the use of a commercial general-purpose FEA package
    • Understand how FEA can be used in the design process

    Prerequisites by Topic
    • Mechanics of materials
    • Statics
    • Integral and differential calculus

    Course Topics
    • Overview of method
    • Overview of commercial software
    • Review of matrix methods
    • Spring elements
    • Truss elements
    • Potential energy approach
    • Beam element
    • Constant strain triangle element
    • Heat transfer application
    • Interpretation of results & mesh design
    • Discussion of symmetry and boundary conditions
    • Advanced element formulations

    Laboratory Topics
    • Introduction to FE program (with simple 1-D truss element)
    • Stress concentration in a plate with a hole
    • 3-D truss analysis
    • 1D cubic beam bending of a frame analysis
    • Plane stress analysis with two-dimensional continuum elements
    • Plate analysis
    • Mesh design & refinement
    • 2D steady-state heat transfer, thermal analysis and/or torsion
    • Solid modeling input to FE commercial software
    • Design project

    Coordinator
    Dr. Nebojsa Sebastijanovic
  
  • ME 480 - HVAC Systems Design

    2 lecture hours 2 lab hours 3 credits
    Course Description
    This course explores major elements in the design of heating, ventilating, and air conditioning systems. Topics include psychrometric analysis, load estimation, duct/piping design, equipment selection, and energy consumption estimating. The Carrier building simulation software is utilized. Students are required to design elements of HVAC systems, resulting in an understanding of the entire process. (prereq: none) (coreq: ME 3105 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Do a heating and cooling load calculation for a building
    • Evaluate the psychrometric processes involved in heating and cooling a building
    • Make appropriate choices for heating and cooling equipment
    • Utilize a commercially-available software package (Carrier E20-II) to simulate the HVAC system for a building

    Prerequisites by Topic
    • Energy balance

    Course Topics
    • Psychrometric analysis
    • System types
    • Heating and cooling load analysis
    • Air distribution and duct sizing
    • Air system acoustics
    • Water systems
    • Equipment and control system selection
    • Supervised Design Project work

    Coordinator
    Dr. Michael Swedish
  
  • ME 481 - Aerodynamics

    3 lecture hours 0 lab hours 3 credits
    Course Description
    Reviews non-dimensional numbers and boundary layer concepts. Covers a physical description and understanding of fluid flow over bluff and streamlined bodies; experimental and theoretical lift and drag results for both two-dimensional and finite airfoils; aircraft stability and control; propeller design; automobile aerodynamics, including airfoil, spoilers, and airdams. (prereq: ME 3104 )
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Have a thorough understanding of fluid flows over bluff and streamlined bodies, including potential flow results, circulation, boundary layers, transition, and experimental results
    • Choose an airfoil and apply lift, drag, and moment coefficients to a design and to be able to measure these coefficients experimentally
    • Make thin airfoil and finite airfoil calculations
    • Make airplane stability and trim calculations
    • Have an introduction to automobile aerodynamics

    Prerequisites by Topic
    • Incompressible flow, Bernoulli equation
    • Laminar and turbulent flows, Reynolds number, viscosity
    • Boundary layers
    • Integral calculus

    Course Topics
    • Review of fluids, non-dimensionalization, boundary layer, friction
    • 2-D flow over cylinders and airfoils
    • Movies and laboratory experiments
    • Airfoil terminology, characteristics, and physical flow description, modern airfoil developments, high lift devices
    • Thin airfoil theory
    • Finite airfoil
    • Stability and control
    • Propellers, vortex motion, model airplanes
    • Automotive applications

    Laboratory Topics
    • Wind tunnel measurements of formula car drag coefficient and airfoil lift, drag, and moment coefficients and instrumentation

    Coordinator
    Dr. Christopher Damm
  
  • ME 485 - Energy Systems Design Project

    3 lecture hours 0 lab hours 3 credits
    Course Description
    This course involves the application of energy principles to an engineering design problem. A project with practical application is chosen, with an emphasis on resource conservation. (prereq: ME 318  or ME 354  or equivalent)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Utilize a design methodology, including creative synthesis of solutions; evaluation of solutions based on criteria and constraints; sensitivity analysis; choice of “best” design
    • Work effectively as part of a team
    • Work with deadlines
    • Communicate ideas
    • Defend his/her decisions

    Prerequisites by Topic
    • Thermodynamics
    • Fluid mechanics
    • Heat transfer

    Course Topics
    • Outline of design process; project assignments
    • Problem statement
    • Literature search techniques
    • Brainstorming/list of solutions
    • Criteria and constraints/criterion function
    • Sensitivity analysis
    • Oral presentation guidelines
    • Report writing guidelines
    • Oral presentations
    • Team meetings with instructor
    • Team project work

    Coordinator
    Dr. Michael Swedish
  
  • ME 490 - Senior Design I

    3 lecture hours 0 lab hours 3 credits
    Course Description
    This course functions as the proposal-writing phase for the major design experience in the Mechanical Engineering Program. Student design teams are organized and paired with a faculty advisor. A detailed design proposal is prepared. Topics covered in lectures and addressed in the design proposal include the design process, engineering specifications, patents and intellectual property, library research techniques, reliability and safety, design for manufacturability, and project management. (prereq: senior standing)
    Course Learning Outcomes
    Upon successful completion of this course, the student will be able to:
    • Have written a detailed design proposal for the major design experience
    • Have researched trade and professional literature, patents, codes, and specifications related to the topic of the design proposal
    • Have made an oral presentation of proposed design efforts to the advisors
    • Have addressed possible societal and environmental impacts of their project

    Prerequisites by Topic
    • None, although students are required to select a project for which they have sufficient expertise

    Course Topics
    • Team formation and project expectations
    • The design process
    • Work place safety
    • Patents and intellectual property
    • Library research
    • Project management
    • Reliability and safety
    • Design for manufacturability
    • Proposal preparation
    • Professional development

    Coordinator
    Dr. Mohammad Mahinfalah
 

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