IE 2030 - Applications of Statistics in Industrial Engineering

• Describe and define basic statistical terminology  
• Create histograms and identify probability distributions 
• Identify and evaluate the clarity of a hypothesis statement  
• Identify the specific research question under investigation through clear hypothesis formation
• Perform statistical analyses including working with probability distributions 
• Draw inferences from data obtained by testing components and systems, using regression analysis as well as other applicable statistical tests
• Improve communication skills, both written and verbal   
• Understand inverse cumulative distribution functions and their role in random number generation   

• Good understanding of probability, statistical distributions, hypothesis testing, and analysis of variance

• Minitab or other statistics software
• Probablity
• Distributions
• Measurement error and propagation
• Confidence intervals
• Descriptive and inferential statistics
• Univariate analysis
• Point and interval estimation
• Hypothesis testing
• Bivariate analysis

• A weekly two-hour lab will use defined projects to exercise student skills as defined in the Course Outcome section

IE 2450 - Work Planning and Methods Development

• Conduct methods, time, and motion studies utilizing a variety of techniques including graphical analysis tools, traditional stop-watch time studies, predetermined time systems, and work sampling
• Develop work standards
• Describe the advantages and limitations associated with standard data systems
• Identify improvement opportunities based on work methods analysis and work measurement
• Understand how labor reporting and incentive systems relate to methods analysis and work measurement

• Basic understanding of statistical distributions and variability

• Introduction to work methods and work methods improvement (1 week)
• Graphical analysis tools (1 week)
• Time studies (1 week)
• Standard data systems (1 week)
• Predetermined time systems (1 week)
• Work sampling (1 week)
• Physiological work measurement (1 week)
• Labor reporting (1 week)
• Incentives (1 week)
• Increasing productivity (1 week)

• A weekly two-hour lab will give time for multiple lab exercises aimed at giving students hands-on experience with analysis of work methods and work measurement, including time studies, predetermined time systems, physiological work measurement, and the effects of incentives

IE 3310 - Production Planning and Inventory Control

• Define and explain common terminology related to production planning and control
• Utilize common forecasting techniques to predict future demand
• Understand inventory management systems, ABC analysis and methods of maintaining inventory accuracy
• Understand the EOQ model and trade-offs between lot size and other parameters (capacity, utilization, lead time)
• Manually apply the MRP algorithm with various lot sizing rules to generate planned order releases
• Perform rough-cut capacity planning and calculate relevant system parameters such as capacity, utilization, and efficiency
• Describe the difference between push and pull production systems and explain how various pull systems operate (kanban, conwip, POLCA)
• Utilize ERP software to analyze data from a sample company and perform common production control transactions
• Describe Supply Chain Management and compare how DRP structures differ from their MRP counterparts

• Basic understanding of statistics, variability, and linear regression

• Overview of production planning and inventory control
• Overview of ERP software packages
• Forecasting
• Sales and operations planning
• Master scheduling
• Inventory management and MRP
• Capacity management
• Production activity control
• Lean manufacturing
• Theory of constraints
• Supply chain management
• Distribution requirements planning

• Two hour laboratory covering ERP software (e.g., SAP & ERPSim)

IE 3470 - Facilities Design

• Generate and evaluate solutions to facilities layout problems using both analytical and qualitative techniques 
• Generate and evaluate detailed layouts for manufacturing cells 
• Utilize the simplified systematic layout planning or systematic planning of manufacturing cells techniques on a real-world facility design project 
• Present 2-dimensional detailed layouts using CAD software 
• Understand both analytical and qualitative solution approaches to facilities location problems, as well as significant criteria to be considered 
• Present facility design project information orally and verbally in class presentations and a formal technical report

• Understanding of manufacturing systems concepts, including bottlenecks, utilization, lead time, cycle time, throughput, work in process, setup time, batches, and transfer batches

• Overview of facilities design and introduction to course project
• Simplified systematic layout planning
• Manufacturing cells and systematic planning of cells
• Equipment and flow analysis 
• Cell layout planning and detailed cell plans
• Project planning and implementation
• Personnel requirements and infrastructure systems
• Warehouse layouts
• Facility location models and site selection
• Use of 2-dimensional CAD software for facility layouts
• Project work and class presentations

• A weekly 2-hour lab is used primarily for learning CAD software and working on the course project, which is typically development of a facility layout for an industry client. The project lab time is used for client visits, team meetings, and preparation of the project deliverables

IE 3621 - Ergonomics

• Understand how people fit into technological systems
• Recognize the capabilities and limitations of human perceptual-motor capabilities
• Recognize the capabilities and limitations of human cognitive functioning and why people make errors
• Explain the negative effects that poor work system design and poor product design have on humans
• Recognize the human indicators of fatigue and stress
• Appreciate the importance of organization and job design factors for performance and satisfaction
• Define the ethical application of human factors in designing products and processes
• Recognize ergonomic deficiencies in different environments (i.e., office, manufacturing and classrooms)
• Evaluate and generate ergonomic solutions to the aforementioned ergonomic deficiencies
• Present project information during class presentations as well as in a formal technical report
• Write reports that describe human performance

• None 

• Introduction to and history of human factors and ergonomics, effectiveness and cost effectiveness of ergonomics, human factors investigations (1 week)
• Human information processing and usability; vision and visual display design; hearing, smelling, auditory and olfactory display design; touch and tactile displays and controls (2 weeks)
• Basic anatomy, physiology and biomechanics; physical workload, heat stress and cold stress (1 week)
• Anthropometry and design, work posture and design (1 week)
• Manual materials handling and design; repetitive motion injuries and hand tool design; vibration; automation (1 week)
• Ergonomics of computer workstations, design of manufacture and maintenance (1 week)
• Training and cognitive task analysis; task, organization and job analysis; shift work (1 week)
• Accidents, human error and safety (1 week)
• Macro-ergonomics: job and organization design; engineering ethics (1 week)

• The course includes a 2 hour lab each week where the students will be engaged in demonstrating their understanding of the lecture topics. Lab time will also be used to work on the course project

IE 3771 - Automation Technologies

• 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
• Analyze a line balancing problem using a heuristic algorithm
• Understand flexible automated production systems through use of the Festo FMS

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

• Robotics, discrete control, PLCs
• Material handling and storage systems
• Automated data capture and identification technologies
• Inspection and inspection technologies
• Flexible manufacturing systems
• Line balancing
• Calculating production and storage capacity

• Programming a robot
• Operating and programming a CMM
• Operating and analyzing a FMS
• Bar codes and RFID
• Line balancing

IE 3820 - Stochastic Processes

• 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

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

• 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

IE 4001 - Industrial Engineering Cooperative Practicum 1

• No course learning outcomes appended

• None

• No course topics appended

IE 4002 - Industrial Engineering Cooperative Practicum 2

• No course learning outcomes appended

• None

• No course topics appended

IE 4003 - Industrial Engineering Cooperative Practicum 3

• No course learning outcomes appended

• None 

• No course topics appended

IE 4260 - Design for Manufacture and Assembly

• 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

• Knowledge of a variety of manufacturing processes

• Product life cycle and design objectives (1 week)
• DFA (2 weeks)
• DFM for various manufacturing processes (5 weeks)
• Design for other objectives (1 week)
• Project work and exams (1 week)

• 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

IE 4332 - Lean

• Explain lean thinking and management methods
• Explain the House of Lean as a sequential methodological approach
• 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

• None

• Toyota Philosophy and culture, lean leadership, and lean wastes (1.5 weeks)
• People development and team building (1 week)
• Process stability, flow and value stream mapping (1.5 weeks)
• Standard work (.5 weeks)
• 5S, cellular layouts, and level loading (1 week)
• Total productivity maintenance (.5 weeks)
• Manufacturing cells and setup reduction (1 week)
• Push vs. pull and kanban systems (1 week)
• Kaizen and change management (1 week)
• Toyota problem solving technique (1 week)

IE 4336 - Quick Response Manufacturing

• 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

• None

• 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

IE 4501 - Healthcare Systems Engineering

• 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

• None

• 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

IE 4621 - Socio-Technical Systems

• 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

• None

• Open and other systems (.5 weeks)
• History of socio-technical systems (.5 weeks)
• Socio-technical systems - The environment (1 week)
• Socio-technical systems - The social system (1 week)
• Socio-technical systems - The technical system (1 week)
• Socio-technical system design, redesign and analysis (2 weeks)
• Macro-ergonomics and organizational design and participation (1 week)
• Socio-technical applications and case studies (3 weeks)

IE 4622 - Organization and Job Design

• 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 and how they impact team/group performance
• Understand how organizational culture impacts employee morale and performance
• Understand the impact of motivation and satisfaction on team/group performance

• None

• Organizational Management Theories - Overview (1 week)
• Job Design Theories (1 week)
• Job Analysis Data Collection Methods (2 weeks)
• Employee Motivation (1 week)
• Teamwork and Participation (1 week)
• Job Redesign and Case Studies (3 weeks)
• Employer/Employee Ethics (1 week)

IE 4773 - Computer Aided Manufacturing/CNC Machining/Rapid Prototyping

• 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

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

• Review of machining processes (1 week)
• CNC machining and programming for mills (2 weeks)
• CAM software and project work (4 weeks)
• Workholding (0.5 weeks)
• Rapid prototyping (1 week)
• CNC machining and programming for lathes (0.5 weeks)
• Canned programs and quick code (0.5 weeks)
• Multi-axis machining (0.5 weeks)

• 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.

IE 4823 - Financial Engineering

• 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

• None

• 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

IE 4880 - Supply Chain Engineering

• 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

• None

• 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
• Integration problems in supply chain management
• Industry applications and case studies

IE 4901 - Industrial Engineering Senior Design Project I

• 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

• 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

• Project proposals (2 weeks)
• Teamwork, performance evaluations, peer feedback (2 weeks)
• Formal presentations (2 weeks)
• Project schedules (1 week)
• Literature review and library research (1 week)
• Data gathering and analysis (1 week)
• Formal technical reports (1 week)

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

IE 4902 - Industrial Engineering Senior Design Project II

• 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

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

• 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

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

IE 4903 - Industrial Engineering Senior Design Project III

• Depends on project objectives and scope

• 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

• 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

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

AC 1103 - Introduction to Actuarial Science

• Know all the details about the two major actuarial societies which is controlling the actuarial science profession: Society of Actuaries and Casualty Actuary Society
• Know the importance of the professional exams in finding jobs as an actaury in the insurance industry and finding internships (which is also required for finding a job) and learn how important it is to prepare for them in a timely manner
• Learn the difference between the casulaty actuaries, health insurance actuaries, pention actuaries and life insurance actuaries, so that they can make a more educated decision when they look for an internship and later for a job
• Know what a typical day of an actuary at work look like by shadowing actuaries in different areas of actuarial profession
• Know combination, permutation and other fundamental counting techniques
• Know general properties of sets

• Precalculus material

• Combinatorics
• Set Theory

AC 2303 - AS LAb I: Exam P Prep

3 lecture hours 0 lab hours 3 credits

• use basic rules of probability
• concept of mutually exclusive events
• addition and multiplication rules
• concept of independent events
• concept of conditional probability
• Bayes’ theorem and law of total probability
• in application problems of these concepts

• The student should also be able to master problem solving related with:
  • binomial, negative binomial
  • geometric, hypergeometric
  • Poisson
  • uniform
  • exponential
  • normal
  • gamma distributions
• Moreover, the student should also be able to solve problems of random variables with multivariate probability distribution, joint probability density function, joint cumulative distribution function, moment generating functions.

• Strong knowledge of probability, random variables with univariate and multivariate probability distributions.

AC 3303 - AS LAb II: Exam FM Prep

• This course will not be offered until Spring 2019, so it will be designed in summer of 2018. Since this course is included in the new curriculum track, we need to have a course description in the catalog at this point. We will write course learning outcomes when the course is designed.

• Content of MA 390 

MA 120 - Precalculus Mathematics

• 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

• MA 125  or equivalent

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

MA 120A - Precalculus Mathematics

• 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

• MA 125  or equivalent

• 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

MA 125 - College Algebra I

• 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

• None

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

MA 125A - College Algebra I

• 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

• None

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

MA 126 - Trigonometry

• 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

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

• 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

MA 127 - College Algebra II

• 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

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

• 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

MA 129 - Business Calculus

• 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

• 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

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

MA 136 - Calculus I

• 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

• 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

• 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

MA 136A - Calculus I

• 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

• 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

• 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

MA 136C - Calculus I

• 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

• 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

• 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

MA 137 - Calculus II

• 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 and 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
• Integrate functions by using trigonometric substitution
• Find areas between curves
• Find volumes of solids of revolution using disk and washer methods

• 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

• 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
• Integration by parts
• Integration of products and powers of trig functions
• Integration using partial fractions
• Integration using trigonometric substitutions
• Integration using tables
• Numerical integration

MA 137A - Calculus II

• 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 and 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
• Integrate functions by using trigonometric substitution
• Find areas between curves
• Find volumes of solids of revolution using disk and washer methods

• 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

• 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
• Integration by parts
• Integration of products and powers of trig functions
• Integration using partial fractions
• Integration using trigonometric substitutions
• Integration using tables
• Numerical integration

MA 231 - Calculus III

• 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

• 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

• 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 

MA 232 - Calculus IV

• 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

• 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

• 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

MA 235 - Differential Equations

• 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

• 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

• 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

MA 262 - Probability and Statistics

• 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

• Algebra
• Trigonometry
• Differentiation of algebraic and transcendental functions
• Integration of algebraic and transcendental functions

• 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

MA 315 - Nursing Statistics

• 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

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

• 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

MA 327 - Mathematical Modeling

• TBD

• Calculus (single and multivariable), differential equations, probability and statistics

• None

MA 330 - Vector Analysis

• Perform elementary vector operations
• Find the equations of lines and planes
• Differentiate vector functions of one variable
• Analyze three-dimensioanl curves
• Calculate the divergence and curl of a vector field
• Calculate line, surface and volume integrals
• Use the divergence and Stokes’ theorems ot faciliatate integral calculuation

• Basic Vector Algebra
• Three DimensionalAnalytic Geometry
• Differential and Integral Calculus

• None

MA 340 - Business Statistics

• 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

• Algebra

• 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

MA 343 - Linear Programming

• Formulate various real-life problems as linear and integer programs
• Be able to solve linear programs using the simplex algorithm
• Be able to 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

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

• 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

MA 344 - Nonlinear Programming

• 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

• 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

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

MA 380 - Advanced Differential Equations

• Solve some linear systems of ordinary differential equations by Laplace transforms and differential operator methods including the Heavyside 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

• 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

• 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

MA 381 - Complex Variables

• 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

• Differential and integral calculus
• Elementary differential equations

• 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

MA 382 - Laplace and Fourier Transforms

• 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

• Improper integrals
• Infinite series
• Linear differential equations

• 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

MA 383 - Linear Algebra

• 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

• Differential and integral calculus
• Basic vector mathematics

• 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

MA 384 - Statistical Methods for Use in Research

• 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

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

• 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

MA 385 - Modern Algebra with Applications

• 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

• None 

• 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

MA 386 - Functions of a Real Variable

• 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

• None

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

MA 387 - Partial Differential Equations

• 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.

• Infinite series
• Ordinary differential equations

• 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

MA 388 - Introduction to Number Theory

• 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

• None 

• 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

MA 390 - Financial Mathematics

• 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 knoeledge of financial instruments, including derivatives, and the concept of no-arbitrage as it relates to financial mathematics
• Successfully complete the FM exam

• Business Finance and Accounting knowledge 

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

MA 461 - Applied Probability Models

• These will be determined next year when the course is designed

• Fundamentals of probability

MA 1830 - Transition to Advanced Topics in Mathematics

• 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

• None

• 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

MA 1840 - Computer Applications in Applied Mathematics

• 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 

• None

• 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

MA 2310 - Discrete Mathematics I

• 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

• Basic concepts of college algebra
• Basic concepts of set theory

• Course introduction
• Propositional logic: normal forms (conjunctive and disjunctive)
• Propositional logic: Validity
• Fundamental structures: Functions (surjections, injections, inverses, composition)
• Fundamental structures: Relations (reflexivity, symmetry, transitivity, equivalence relations
• Fundamental structures: Discrete versus continuous functions and relations
• Fundamental structures: Sets (Venn diagrams, complements, Cartesian products, power sets)
• Fundamental structures: Cardinality and countability
• Boolean algebra: Boolean values, standard operations, de Morgan’s laws
• Predicate logic: Universal and existential quantification
• Predicate logic: Modus ponens and modus tollens
• Predicate logic: Limitations of predicate logic
• Recurrence relations: Basic formulae
• Recurrence relations: Elementary solution techniques
• Graphs: Fundamental definitions
• Graphs: Directed and undirected graphs
• Graphs: Spanning trees
• Graphs: Shortest path
• Graphs: Euler and Hamiltonian cycles
• Graphs: Traversal strategies

MA 2320 - Introduction to Graph Theory

3 lecture hours 0 lab hours 3 credits

  (prereq: MA 1830  or MA 2310 )

• 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

• Basic concepts of college algebra
• Basic concepts of set theory
• Basic concepts of logic and proofs 

• Basic definitions and notions for graphs
• Matching and covering
• Planarity and colouring
• Graph Algorithms
• Ramsey Theory

MA 2410 - Statistics for AS

• Know which probability distribution applies to a given statistical situation
• Know how to perform a complete hypothesis test
• Know how to correctly calculate and interpret a p-value
• Recognize the similarities between the various hypothesis tests and the formulas used by these tests
• Be able to construct appropriate confidence intervals for various statistical situations
• Recognize the complementary nature of hypothesis testing and the construction of confidence intervals
• Perform analysis of variance when appropriate and interpret the results
• Know how to perform simple linear regression and understand how the formulas used were derived

• Algebra
• Differential and Integral Calculus

• Four major probability distributions used in hypothesis testing: Normal, Student-t, Chi-Squared, F
• Review binomial distribution (to use in hypothesis testing)
• One-sample hypothesis testing
• Two-sample hypothesis testing
• Analysis of Variance
• Time Series/Forecasting
• Nonparametric Statistics
• Simple Linear Regression and Correlation/Hypotheses
• Multiple Linear Regression

MA 2411 - Time Series Analysis

• 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

• Calculus (single variable and multivariable), probability theory and application, statistics including regression

• Simple Linear Regression
• Multiple Linear Regression
• Model Building
• Residual Analysis
• Time Series Regression
• Exponential Smoothing

MA 2630 - Probability I for AS

• 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
• Be able to use various discrete probability distributions to determine probabilities
• Be able to understand, derive and use discrete probability mass functions, distribution functions, and moment-generating functions
• Be able to 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
• Be able to understand and use the results of the Central Limit Theorem
• Be able to use a transformation function to transform one probability mass function into another

• Algebra
• Calculus

• 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

MA 2631 - Probability II for AS

• Be able to understand and apply continuous probability distributions to appropriate probability situations
• Be able to understand, derive and use continuous probability density functions, conditional probability density functions, marginal functions, and moment-generating functions
• Be able to understand, derive, and use continuous joint probability functions
• Be able to understand the meaning and relevance of, and use, measures of dispersion for continuous multi-variable probability distributions
• Be able to understand, calculate, and use covariance
• Be able to understand, calculate, and apply to correlation coefficient appropriate situations
• Be able to perform transformations of continuous random variables
• Be able to form and use linear combination of random variables with respect to calculation of probabilities and moments

• Multivariable calculus
• Discrete random variables

• 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

MA 2830 - Linear Algebra for Math Majors

• 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, linear transformations, and the relationship between them
• Perform 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
• Find the eigenvalues and corresponding eigenvectors of matrices 
• 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 

• None

• Systems of linear equation, solutions using matrices, row operations
• Vector and matrix equations 
• Solution sets of linear systems 
• Linear independence 
• Linear transformations
• Matrix algebra 
• Subspaces, dimension, and rank 
• Determinants and their properties
• Real eigenvalues and eigenvectors 
• Diagonalization 
• Complex eigenvalues  
• Inner products and orthogonality 
• Orthogonal projections  
• The Gram-Schmidt Process  
• Least-squares solutions  

MA 3320 - Discrete Mathematics II

• Illustrate by examples proof by contradiction
• Synthesize induction hypotheses and simple induction proofs
• Apply the Chinese Remainder Theorem
• Illustrate by examples the properties of primes
• Calculate the number of possible outcomes of elementary combinatorial processes such as permutations and combinations
• Identify a given set as countable or uncountable
• Derive closed-form and asymptotic expressions from series and recurrences for growth rates of processes
• Be familiar with standard complexity classes
• Apply Bayes’ rule and demonstrate an understanding of its implications
• Apply conditional probability to identify independent events

• Predicate logic
• Recurrence relations
• Fundamental structures
• Continuous probability

• Course introduction
• Proofs: direct proofs
• Proofs: proof by contradiction
• Number theory: factorability
• Number theory: properties of primes 
• Number theory: greatest common divisors and least common multiples
• Number theory: Euclid’s algorithm
• Number theory: Modular arithmetic
• Number theory: the Chinese Remainder Theorem
• Computational complexity: asymptotic analysis
• Computational complexity: standard complexity classes
• Counting: Permutations and combinations
• Counting: binomial coefficients
• Countability: Countability and uncountability
• Countability: Diagonalization proof to show uncountability of the reals
• Discrete probability: Finite probability spaces
• Discrete probability: Conditional probability and independence
• Discrete probability: Bayes’ rule
• Discrete probability: Random events
• Discrete probability: Random integer variables
• Discrete probability: Mathematical expectation

MA 3501 - Engineering Mathematics I

• Perform vector operations and their applications to area and volume
• Determine the length of parametrically defined curves
• Find tangent lines to parametrically defined curves
• Find gradients and directional derivatives
• Find tangent planes and normal lines to surfaces
• Find extrema of functions of two variables
• Evaluate line integrals and interpret the result as work
• Evaluate curl and divergence of a vector field
• Evaluate iterated integrals, including the interchange of order in rectangular and polar coordinates
• Evaluate moments and centroids
• Apply Green’s Theorem to evaluate line integrals around simple closed curves

• Differentiation of trigonmetric, inverse trigonometric, exponential and logarithmic functions, techniques of integration (direct and inverse substitution, integration by parts, trigonometric integrals and partial fractions)

• Vector operations
• Calculus of several variables, including use of gradients, partial differentiation and multiple integrals, curl and divergence and Green’s Theorem

MA 3502 - Engineering Mathematics II

• 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

• 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

• 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

MA 3611 - Biostatistics

• Be able to recognize and evaluate conditional probability situations such as Bayes’ Rule, specificity, sensitivity, predictive value positive, and predictive value negative
• Be able to set up and evaluate inferences using hypothesis tests and confidence intervals
• Be able to perform hypothesis tests for one- and two-sample situations
• Be able to recognize when analysis of variance (ANOVA) is applicable, and subsequently be able to apply and evaluate ANOVA calculations
• Be able to recognize when nonparametric situations are present and then be able to apply the correct nonparametric test, evaluate it, and interpret it
• Be able to use SAS (or SPSS if it is the statistical package being used) when appropriate
• Be able to read and interpret the statistical content of assigned articles in the NEJM

• To be determined

MA 3710 - Mathematical Biology

• 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

• 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

• 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

ME 190 - Computer Applications in Engineering I

• Have learned to apply problem-solving skills to engineering problems
• Have learned how to present formal solutions to engineering problems
• Have learned a variety of computer tools, and understand how they can be applied to mechanical and industrial engineering problems

• College Trigonometry and Algebra

• Problem Solving Methodologies, Introduction to Matlab (1 class)
• Simple and symbolic operations (3 classes)
• Working with Arrays, Plotting (2 classes)
• Programming - Loops (3 classes)
• Programming - Logic (2 classes)
• Solving Equations - Matlab (2 classes)
• Numerical Integration - Matlab (2 classes)
• Matrix Methods - Matlab (1 class)
• Optimization - Excel (2 classes)
• Testing and Review

• Problem Solving with Matlab
• Plotting data
• Roots of Equations
• Numerical Integration
• Solution of Simultaneous Equations
• Optimization

ME 205 - Engineering Statics

• 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

• Vector mathematics
• Physics of mechanics
• Integral calculus

• 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)

ME 206 - Engineering Dynamics

• 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

• None

• Rectilinear motion of particles (6 classes)
• Relative and dependent motion of particles (2 classes)
• Curvilinear motion of particles (4 classes)
• Plane kinematics of rigid bodies-velocities (5 classes)
• Plane kinematics of rigid bodies-accelerations (2 classes)
• Kinematics of particles-Newton’s 2nd Law (3 classes)
• Work and energy (3 classes)
• Conservation of energy (2 classes)
• Impulse and momentum (1 class)
• Kinetics of rigid bodies (3 classes)
• Review/problem sessions (5 classes)
• Testing & Review (3 classes)

ME 207 - Mechanics of Materials

• 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

• Statics, integral and differential calculus

• Review of statics, reactions, internal loads (2 classes)
• Concept of stress and strain (5 classes)
• Mechanical properties of materials (3 classes)
• Axial loading (3 classes)
• Stress concentrations (1 class)
• Torsion (3 classes)
• Shear and moment diagrams (3 classes)
• Bending stresses (3 classes)
• Transverse shear (3 classes)
• Combined loads (2 classes)
• Stress and strain transformations, including Mohr’s circle and strain rosettes (4 classes)
• Principal stresses (2 classes)
• Beam deflections (3 classes)
• Testing (3 classes)

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

ME 230 - Dynamics of Systems

• 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

• Electrical circuits
• Differential equations
• Dynamics

• Introduction to dynamic systems
• Review of time domain solutions for 1st and 2nd order systems
• Free and constant force responses (step input)
• Finding characteristic parameters from system dynamic responses (time constant, log decrement, wn, wd, P.O. ts)
• Laplace Transforms
• 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 sytems (Thermo and Fluid Systems)
• State-space representation
• Numerical integration with Euler and ODE45
• Frequency domain analysis of dynamic systems
• Bode plots and 1st and 2nd order system characteristics

ME 300 - Modeling and Numerical Analysis

• 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

• Programming
• Differential equations
• Differential and integral calculus

• Introduction to modeling (2 classes)
• Error analysis/Taylor Series (2 classes)
• Root finding (3 classes)
• Curve fitting (3 classes)
• Matrix applications (3 classes)
• Numerical differentiation (3 classes)
• Numerical integration (3 classes)
• Differential equations (7 classes)
• Partial differential equations & boundary value problems (2 classes)
• Testing and review (2 classes)

• Programming/computing techniques
• Matrix solution methods
• Solution of simultaneous equations
• Modeling 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 thermal heat flow

ME 311 - Principles of Thermodynamics I

• Use thermodynamic tables to find properties
• Apply the ideal gas and incompressible liquid and pure substance models to thermodynamic problems
• Write an energy balance for a closed system
• Use the closed system energy balance to evaluate processes, including determining work and heat transfer
• Write an energy balance for steady flow open system
• Use the open system energy balance to evaluate processes, including determining work and heat transfer

• Partial derivatives
• Differential and integral calculus
• Physics of liquids and gases

• Introduction, Definitions, Dimensions and Units
• Thermodynamic Properties, State, Temperature and Pressure
• Energy Transfer by Work, Forms of Mechanical Work, Moving Boundary Work
• The First Law of Thermodynamics, Energy Balances
• Pure Substance Model, Phases and Phase Change of a Pure Substance, Property Tables
• Ideal Gas Model
• Internal Energy, Enthalpy, and Specific Heats of Ideal Gasses and Liquids
• Open Systems - Conservation of Mass
• Steady-Flow System Energy Analysis of Devices - Nozzles, Diffusers, Turbines, Compressors, Throttling Valves, Mixing Chambers, Heat Exchangers
• Energy and the Environment
• Connections between Energy Generation, Energy Consumption and Global Climate Change

ME 314 - Principles of Thermodynamics II

• 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

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

• 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

ME 317 - Fluid Mechanics

• Apply the fluid-static equation to determine pressure at a point
• Apply the control volume forms of the mass, energy, and momentum equations to a variety of problems, including pump/turbine problems with pipe friction and minor losses
• Determine the drag force on objects subjected to fluid flow
• Utilize instrumentation for measurement of fluid and flow properties, with an understanding of the accuracy and precision of the measuring systems

• Vector analysis
• Differential and integral calculus
• Partial derivatives
• Newton’s second law

• Definitions and properties
• Statics and pressure gauges
• Fluid kinematics
• Control volume and conservation of mass, momentum and energy
• Bernoulli, pipe friction, minor losses
• Differential analysis and viscous flow
• Boundary layer and drag

• Instrument calibration
• Measurement of air flow in a duct
• Determination of friction factor and minor losses
• Analysis of a pump system
• 1st order Error propagation and statistical analysis of data
• Dimensional analysis and similitude

ME 318 - Heat Transfer

• 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

• Fluid mechanics
• Differential equations
• 1st Law of Thermodynamics

• 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

ME 321 - Materials Science

• 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

• Introductory Solid State Chemistry
• Introductory Strength of Materials
• Differential/Integral Calculus

• Types of materials (metals, ceramics and polymers) and the structure-property-processing relationship (1 class)
• Properties of materials. Sources of material property data, standards for testing. Relative property values for the major classes of materials (2 classes)
• Mechanical and physical properties of materials (metals, ceramics and polymers) (6 classes)
• Bonding and structure in materials (metals, ceramics and polymers), including defects and imperfections (6 classes)
• Atomic movement (diffusion) in crystalling solids (3 classes)
• Ceramics and ceramic-matrix composites (3 classes)
• Polymers and polymer-matrix composites (4 classes)
• Exams (2 classes)

ME 322 - Engineering Materials

• 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

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

• Review of Mechanical Properties (1 class)
• Overview of strengthening mechanisms in metals and alloys (2 classes)
• Deformation of Metals and Strain hardening (3 classes)
• Principles of Solidification (3 classes)
• Isomorphous Phase Diagrams and Phase Rule (3 classes)
• Eutectic Phase diagrams and solidification in Eutectic Systems (3 classes)
• Precipitation Hardening (3 classes)
• Microstructure and Heat Treatment of Steels (3 classes)
• Martensite Transformation, Tempering (2 classes)
• Effect of Alloy Elements in Steels (1 classe)
• Stainless Steels (2 classes)
• Cast Iron (2 classes)
• Exams (2 Classes)

• Hardness Testing
• Metallographic Methods
• Recrystallization of Brass
• Impact Testing
• Cooling Curves/Pb-Sn Phase Diagram
• Precipitation Strengthening of Aluminum
• Heat Treatment of Steel (2 weeks)
• Jominy Test/Hardenability of Steel

ME 323 - Manufacturing Processes

• 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

• None

• Attributes of manufacturing systems (2 classes)
• Measurement and Statistical Process Control (2 classes)
• Casting Processes (4 classes)
• Powder Metallurgy (3 classes)
• Deformation Processing (2 classes)
• Sheet Metal Forming (1 class)
• Machining - traditional metal cutting (2 classes)
• Non-traditional Machining - EDM, Laser and Waterjet (2 classes)
• Welding (2 classes)
• Design for Manufacturing and Assembly (2 classes)
• Sustainable Manufacturing (2 classes)
• Polymer Part Processing (2 classes)
• Fiber Reinforce Composite Processing (2 classes)
• Exams (2 classes)

• 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

ME 354 - Thermodynamics and Heat Transfer

• 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

• Introductory thermal physics

• 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)

ME 362 - Design of Machinery

• 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 synamic balancing
• Design flywheels
• Perform dynamic analysis of cam/follower systems

• Machine dynamics

• Fundamentals of dynamics (3 classes)
• Practical considerations, actuators and motors (3 classes)
• Computer-aided engineering (3 classes)
• Linkage synthesis (8 classes)
• Machine Balancing (3 classes)
• Design of Flywheels (3 classes)
• Dynamics of Cams (3 classes)
• Testing and project presentations (4 classes)

• Design of a mechanism

ME 363 - Design of Machine Components

• 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

• Mechanics of materials, dynamics of machinery

• Static design
• Traditional tolerances
• Static failure criteria
• Fatigue failure criteria
• Shafts, including keys and keyways
• Rolling-element bearings
• Spur gears
• Helical gears
• Threaded fasteners
• Helical springs
• Testing

• Example problems and design problems covering the class topics, including use of computing tools in design problems

ME 401 - Vibration Control

• 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

• Dynamics
• Calculus
• Differential equations
• Computer programming

• Review: Modeling mechanical systems (3 classes)
• Review: Solving differential equations - analytical, numerical methods (2 classes)
• Free vibration (4 classes)
• Harmonically excited vibration (4 classes)
• Fourier series, periodic functions (2 classes)
• Transient vibration (3 classes)
• Systems with two or more degrees of freedom (4 classes)
• Lagrange’s equation (2 classes)
• Vibration control (2 classes)
• Vibration measurement and applications (2 classes)
• Exams (2 classes)

• Free and Forced vibration demonstration and measurement on 1 and 2 DOF systems

ME 402 - Vehicle Dynamics

• 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

• Kinematics
• Dynamics of systems

• Introduction to modeling and dynamic loads (3 classes)
• Power and traction limited acceleration models (3 classes)
• Braking performance, forces, and systems (3 classes)
• Road loads, aerodynamic drag, and rolling resistance (3 classes)
• Ride and suspension models (3 classes)
• Steady state cornering, forces, and suspension effects (3 classes)
• Analysis of common suspensions (2 classes)
• Analysis of common steering systems (3 classes)
• Properties and construction of tires (3 classes)
• Safety ratings and roll-over propensity (2 classes)
• Review and testing (2 classes)

ME 409 - Experimental Stress Analysis

• 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

• Intermediate Mechanics of Materials

• Review of states of stress (2 classes)
• State of Strain at a Point (3 classes)
• Principal Strains and Mohr’s Circle (3 classes)
• Electrical Resistance Strain Gages (3 classes)
• Strain Gage Circuits (3 classes)
• Transducer Design (2 classes)
• Exams (2 classes)

• Strain measurement on a cylindrical pressure vessel
• Strain gage mounting practive
• Strain gage mounting and soldering
• Strain measurements of Lab 3 projects
• Photoelasticity demonstration
• Photoelastic Measuremen

ME 411 - Advanced Topics in Fluid Mechanics

• Determine various kinematic elements of flow given the velocity field
• Explain the conditions necessary for a velocity field to satisfy the continuity equation
• Apply the concepts of stream function and velocity potential
• Characterize simple potential flow fields
• Analyze certain types of flows using Navier-Stokes equations
• Use numerical analysis to solve potential flow problems
• Apply the Pi theorem to determine the number of dimensionless groups governing fluid flow phenomena
• Develop a set of dimensionless variables for a given flow situation
• Recognize and use common dimensionless groups
• Discuss the use of dimensionless variables in the design and analysis of experiments
• Apply the concepts of modeling and similitude to develop prediction equations
• Identify and explain various characteristics of the flow in pipes
• Discuss the main properties of laminar and turbulent pipe flow and appreciate their differences
• Calculate losses in straight portions of pipes as well as those in pipe system components
• Predict the flowrate in a pipe by use of common flowmeters
• Identify and discuss the features of external flow
• Explain the fundamental characteristics of a boundary layer, including laminar, transitional, and turbulent regimes
• Calculate boundary layer parameters for flow past a flat plate
• Explain the physical process of boundary layer separation
• Calculate the drag force for various objects
• Quantify the uncertainty of results of fluid flow experiments

• Introductory fluid mechanics
• Vector calculus
• Differential equations
• Partial derivatives

• Differential analysis of fluid flow
• Fluid element kinematics
• Differential forms of conservation of mass, momentum and energy equations
• Euler’s equations of motion
• Bernoilli equation
• Irrotational flow
• The velocity potential
• Potential flow
• Stress-deformation relationships for viscous flow
• The Navier-Stokes equations
• Numerical methods for differential analysis of fluid flow
• Dimensional analysis, similitude, and modeling
• Pi theorem
• Determination of Pi therms
• Common dimensionless groups in fluid mechanics
• Correlation of experimental data
• Modeling and similitude
• Theory of models
• Scale models
• Viscous flow in pipes
• Laminar vs. turbulent flow
• Entrance region and fully developed flow
• Fully developed laminar flow
• Fully developed turbulent flow
• Turbulence modeling
• External flow
• Lift and drag force
• Boundary layer characteristics
• Prandtl/Blasius boundary layer solution
• Effects of pressure gradient
• Friction drag
• Pressure drag
• Drag coefficient
• Design of experiments

ME 416 - Thermodynamics Applications

• Analyze Otto and Diesel cycles
• Perform 1st Law analysis of combustion processes
• Perform basic integrated thermal systems design
• Apply 1st and 2nd law to real systems
• Demonstrate the principles of thermodynamics and heat transfer in laboratory experimentation. Experiments will include the analysis of: power cycles and refrigeration cycles, solar photovoltaic systems, solar thermal systems, and cogeneration systems

• First and Second Laws of Thermodynamics
• Ideal gas and incompressible liquid models, steam tables
• Rankine, refrigeration, and Brayton cycles
• Heat transfer- conduction, convection, radiation

• Internal combustion cycles (otto and diesel) cycles
• Reacting mixtures (combustion processes)
• Design project(s)
• Additional topics (compressible flow, cogeneration, psychrometrics, solar energy systems, fuel cells) chosen by instructor

• Internal Combustion Engine analysis
• Combustion analysis
• Refrigeration cycle
• Heat transfer: conduction, convection, radiation
• Cogeneration
• Solar thermal energy systems
• Solar photovoltaic energy systems
• Fuel cells

ME 419 - Internal Combustion Engines

• 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)

• Thermodynamic cycles and processes
• Combustion chemistry

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

ME 423 - Materials Selection

• Optimize material and shape selection factors
• Screen candidate materials and select suitable choices to fit given application requirements

• 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

• Categorization of materials and processes  (3 hours)
• Design process and materials selection (3 hours)
• Identification of design functions constraints and objectives (12 hours)
• Screening selection with multiple constraints (3 hours)
• Influence of shape (6 hours)
• Product characteristics (3 hours)

ME 424 - Engineering with Plastics

• 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

• Mechanical & physical properties of materials
• Basic mechanics of materials

• Classification and description of polymers (6 classes)
• Properties of polymers (3 classes)
• Processing of polymers (3 classes)
• Polymer design criteria and considerations (2 classes)
• Applications of polymers (such as creep, wear, friction, damping, etc.) (5 classes)
• Fiber-reinforced composites, macroscopic composites (5 classes)
• Structural and component analysis (3 classes)
• Tests (3 classes)

ME 429 - Composite Materials

• Be familiar with indicial notation
• Transform tensor quantities from one coordinate system to another
• Compute stresses and strains for composite laminates 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 composite laminates

• Mechanics of materials

• Introduction to composite materials (1 class)
• Indicial notation, matrices, and tensors (4 classes)
• Mechanics of a composite lamina (3 classes)
• Extensional behavior of a symmetric laminate (3 classes)
• Failure criteria (3 classes)
• Bending behavior of a symmetric laminate (2 classes)
• Thermal stresses in a symmetric laminate (2 classes)
• Mechanical behavior of general laminates (3 classes)
• Manufacturing processes (4 classes)
• Test methods (4 classes)
• Testing lab demonstration (1 class)
• Review and examinations (3 classes)

ME 431 - Automatic Control Systems

• 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

• Differential Equations
• System Dynamics

• 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
• Final Exam

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

ME 433 - Electromechanical Systems

• 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 electomechanical system to achieve specified performance objective
• Determine component and system-wide frequency response characteristics
• Develop frequency response design tools

• Laplace transforms
• Feedback control systems
• Numerical methods

• DC motor modeling
• Analog component selection
• Z-transforms
• Difference equations
• State feedback
• Z-domain root locus design
• Digital system effects
• Advanced topics
• Review and testing and comprehensive final exam

• Analog control circuit design
• Electric motor characteristics
• Discrete equivalent PID controller implementation
• Electromechanical design and simulation

ME 460 - Finite Element Methods

• 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

• Mechanics of materials, statics, integral and differential calculus

• Overview of method (1 class)
• Review of matrix methods (1 class)
• Spring elements (2 classes)
• Truss elements (2 classes)
• Potential energy approach (5 classes)
• Beam element (3 classes)
• Constant strain triangle element (4 classes)
• Heat transfer application (2 classes)
• Interpretation of results & mesh design (2 classes)
• Discussion of symmetry and boundary conditions (2 classes)
• Overview of commercial software (1 class)
• Advanced element formulations (3 classes)

• 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