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 1204 - Quantitative Reasoning for Health Care Professionals

4 lecture hours 0 lab hours 4 credits

• Perform arithmetic operations involving ratio, proportion, percentage and rate
• Use rounding principles and scientific notation to report results of calculations
• Interpret numerical values as magnitude, quantity and scale
• Interpret and convert units
• Solve and interpret equations involving ratio, proportion, percentage and rate
• Solve and interpret applied problems relating to concentrations and mixtures
• Interpret graphs involving time relationships
• Evlauate formulas encountered in pediatric medication and statistics

• None

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

• None

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

• 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 Math II

• Upon successful completion of this course, the student will be able to:
  • 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

• 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
• Simple and symbolic operations
• Working with Arrays, Plotting
• Programming - Loops
• Programming - Logic
• Solving Equations - Matlab
• Numerical Integration - Matlab
• Matrix Methods - Matlab
• Optimization - Excel

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

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

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

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

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

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
• Overview of strengthening mechanisms in metals and alloys
• Deformation of Metals and Strain hardening
• Principles of Solidification
• Isomorphous Phase Diagrams and Phase Rule
• Eutectic Phase diagrams and solidification in Eutectic Systems
• Precipitation Hardening
• Microstructure and Heat Treatment of Steels
• Martensite Transformation, Tempering
• Effect of Alloy Elements in Steels
• Stainless Steels
• Cast Iron

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

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
• Casting Processes
• Powder Metallurgy
• Deformation Processing
• Sheet Metal Forming
• Machining - traditional metal cutting
• Non-traditional Machining - EDM, Laser and Waterjet
• Welding
• Design for Manufacturing and Assembly
• Sustainable Manufacturing & Recycling
• Polymer Part Processing
• Additive Manufacturing

• 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

• Rigid Body Motion

• Fundamentals of dynamics
• Practical considerations, actuators and motors
• Computer-aided engineering
• Linkage synthesis
• Machine Balancing
• Design of Flywheels
• Dynamics of Cams
• Project presentations

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

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

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
• State of Strain at a Point
• Principal Strains and Mohr’s Circle
• Electrical Resistance Strain Gages
• Strain Gage Circuits
• Transducer Design

• 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 Measurement

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

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

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
• Indicial notation, matrices, and tensors
• Mechanics of a composite lamina
• Extensional behavior of a symmetric laminate
• Failure criteria
• Bending behavior of a symmetric laminate
• Thermal stresses in a symmetric laminate
• Mechanical behavior of general laminates
• Manufacturing processes
• Test methods
• Testing lab demonstration
• Review and examinations

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

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

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
• Digital system effects

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

• 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

ME 480 - HVAC Systems Design

• Do a heating and cooling load calculation for a building
• Evaluate the psychrometric processes involved in heating and cooling a building
• Make appropriate choices for heating and cooling equipment
• Utilize a commercially-available software package (Carrier E20-II) to simulate the HVAC system for a building

• Energy Balance

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

ME 481 - Aerodynamics

• Have a thorough understanding of fluid flows over bluff and streamlined bodies, including potential flow results, circulation, boundary layers, transition, and experimental results
• Choose an airfoil and apply lift, drag, and moment coefficients to a design, and to be able to measure these coefficients experimentally
• Make thin airfoil and finite airfoil calculations
• Make airplane stability and trim calculations
• Have an introduction to automobile aerodynamics

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

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

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

ME 485 - Energy Systems Design Project

• Utilize a design methodology, including creative synthesis of solutions; evaluation of solutions based on criteria and constraints; sensitivity analysis; choice of “best” design
• Work effectively as part of a team
• Work with deadlines
• Communicate ideas
• Defend his/her decisions

• Thermodynamics
• Fluid mechanics
• Heat Transfer

• Outline of design process; project assignments (1 class)
• Problem statement (1 class)
• Literature search techniques (1 class)
• Brainstorming/list of solutions (1 class)
• Criteria and constraints/criterion function (2 classes)
• Sensitivity analysis (1 class)
• Oral presentation guidelines (1 class)
• Report writing guidelines (1 class)
• Oral presentations (3 classes)
• Team meetings with instructor (4 classes)
• Team project work (3 classes)

ME 490 - Senior Design I

• Have written a detailed design proposal for the major design experience
• Have researched trade and professional literature, patents, codes, and specifications related to the topic of the design proposal
• Have made an oral presentation of proposed design efforts to the advisors
• Have addressed possible societal and environmental impacts of their project

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

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

ME 491 - Senior Design II

• Have designed a mechanical or thermal system in a team setting
• Have prepared a formal design report
• Have made an oral presentation of design efforts to the class
• Have made an oral presentation in defense of his or her design work

• None

• Organizational Meeting
• Report writing
• Geometric Dimensioning and Tolerancing
• Other topics
• Design group presentations

ME 492 - Senior Design III

• Have designed a mechanical or thermal system in a team setting
• Have prepared a formal design report
• Have made a poster presentation in defense of his or her design work

• None

• Organizational Meeting
• Supervised design and prototyping work

ME 498 - Topics in Mechanical Engineering

• Have studied an engineering topic of special interest

• Varied

• Varied

ME 499 - Independent Study

• Have studied an engineering topic of special interest

• None

• To be determined by the faculty supervisor

ME 1301 - Introduction to Mechatronics

• Have applied concepts of structured programming in the control of electromechanical systems
• Have implemented computer-based data acquisition systems
• Be able to document all engineering activities

• Programming

• Programming with the Arduino Microcontroller
• Digital I/O
• Analog I/O, A/D and D/A conversion
• PWM and Servo Motor Control
• Control of Stepper Motors

• Discrete I/O: Switches and LEDS
• Analog I/O:  DC Motors, Solar Cells, Temperature Sensors, Infrared Sensors, and Potentiometers
• Control of a Stepper Motor: Coordinated Control of a Two-Axis Positioning System
• Introduction to C programming concepts
• Introduction to Robotics : Coordinated Control of a Multi-Axis Robotic Arm
• Student Design Projects

ME 1601 - Introduction to Engineering Design

• Understand a formal design process as used in mechanical engineering
• Generate 2-D engineering drawings
• Generate solid models of parts and assemblies

• None

• Sketching
• Part Modeling
• 2D Engineering Drawings
• Parametric Modeling Techniques
• Assembly Models
• Assembly Drawings
• Surface Part Models
• The Design Process

• Solid Modeling of Parts (Extrusions/Revolves)
• Generation of Engineering Drawings
• Solid Modeling of Parts (Loft/Shell/Sweep)
• Solid Modeling of Assemblies
• Engineering Design Project

ME 2001 - Mechanics I

• 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 and/or moments in trusses, frames, beams, and machine components
• Draw shear force and bending moment diagrams

• Scalars and Vectors
• Forces and Moments
• Differentiation
• Engineering Problem Formulation and Solving Approach
• Engineering Design and Model Development
• Numerical Methods
• Graphical Communication

• Forces, Vectors and the Resultant
• Forces in Space
• Vector Products
• Equilibrium of Particles in 2-D and 3-D
• Moment of a Force
• Couples, System of Forces
• Two & Three-Force Bodies
• Equilibrium of Rigid Bodies in 2-D and 3-D
• Analysis of Trusses, Frames, and Machines
• Distributed Forces & Internal Forces
• Shear Force & Bending Moment Diagrams

ME 2002 - Mechanics II

• 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 

• Free Body Diagram
• Vector Mechanics
• Derivatives of a Function
• Integral of a Function

• Laws of Friction: Basic Concepts 
• Multi-Contact Surfaces (Wedges) 
• Multi-Contact Surfaces (Screws)
• Flat Belts
• Cantroids 
• Area Moments of Inertia 
• Parallel Axis Theorem 
• Mass Moments of Inertia 
• Moments of Inertia of Composite Bodies 
• Position, Velocity, Acceleration 
• Uniform Rectilinear Motion and Acceleration 
• Projectile Motion 
• Normal and Tangential Components 
• Polar Coordinates 
• Relative Motion of Several Particles 
• Kinetics of Particles, Rectilinear Motion 
• Kinetics of Particles, Curvilinear Motion 
• Principle of Work and Energy for a particle 
• Principle of Impulse & Momentum
• Direct Central Impact
• Oblique Central Impact

ME 2003 - Mechanics III

• 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 forces acting on rigid bodies in motion

• Location of centroids
• Evaluation of area and mass moments of inertia
• Kinematics and kinetics
• Impulse and momentum of particles (rectilinear and curvilinear motion)

• Principle of Impulse & Momentum (Review)
• Planar Kinematics of Rigid Bodies
• Pure Translation & Rotation
• Rigid Body Rotation Around a Fixed Axis
• Absolute & Relative Plane Motion
• Instantaneous Center of Rotation
• Absolute and Relative Acceleration
• Coriolis  Acceleration
• Kinetics of Rigid Body Motion Forces & acc
• Plane Motion of Rigid bodies Energy & Momentum
• Principle of Impulse & Momentum rigid Body
• Conservation of Angular Momentum
• Impulsive Motion
• Eccentric Impact

ME 2004 - Mechanics of Materials I

• Determine stresses resulting from axial, bending, torsion, and transverse loading
• Apply Hooke’s Law for materials with linear stress-strain behavior
• Determine the stress state in a member resulting from combinations of loads
• Determine principal stresses for a state of plane stress
• Determine beam deflections
• Be familiar with the Euler buckling load for columns of various end conditions

• Statics
• Integral calculus
• Differential calculus

• Review of statics, reactions, and internal loads, basic axial stress and 1D Hooke’s Law
• Axial stress concentrations, axial deformation, and mechanical properties of materials
• Poisson’s ratio, Shear stress and strain, 3D Hooke’s Law, and Plane stress and Strain
• Stress on an inclined surface and stress transformation
• Mohr’s circle for plane stress principle stresses, maximum shearing stresses, principle planes, and planes of maximum shear
• Statically indeterminate axial members, torsion, angle of twist, and power transmission
• Simple bending (flexural formula), trasnverse shear
• Combined loading
• Beam deflection
• Euler Buckling

ME 2101 - Principles of Thermodynamics I

• Use thermodynamic tables to find properties
• Apply the ideal gas, 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 a steady flow open system
• Use the open system energy balance to evaluate processes, including determining work and heat transfer
• Use the open system energy balance to evaluate transient processes
• Appreciate the link between energy use and the environment

• Multivariable Calculus

• Systems and control volumes
• Properties of a system
• State and equilibrium
• Processes and cycles
• Temperature and the zeroeth law of thermodynamics
• Standard thermal science problem solving methodology
• Forms of energy
• Mechanisms of heat transfer
• Mechanisms of work transfer
• First law of thermodynamics
• Energy conversion efficiencies
• Energy and the environment
• Phases of a pure substance
• Phase-change processes
• Property diagrams
• Property tables
• Ideas gas law
• Closed system energy balances
• Boundary work
• Specific heats
• Internal energy, enthalpy, and specific heats of ideal gases
• Internal energy, enthalpy, and specific heats of liquids and solids
• Conservation of mass
• Energy of a flowing fluid
• Open system energy balances
• Steady flow engineering devices
• Unsteady flow processes

ME 3005 - Mechanics of Materials II

• Determine column buckling loads
• Determine principal stresses in 3D state of stress
• Analyze members subject to temperature change
• Determine stresses in thick and thin-walled pressure vessels
• Use failure theories under static loading
• Use fatigues failure criteria for members subject to fluctuating loads
• Apply enery method and solve for deflection of curved members
• Determine stresses in circular plates
• Become familiar with unsymmetric bending in cured beams

• Mechanics of Materials I

• Introduction to Workbench
• Secant formula
• Design of concentric and eccentric column
• Thermal stress and strain
• 3D deformation
• Normal and shear strains
• 3D stress
• Thin-walled pressure vessels
• Polar coordinates
• Thick-walled pressure vessels
• Torsion of non-circular cross-sections
• Circular plates
• 3D principle stresses
• Tresca and Von Mises failure criterion
• Columb-Mohr failure criterion
• Fully reversed fatigue
• S-N cure prediction
• Effect of fluctuating stresses

• Deflection of a Statically Indeterminate Beam
• Stresses in a Plate
• Column Buckling
• Curved Beam Stresses

ME 3102 - Principles of Thermodynamics II

• Explain the different statements of the 2nd Law of Thermodynamics
• Determine when the 2nd Law is violated in hypothetical engineering scenarios
• Interpret processes and cycles on T-s and P-v diagrams
• Apply a 2nd Law analysis (entropy balance) to processes involving both closed and open systems
• Evaluate the performance of Rankine and Brayton cycles, with their modifications
• Analyze refrigeration cycles
• Relate energy conversion efficiency to emissions and economics

• Multivariable calculus
• First-law analysis of open and closed systems
• Thermodynamic properties
• Thermodynamic processes and cycles

• Thermal energy reservoirs
• Heat engines
• Thermal efficiency
• Kelvin Planck statement of the 2nd Law
• Refrigerators and heat pumps
• Coefficient of performance
• Clausius statement of the 2nd Law
• Perpetual motion machines
• Reversible and irreversible processes
• Carnot cycle
• Carnot principles
• Carnot heat engine
• Carnot refrigerator and heat pump
• Entropy
• The increase in entropy principle
• Entropy change of pure substances
• Isentropic processes
• Property diagrams
• Statistical thermodynamics interpretation of entropy
• T-s diagrams
• Tds relations
• Entropy change of solids and liquids
• Entropy change of ideal gases
• Isentropic efficiency of steady flow devices
• Entropy balances on open and closed systems
• Exergy
• Reversible work and irreversibility
• 2nd Law efficiency
• The decrease in exergy principle
• Carnot cycle
• Air-standard assumptions
• Brayton cycle
• Brayton cycle with regeneration
• Brayton cycle with reheat and intercooling
• Carnot vapor cycle
• Rankine cycle
• Actual vs. ideal Rankine cycle processes
• Increasing the efficiency of the Rankine cycle
• Ideal reheat Rankine cycle
• Ideal regenerative Rankine cycle
• Cogeneration
• Combined gas-vapor power cycles
• Reversed Carnot cycle
• Ideal vapor-compression refrigeration cycle
• Actual vapor-compression refrigeration cycle

ME 3103 - Fluid Mechanics I

• Define a fluids properties and their relations to stress and strain rates
• Apply the fluid-static equation to determine pressure at a point
• Apply the Bernoulli equations to a variety of problems and define when it can and cannot be used
• Apply the control volume forms of the mass, energy, and momentum equations to variety of problems
• Determine the equation for a streamline and the acceleration of fluid for a given flow field

• Dynamics
• Multivariable Calculus
• Differential Equations
• Thermal Physics (at college sophomore level)

• Fluid Fundamentals: definitions and properties
• Fluid Statics
• Elementary Fluid Dynamics
• Control Volume Approach for Mass, Energy, and Momentum
• Fluid Kinematics
• Laminar vs. Turbulent Flow
• Introduction to viscous pipe flow
• Major and minor losses in pipe networks

ME 3104 - Fluid Mechanics II

• 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

• Required labs:
  • Calibration of an Orifice
  • Pump Test
  • Vortex shedding from a cylinder in cross-flow  
  • Drag on a scale model of a race car and driver
• Other labs:
  • Vortex shedding CFD - Ansys
  • Race car CFD - Ansys
  • Numerical solution of velocity distribution in a Boundary Layer - MATLAB/Ansys
  • Velocity profile in circular & rectangular ducts - MATLAB/Ansys
  • Potential Flow over an object - MATLAB/Ansys

ME 3105 - Applied Thermodynamics

3 lecture hours 2 lab hours 4 credits

• Explain the characteristics and differences among reciprocating engine cycles
• Perform energy balances on processes used to model reciprocating engine cycles
• Calculate reciprocating engine performance parameters
• Apply partial differential relations to develop thermodynamic property relations
• Use Maxwell relations to solve thermodynamic problems
• Calculate thermodynamic properties of gas mixtures
• Evaluate relative humidity by using the psychrometric chart
• Balance combustion reactions involving hydrocarbon fuels
• Perform energy balances on combustion processes
• Calculate the adiabatic flame temperature for combustion processes
• Use exhaust gas measurements to determine air fuel mixtures in combustion systems
• Assess the impact of combustion parameters on pollutant emissions and control
• Explain the current status and relative importance of different forms of renewable energy systems including solar, wind, and biomass
• Design an experiment for performance characterization of an energy supply system

• Multivariable calculus
• Differential equations
• 1st law analysis
• 2nd law analysis
• Power and refrigeration cycles
• Heat transfer

• Overview of reciprocating engines
• Otto cycle
• Diesel cycle
• Dual cycle
• Engine design and performance parameters including IMEP, BMEP, friction work, bsfc, volumetric efficiency
• Thermodynamic property relations
• Partial differential relations
• Developing property relations
• Maxwell relations
• Clapeyron equation
• Joule-Thomson coefficient
• Gas mixtures
• Mass and mole fractions
• Properties of gas mixtures
• Psychrometerics and air conditioning
• Relative humidity
• Dew-point temperature
• Web-bulb temperature
• The psychrometric chart
• Air conditioning processes
• Chemical reactions
• Balancing combustion reactions
• Air fuel ratio
• Equivalence ratio
• Exhaust gas analysis for determining air fuel ratio
• Enthalpy of formation, enthalpy of combustion, and heating values
• First-law analysis of reacting systems
• Adiabatic flame temperature
• Pollutant emissions and control from combustion systems
• Overview of renewable energy systems
• Design and performance of one or more of the following: solar photovoltaic systems, solar thermal systems, wind energy systems, biomass energy systems

• Cooperative Fuel Research (CFR) reciprocating engine performance
• Cogeneration system performance characterization
• Design of an energy systems experiment

Other labs:

• Hydrogen fuel cell performance
• Vapor compression refrigeration performance
• Solar photovoltaic system performance
• Solar thermal system performance parameter modeling, characterization,  and validation
• Modeling and validation of a lumped capacitance transient energy system
• Psychrometric processes

ME 3301 - Instrumentation

• Describe the physical operating principles of common sensor technologies
• Know the characteristics and performance parameters of sensors
• Measure physical phenomenon with proper sensors
• Address sampling and quantization challenges

• Basic circuits
• System dynamics
• Simulation with MATLAB and Simulink

• Measurement and Uncertainty Analysis
• 1^st and 2^nd - Order Response
• Data Acquisition and A/D conversion
• Sampling and Quantization Effects
• Op-amps and signal conditioning (amplification and filtering)
• Digital Filters 
• Wheatstone Bridge
• Fast Fourier Analysis
• Sensor Calibration
• Measurement: current, voltage, temperature, velocity, acceleration, strain and force

• Density Determination of a Metal and Propagation of Error
• Introduction to Instrumentation Equipment
• Effects of Sampling, A/D conversion, and Digital Filters
• Op-amps and Signal Conditioning
• Measurement of Temperature
• Acceleration Measurement
• FFT and the Vibration of a Marimba Bar
• Encoders and Angular Velocity Measurement
• Measurement of Strain and Force

ME 3650 - Systematic Engineering Design

• Arrange in a team environment, distributing work even
• Demonstrate problem-solving methods and their use
• Implement a basic product development process
• Define problems and evaluate solution methods
• Determine requirements and specifications
• Assess solutions and their variants
• Produce sketches and drawings
• Construct a simple physical model of the final concept to show scale and interdependencies
• Produce a technical document with the necessary information
• Develop information according to rules, legislation and/or standards
• Skill in team-work
• Present project results in front of an audience

• Junior Standing

• Machine component design process
• Literature search
• Drawing and computer drafting
• Written and oral presentation techniques
• Intercultural and social competence

ME 4220 - Fatigue and Fracture in Mechanical Design

• Understand the distinction between “high” cycle versus “low” cycle fatigue problems and correctly choose an appropriate analysis method for a design problem
• Understand cyclic plastic strain behavior and be able to apply mathematical models for cyclic plastic strain to design problems
• Apply strain-life methods for low cycles fatigue
• Combine notch-strain analysis with low cycle fatigue analysis for component life predictions
• Understand basic concepts in Linear Elastic Fracture Mechanics (LEFM)
• Apply basic LEFM models to problems in 1) fracture of metals, 2) fatigue crack growth rate and 3) fail safe design

• Stress-Life approach to fatigue problems
• Mechanics of Materials

• Review - Fatigue basics, Stress-Life Diagrams, Stress Concentrations, Notch Sensitivity, Mean Stress Effects
• Variable Amplitude Load Histories
• Low cycle fatigue (Plastic strain cycling, 2 to 1000 cycle life)
• Cyclic Stress-strain Curves & Plastic Strain-life Diagrams (ε-N diagrams)
• Notch Strain Analysis, Neuber’s Rule
• Microscopic/Material Aspects of Fatigue
• Fracture Mechanics (Stress Intensity Factor & Plane Strain Fracture Toughness)
• Fatigue Crack Growth Rate
• Failure Analysis - Observations on Failed Parts
• “Fail Safe” Design Practices

ME 4302 - Automatic Control Systems

• Use Laplace transformation and selected linearization techniques
• Develop mathematical models of selected systems
• Determine system stability using root locus techniques
• Determine steady state errors due to reference and disturbance inputs
• Construct root locus plots and use them as appropriate to evaluate system transient response characteristics
• Construct and analyze Bode plots

• System dynamics
• Instrumentation

• Mathematical Models of Systems
• State Variable Models
• Feedback Control Systems Characteristics
• Performance of Feedback Control Systems
• Stability of Linear Feedback Systems
• Root Locus Method
• Frequency Response Methods
• Stability in the Frequency Domain

• Laboratory measurement techniques
• Dynamic system measurements and system identification
• Steady-state valve characteristics
• Dynamic response characteristics
• Control system simulation
• Rotary speed control
• Position control

ME 4303 - Electromechanical Systems

• Develop mathematical models of electromechnical components and systems
• Formulate and evaluate analog and digital controllers
• Specify and evaluate state feedback controllers
• Design an electomechanical system to achieve specified performance objectives
• Apply frequency response design tools for stability analysis

• Laplace transforms
• Feedback control systems
• Numerical methods

• Gain and phase margins
• Phase lead and phase lag controllers
• DC motor modeling
• Z-transforms
• Difference equations
• State feedback
• Z-domain control implementation
• Digital system effects

ME 4304 - Introduction to Robotic Systems

• Determine the forward and inverse kinematics for typical serial chained robots
• Use rotational matrices and homogeneous transformations to describe coordinate frames
• Simulate robot motion using MATLAB/Simulink
• Model the kinematics of a differential drive robot
• Implement control strategies to plan robot motions

• Differential equations
• Dynamics of Systems
• Block diagrams
• Matrix Operations

• Introduction to robots
• Coordinate Frames, Rigid Motion and Homogeneous Transforms
• Rotation Matrices and Parameterized Rotations
• Displacements, Compositions of Rigid Motions
• Forward and Inverse Kinematics
• Velocity Kinematics & Manipulator Jacobian
• Singularities
• Static Forces
• Motion Planning and Trajectory Generation
• Dynamics
• Independent Joint Control
• Feedforward Compensation
• PD with Gravity Compensation
• Mobile Robot Kinematics
• Differential Drive kinematics

ME 4305 - Mechanical System Simulation

• Implement a variety of mathematical relationships into block diagram models
• Create and validate simulation models of basic component behavior
• Combine basic models into more complex system models
• Conduct design analyses to understand the influence of specific parameters on system performance
• Develop a better understanding of system behavior pertaining to fluid power, power trains, and mechanics
• Learn to learn from system modeling activity

• Laplace transfer functions
• Differential equations
• Mechanical system modeling
• Dynamic systems

• Behavioral models of fluid power elements: pumps, motors, cylinders, volumes and valves
• Behavioral models of power train elements: engines, clutches, torque converters, gear reductions
• Behavioral models of spring-mass-damper systems: translational and rotational
• Using Simulink to study sub-system interactions and system performance
• Using MATLAB to automate design studies that implement the Simulink models

• None

ME 4602 - Transient and Nonlinear Finite Element Methods

• Have reviewed the procedural steps involved in FEA analysis
• Derive a finite element formulation from a governing differential equation
• Understand and implement time integration of dynamic systems with inertia
• Understand step-wise linearization of nonlinear systems
• Understand and implement iterative solution techniques for nonlinear systems
• Be familiar with use of a commercial general-purpose FEA software package for transient and nonlinear applications
• Understand how to validate results for problems involving systems design

• Mechanics of materials, statics, dynamics, heat transfer, linear algebra, integral and differential calculus

• Review of the method
• Method of weighted residuals
• Comparison with energy methods
• Modal analysis
• Modeling inertia and mass distribution using FEA
• Modeling damping in continuous systems using FEA
• Understanding and implementing time integration algorithms for dynamic FEA analysis
• Implementing nonlinear FEA solutions as a set of iterative, quasi-linearized sub-problems
• Use commercial general-purpose FEA software package for transient and nonlinear applications
• Review of static analysis
• Modal analysis and transient analysis
• Nonlinear structural analysis
• Transient, nonlinear thermal conduction, convection, and radiation

• Validate results for real design of an engineering system (4 week course project)

ME 4610 - Medical Applications in Mechanical Engineering

• Discern the role that engineering mechanics and engineering design play in the development, analysis and utilization of mechanical devices
• Understand how mechanics and mechanical engineering principles may be applied to the modeling of bone and soft tissues
• Understand the kinematics and kinetics involved in human gait
• Understand general bone, muscles and tendons structure and their functions

• Basic strength of materials and statics

• Basic anatomy
• Biomedical engineering material
• Mechanics, material and mechanical properties of bone, bone remodeling
• Implants and failure of implants
• FEA modeling of biomedical systems (and laboratory exercise)
• Spine Mechanics
• Torso mechanics
• Clinical function of the spine
• Mechanics of scoliosis and correction
• Experimental testing and verification of spinal mechanics (and laboratory exercise)
• Viscoelastic models
• Muscle mechanics
• Link-Segment models
• Forces in joints
• Force plates
• Pressure sensors
• Practical gait lab analysis

ME 4701 - Fluid Power Circuits

• Size hydraulic components based on steady state requirements
• Read a hydraulic schematic to determine the function of the circuit
• Analyze a hydraulic circuit based on component specifications
• Select pump controls to minimize energy consumption

• Ability to use free body diagrams
• Understanding of forces and motion

• Fluid properties 
• Unit conversions 
• Hydraulic system schematics
• Pumps & motors
• Cylinders
• Directional control valves 
• Flow and pressure control valves
• Flow losses
• Valve controlled cylinders and motors
• Cavitation
• Hydrostatic transmissions
• Auxiliary components
• Fixed vs. variable displacement pumps
• Load sensing
• Pressure and flow compensation
• Power consumption and efficiency
• Accumulator application and sizing

ME 4702 - Fluid Power Modeling

• Develop dynamic models of pumps, valves, motors, cylinders and accumulators
• Combine component models to form system models
• Use the developed models to assess hydraulic circuit performance
• Conduct design studies to understand how parameters affect performance

• Interactions of components in a system
• Dynamic systems
• Fluid Power circuit analysis

• Dynamic system modeling
• Causality
• Fluid compressiblity
• Block diagram modeling
• Fluid power component functionality
• Component power interactions

• None

ME 4802 - Compressible Flow

• Demonstrate the ability to utilize the adiabatic and isentropic flow relations to solve typical flow problems
• Demonstrate the ability to solve typical normal-shock problems, problems involving moving normal shocks or oblique shocks and Prandtl-Meyer flow problems by use of appropriate equations or tables or charts
• Demonstrate the ability to solve typical Fanno flow problems and Rayleigh flow problems by use of appropriate equations and tables
• Explain choking and shock in various applications and contexts

• Fluid Mechanics
• Thermodynamics-II (covering Second Law of Thermodynamics)

• Review of the fundamentals (Laws of Thermodynamics, Conservation of Mass, Momentum and Energy, Entropy changes for perfect gases, Stagnation properties)
• Introduction to Compressible Flow (Sonic velocity, Mach number, Stagnation relations in terms of Mach number, total pressure loss and entropy change relation)
• Varying-Area Adiabatic flow (convergent-divergent nozzle, diffuser, choking, isentropic flow tables)
• Standing Normal Shocks
• Moving and Oblique (planar or conical) Shocks
• Prandtl-Meyer Flow (including lift and drag calculations on airfoils at various angles of attack, and discussion on overexpanded and underexpanded nozzles)
• Supersonic Nozzle Experiment and Mach number calculations
• Fanno Flow and applications
• Rayleigh Flow and applications
• Topic: Applications of Compressible Flow in Propulsion Systems (Example-ramjet engine)

ME 4804 - Advanced Energy Technologies

• Course outcomes vary depending on the selected topics for the quarter

• Classical thermodynamics (energy balances)

• Topics are chosen from the list given above in the course description based partly on student interest

ME 4805 - Renewable Energy Utilization

• Appreciate the challenges facing world energy supply and use
• Predict the solar energy resource at any location on earth
• Develop an understanding of the science of photovoltaic devices and solar thermal systems
• Apply engineering design principles to solar power generation installations
• Perform economic analysis of solar power systems
• Analyze the energy potential of biofuels, the technology of biofuels production, and the economic advantages and disadvantages of energy from biomass
• Develop an understanding of the science and engineering of wind energy systems
• Appreciate the engineering necessity and comparable performance of storage systems for renewable energy

• Classical thermodynamics (energy balances)

• World and US energy picture
• The solar resource
• Solar photovoltaic systems
• Solar thermal systems
• Energy from biomass
• Wind resources
• Wind turbine performance prediction
• Simulation tools for solar energy simulation

ME 4806 - Computational Fluid Dynamics

• Demonstrate working knowledge of the governing equations of fluid mechanics
• Understand the mathematical properties of the governing equations and be able to evaluate boundary/initial value problems
• Demonstrate a systematic approach to solving the appropriate governing equations using CFD
• Qualitatively analyze numerical results and provide appropriate data plotting
• Recognize strengths and limitations of CFD techniques
• Understand the differences between different CFD turbulence models
• Exercise simulation capability with commerical software

• Fluid mechanics
• Numerical methods

• Fluid dynamics
• Numerical Methods
• Vorticity-Streamfunction
• RANs Turbulence Modeling
• Finite Volume Analysis
• Post Processing
• Simulation with commercial software

• Simulation with commercial CFD software, e.g. ANSYS Fluent
• Simulation of cavity flow: vorticity/steam function
• Flow around bluff bodies: turbulence and flow separation
• Post processing

ME 4906 - Applied Numerical Methods

• Solve fully nonlinear ordinary differential equations/initial value problems (IVP)
• Apply principles from linear systems to fully nonlinear systems
• Postulate and solve eigenvalue/eigenvector problems with applications to modal analysis and buckling

• Numerical integration of ordinary differential equations
• Linear algebra

• Differential equations
• Linear algebra
• System similitude
• Review of system dynamics
• Lagrange’s equations
• Constraints vis Lagrange multiplers
• Dynamic system simulation ODE’s and OAE’s
• Multiple D of systems
• Eigen analysis
• Lagrange multipliers

ME 4951 - Bachelor Thesis I

• The student is expected to write an in-depth thesis documenting the student’s process that recognizes, defines, solves and validates a scientific or engineering task within a specified time

• None

• Project dependent

ME 4952 - Bachelor Thesis II

• The student is expected to write an in-depth thesis documenting the student’s process that recognizes, defines, solves and validates a scientific or engineering task within a specified time

• None

• Project dependent