All courses are 3 credits unless otherwise noted. Graduate
Students should consult the online departmental course schedules at
the Student Response Center to ascertain which
semester a course is being taught.
MAE 501 Individual Problems (1-6 credits)
For Master of Science candidates. Investigation carried out under
thedirection of a member of the graduate faculty. TUT.
Prerequisite: Permission of instructor and approval of the
MAE 503 Graduate Seminar (no credit)
A weekly seminar for graduate Mechanical and Aerospace Engineering
students on topics in the fluids/thermal sciences, systems/design
and mechanics/materials areas. Seminar speakers will be invited
from outside the University as well as from inside the school.
MAE 505 SP TP: Probability Essentials and
The objective of this course is to rigorously study the fundamental
concepts of measure-theoretic probability, and how these abstract
concepts can be directly applied to the experimental or physical
world. Topics include: Probability space (triple), Borel
sigma-field; Random variable, Probability distribution function,
Simulation of random variables, Introduction to MATLAB statistical
toolbox; Random vector, Vector-valued functions of random vector;
Mathematical expectation, Problem of moments, Data uncertainty;
Characteristic function; Modes of convergence of random variables,
Central limit theorem; Introduction to stochastic process and
random fields, Concept of stationarity, non- stationarity and
ergodicity; Gaussian random processes and sampling techniques;
Maximum likelihood estimation; and Basic Markov Chain Monte Carlo
Pre-requisites for this course are working knowledge of
multivariate calculus, basic knowledge of optimization theory, and
MAE 507 Engineering Analysis 1
Linear algebra, linear spaces and applications to ordinary
differential equations, introduction to dynamical systems,
bifurcations and chaos, Green's functions and boundary value
problems, adjoint operators, alternative theorems, orthogonal
expansions, Sturm - Liouville systems. LEC.
MAE 508 Engineering Analysis 2
Continuation of MAE 507. Classification of linear second order
partial differential equations, characteristics method, Riemann
invariants, application to compressible fluid flows, wave and heat
equations in one space dimension, eigenfunction expansion,
transform methods and fundemental solutions, first order
quasilinear partial differential equations, generalized
conservation laws and kinematic waves, Burger's equation, shallow
water waves, Korteweg - deVries equation and solitons. LEC.
Prerequisite:MAE 428 or permission or instructor.
MAE 556 Numerical Modeling of Moving Interfaces
Moving interfaces occur in a wide range of scientific and
engineering applications. Some are obvious, for example bubbles
rising in a fluid or crystals solidifying in an aqueous solution.
Some are not so obvious, for example optimizing solutions for
robotic path planning. In this course, we will study the numerical
methods used for simulating these complex problems.
MAE 512 Machines & Mechanisms 2
Kinematics and dynamics of machinery; linkages, geometry of
motion,mobility; velocity and acceleration analysis by graphical,
analytical, and numerical techniques; static and dynamic force
analysis in machinery; engine analysis; flywheels; balancing.
Emphasis upon using multibody dynamic simulation tools for
enchancing functional performance of machinery.
MAE 514 Evaluation of Biomedical Materials
This course serves multidisciplinary teams of students from a
variety of backgrounds. Detailed discussions review the critical
characteristics of specific materials useful for various types of
medical and dental devices; selection criteria based on function
and longevity; performance testing in-vitro and in-vivo; evaluation
of material breakdown in biological media, and potential
toxicologic consequences; design of clinical trials; surgical
considerations; and regulatory and legal issues. This course
utilizes each student's primary field of expertise as guide to
specific topics of biomaterials evaluation. A "case study" midway
through the course allows students to actually design and promote a
new implant device for an unmet medical need, with particular
attention to meeting regulatory and marketing requirements.
Crosslisted as: BMA 520
MAE 515 Fluid Mechanics 1
Vector and tensor notation; continuity equation; fluid kinematics
and stress-strain relations; Navier-Stokes equations; general
integral formulations; energy equations; incompressible viscous
flows at low Reynolds numbers; boundary layer approximations.
MAE 516 Fluid Mechanics 2
A continuation of MAE 515. Laminar boundary layers; linear
stability theory and transition; turbulent flow; inviscid potential
flow; compressible flow. LEC.
Prerequisite: MAE 515 of permission of instructor.
MAE 517 Applied Orthopaedic Biomechanics
Design of implants and prosthetics in relation to the biomechanics
of the musculoskeletal system. Topics include bone physiology,
testing methods (tension, compression, bending, torsion, shear, and
fatigue, including nondestructive testing), strain gage
application, composite theory of bone, stress fractures and fatigue
properties in the musculoskeletal systems, fracture healing
external/internal fixation (AO, Ilizarov etc.), aging and
osteoporosis, pathology of osteoarthritis, joint replacement and
arthroplasty, and spine biomechanics.
MAE 518 Electrodynamics of Fluids
This course is intended to provide an introduction to the
electrodynamics of fluids and particles at the graduate level.
Topics include Maxwell's equations, electromagnetic forces and
energy, elementary plasma theory, MHD and EHD flows,
electromagnetic effects on heat and mass transfer, dynamics of
charged suspensions, and various applications. LEC.
Prerequisite: Undergraduate courses in electromagnetic theory and
MAE 519 Turbulent Flow
A brief review of fluid mechanics will be followed by an
introduction to the phenomena of instability and transition to
turbulence. The bulk of the course will then focus on the study of
turbulence. Receiving special emphasis will be the energetics of
turbulent flow, the multiplicity of scales of motion, and the
tendency of turbulent flows toward equilibrium and self-preserving
states. The course should be of interest to anyone interested in
aerodynamics, convective heat transfer and fluid mechanics. Course
crosslisted as CIE 561. LEC.
Prerequisite: Course in Fluid Mechanics.
MAE 520 Biomechanics of the Musculoskeletal System
Basic aspects of anatomy; forces transmitted in the body; bones as
structural members; joint and muscle forces. Kinematics of body
motions; instantaneous centers of joint motions; behavior of normal
and abnormal joints; remodeling. Biomaterials; ligaments and
tendons. Functions of orthotics and prostheses; design
considerations. The course includes a weekly seminar and one or two
laboratory sessions. LEC/SEM.
Prerequisite: EAS 205, EAS 206, or equivalent.
MAE 522 Heat Exchanger Design
Classification of heat exchangers, overview of heat exchanger
design procedure, log mean temperature difference and exchanger
effectiveness, number of transfer units analyses, exchanger
pressure drop analysis, surface basic heat transfer and flow
friction characteristics, experimental correlations and theoretical
solutions, special design considerations to regenerators,
plate-fin, tube-fin and shell-and-tube exchangers; heat exchanger
surface selection and optimization; flow distribution and header
design; heat exchanger fouling; flow-induced vibrations; and
transient response of heat exchangers. LEC.
Prerequisite: Undergraduate training in mechanical engineering
fluid mechanics and heat transfer.
MAE 523 Theory of Turbomachinery
Similarity considerations; dimensionless performance
characteristics; Reynolds number and scale effects; thermodynamics
and fluid mechanics of turbomachinery; energy transfer in
turbo-machinery; one-, two-, and three-dimensional analysis of
inviscid flow in turbomachinery; loss mechanisms; performance
characteristics of radial and axial flow fans, pumps, compressors,
MAE 524 Elasticity
A rigorous introduction to the theory and application of classical
elasticity theory. Tensor analysis, stress, deformation, strain and
elastic constitutive equations. The field equations of elasticity.
Uniqueness theorem. Formulation and solution of boundary value
problems, including bending, torsion, plane strain and plane
stress. Same as CIE 621. LEC.
MAE 525 Space Dynamics & Control
Introduces the concepts of spacecraft orbital mechanics and
attitude dynamics. Orbital mechanics is the study of the positional
motion, while attitude dynamics describes the orientation of the
spacecraft. Topics include: review of rotational kinematics and
dynamics, orbital mechanics, gravity turn and trajectory
optimization, orbit lifetimes, three-body problem, orbit
perturbations, orbit determination, spacecraft dynamics, spinning
and three-axis stabilized spacecraft, and attitude
MAE 529 Finite Element Structural Analysis
This course is intended to bridge the gap between the theory and
application of finite element modeling. At the end of the course
the student will be able to judge if a problem is appropriate for
finite element analysis, will know how to determine the model type,
will be able to determine the type of elements to use and how many,
and will have the background to judge the accuracy of the results
obtained. These practical skills are difficult to acquire in a
strictly theoretical course. Specific topics will include:
fundamentals of FEM, basic input data required, definition of the
problem, the finite element model, debugging the model, element
performance and distortion, use of refined mesh modeling and
substructuring, dynamic FEM, application for thermal analysis, and
calibrating the accuracy of finite element models. LEC.
MAE 530 Aerosol Mechanics
Studies of the physical and dynamic behavior of aerosol particles
in the atmospherical environment with application to gas cleaning,
cloud physics, and air-pollution control problems. Topics discussed
include: the formation of disperse systems; the particle size
distribution function; mechanism of condensation and coagulation of
aerosols; rectilinear and curvilinear motion of aerosol particles;
theories of convective diffusion, impaction and sedimentation in
flow systems; theories of aerosol filtration and experimental
measurements of particle size distribution and chemical
MAE 534 Combustion
Examines the fundamentals of combustion. Topics will include
thermophysical calculations, chemical kinetics, premixed and
diffusion combustion phenomena. Specific subject matter will range
from homogeneous gas phase combustion to heterogeneous droplet and
particle combustion. The fluid mechanics of chemically reacting
flows will be discussed with an emphasis on turbulent combustion. A
variety of current applications will be presented. LEC.
Prerequisite: MAE 515 or MAE 546 or equivalent.
MAE 535 Principles of Material Design
The design of materials is central to the development of materials
for applications. Knowledge on the principles of material design is
needed for engineers and scientists that are involved with material
development or research. This knowledge entails broad understanding
of the types of structures that materials can exhibit, how the
structures can be fabricated, and how the structures impact the
behavior, which includes mechanical, thermal, electronic,
dielectric and electrochemical behavior. Particularly valuable for
material design is broad knowledge of the types of material
structures, which are in scales ranging from the nanoscale to the
macroscale and include interfaces. This course covers the
principles of material design, with emphasis on the interplay among
processing, structure, properties and applications. The material
tailoring involves consideration of the architecture, composition,
phases, porosity, connectivity, interfaces, surfaces and scales.
The materials include single-phase materials, multi-phase
materials, multi-scale materials, two-dimensional materials,
one-dimensional materials and pastes. The design is illustrated
with materials that are relevant to structural, electronic, thermal
and electrochemical applications, with consideration of the
relationship between the structure and properties of the materials
and that between the processing and the structure.
MAE 536 Random Vibrations and Stochastic Structural
This course is an introduction of random vibrations, including a
review of probability theory; concepts and applications of
summation and multiplication of random variables; descriptions of
random processes and their origin; single and multiple
degree-of-freedom linear system such as responses of machines and
structures due to transient and random excitations; analyses in the
time and frequency domains for reliability design, system
identifications, vibration testing and control in engineering
practice; non-linear systems and structures and statistical
linearization as well as a brief discussion on Monte Carlo
simulations. Also listed as CIE 520. LEC.
MAE 538 Smart Materials
This course introduces the students to smart materials, which refer
to materials that can sense a certain stimulus and, in some cases,
even react to the stimulus in a positive way so as to counteract
negative effects of the stimulus. Emphasis is on strain/stress
sensors and actuators. Topics include electrically conducting
materials, piezoelectric and electrostrictive materials,
magnetostrictive materials, electrorheological and
magnetorheological fluids, electrolytic polymer gels, shape memory
materials, intrinsically smart structural materials, optical fibers
and photoelastic materials. LEC
MAE 539 Heating, Ventilation and Air-Conditioning
Review of psychrometrics; physiological factors; heating and
cooling load calculations; refrigeration methods and applications
to air conditioning; cryogenic methods; fan and duct analyses;
solar energy applications. LEC.
MAE 540 Computational Fluid Mechanics
The numerical methods for solving various types of flow problems.
Discusses the elliptic, parabolic and hyperbolic properties of
partial differential equations governing the fluid flow. Different
spatial discretization techniques for finite difference and finite
volume methods. Different time integration techniques for unsteady
problems and solving system of linear equations. Computer program
development for a simple flow problem. Also listed as CIE 548.
MAE 541 Topics in Finite Element Analysis
Advanced topics in finite element analysis including but not
necessarily limited to mathematical foundations, linear transient
analysis, basic non-linear analysis - material properties and
geometric non-linearities, error estimation and adaptivity,
advanced solution techniques, and special problems e.g.
incompressible materials, thin structures. Course will involve
extensive project work on realistic applications.
Prerequisite: Consent of instructor.
MAE 542 Engineering Applications of Computational Fluid
This course is intended for seniors and beginning graduate students
interested in computer based analysis of engineering problems in
fluid mechanics and heat transfer. Application of computer analysis
to engineering design of fluid/thermal systems will be emphasized.
Students need not have a graduate level background in fluid
mechanics or heat transfer, however, an undergraduate level is
necessary. The general governing equations and methods to solve
them, including; finite-difference, finite-volume, panel methods,
and finite element methods, will be surveyed. Introduction to the
use of state-of-the-art computer tools for analysis and graphical
representation of results will give the student a broad view of
computational fluid mechanics for engineerin applications in the
fluid/thermal sciences. This course is particularly suited for
Masters of Engineering students. LEC.
Prerequisite: MAE 335, MAE 336, MAE 376, FORTRAN.
MAE 543 Continuous Control Systems (Lec and Lab)
Transfer function representation of dynamic systems, concepts of
feedback control, block diagrams, computer simulation of control
systems. Analysis and implementation of electro-mechanical,
electronic and hydraulic control systems. Time domain analysis with
respect to speed of response, overshoot, steady state error, and
stability. Root locus plots, basics of frequency response in
control analysis and dynamic compensation. LEC/LAB
MAE 544 Digital Control Systems (Lec and Lab)
Control of dynamic systems by digital computer. Characterization of
discrete-time systems, discrete state space, Z transforms, time
domain analysis of discrete-time control systems. Effects of
sampling time. Discrete root locus. Frequency domain methods for
compensator design. Laboratory experiences in the computer control
of electromechanical systems with C/C++ programming, LabView and
programmable logic controls (PLCs). LEC/LAB
MAE 545 Heat Transfer 1
Development of the equations for mass, momentum, heat and entropy
transport with emphasis on the first and second laws of
thermodynamics. Discussion of the constitutive laws for conduction
and radiation. Conduction: steady-state, transient, 1-D and
multidimensional, moving boundary; method of Froebenius, separation
of variables, transform techniques, similarity; approximate
physical models and solution methods. Radiation: basic physical
concepts, definition of intensity, blackbody radiation, properties
of real materials, models of radiative properties, absorbing,
emitting and scattering media, enclosure analysis. LEC.
MAE 546 Heat Transfer 2
Forced convection: governing equations for laminar and turbulent
flows, similarity analysis, flow and heat transfer in tubes,
boundary layer theory, heat transfer in external flows, temperature
dependent properties, and high speed applications. Natural
convection: Boussinesq and other approximations, boundary layer
equations for laminar and turbulent flows, similar and near similar
solutions, horizontal and inclined surfaces, transient flows, and
combined forced and natural convection regimes. Condensation and
boiling: physics of the phenomena, correlations. LEC.
Prerequisite: MAE 545 and MAE 515 helpful but not absolutely
MAE 547 Radiation Heat Transfer
Physical concepts: photons/electromagnetic waves, intensity,
blackbodies, directionality, spectra. Properties of real materials:
EM theory, dispersion theory. Radiation exchange between surfaces.
Multimode energy transfer. Fundamentals of absorbing, emitting and
scattering media. Exact and approximate solutions to the equation
of radiative transfer. Engineering approaches to radiation in
enclosures. Applications to combustion, atmospheric radiation and
various energy systems. LEC
MAE 548 Issues in Concurrent Design
(offered alternate Spring semesters with MAE 552-Heuristic
Optimization) Current interest in incorporation of quality and
manufacturing concerns in the early stages of the design process
has resulted in such concepts as Concurrent Engineering, Total
Quality Management, Quality Function Deployment, Robust Design,
Traguchi's Quality Functions, Teaming Approaches for Complex
Design, and many others. The course will address these concepts --
particularly as they pertain to complex engineering systems.
Industrial case studies will be investigated and design projects
incorporating some or all of the above concepts will provide
first-hand experience. As teamwork will be emphasized, good
communication skills are essential. LEC
Prerequisite: Programming and communication skills.
MAE 549 Design of Complex Engineering Systems
The design of complex engineering systems such as aircraft or
automobiles requires the interaction of multiple designers, design
teams, and their associated computer tools. In this course, methods
and tools to model interactions, cooperation, and communication are
investigated using industrial and social design examples. In
addition, issues in optimization, decision support, design theory,
and concept exploration will be investigated.
MAE 550 Optimization in Engineering Design
Optimization techniques with applications in various aspects of
engineering design. Concepts of design variables, constraints,
objective functions, penalty functions, Lagrange multipliers.
Techniques for solving constrained and unconstrained optimization
problems: classical approaches, steepest descent, conjugate
directions, conjugate gradient, controlled random searches, etc.
Discussion of generalized reduced gradient, sequential linear
programming, and recursive quadratic programming strategies.
Computer implementation of optimization schemes. Applications and
examples in the design of engineering components and systems.
Prerequisite: Graduate standing and knowledge of FORTRAN.
MAE 551 Advanced Design Theory
In this course, a number of advanced theories, methods, and
approaches to the design of systems and products are covered and
researched. These topics include but are not limited to Systematic
Design, Total Design, Theory of Technical Systems, Design Failure
Paradigms, Decision-Based Design, Game Theory, Axiomatic Design,
Multiobjective Optimization and Product Family Design. The topics
are discussed and researched in groups using case studies from both
modern and historical design examples.
MAE 552 Heuristic Optimization
Topics for this class include heuristic-based Optimality Criteria
methods, some newer discrete and integer programming approaches
(e.g. Tabu Search, Genetic Algorithms, Simulated Annealing),
multi-level hierarchical approaches, complex non-hierarchical
methods (such as are used in multidisciplinary design problems and
for IPPD-Integrated Product and Process Development), Geometric
Programming methods, some Taguchi approaches, and fuzzy logic. This
course addresses optimization topics not covered in Optimization in
Engineering Design (MAE 550) and does NOT require MAE 550 as a
MAE 553 Inelastic Stress Analysis
Physical basis of inelastic behavior of materials. Careful
development of inelastic constitutive laws -- thermoelastic,
viscoelastic, plastic, nonlinear creep, viscoplastic. Applications
-- flexure of beams, torsion of bars, plane strain, plane stress.
MAE 554 Road Vehicle Dynamics
Forces and torques generated by tires (under both traction and
braking) and by the relative wind; Two-wheel and Four-wheel models
of a vehicle; simplified stability and control of transients;
steady-state response to external disturbances; effects of the roll
degree of freedom; equations of motion in body-fixed coordinates;
lateral load transfer; Force-Moment analysis; applications of
feedback-control theory to the design of subsystems for improved
MAE 555 Continuum Mechanics
Definitions of stress, strain, and rotation for finite and
infinitesimal theory; global and local forms of conservation laws
of mass, momentum, moment of momentum, and energy; use of the
second law of thermodynamics in the development of constitutive
laws; presentation of constitutive laws for isotropic and
anisotropic linear elastic, thermoelastic, linear viscous,
viscoelastic, and plastic materials.
MAE 558 Tribology
An introduction to friction, lubrication and wear. Contact of real
surfaces, mechanics of friction, surface failures, boundary
lubrication, fluid properties, thin film lubrication, thick film
lubrication, bearing and lubricant selection. LEC.
Prerequisite: Permission of instructor.
MAE 560 Masters Research Guidance (1-6 credits)
For Master of Science candidates. Approval of the thesis advisor is
required for registration. TUT.
MAE 562 Analytical Dynamics
Review of Newtonian mechanics for systems of particles. Lagrange's
equations of motion for conservative and nonconservative systems.
Variational mechanics and Hamilton's principle. Application to
various nonlinear problems and specifically to the two-body problem
and celestial mechanics. The kinematics and dynamics of rigid
bodies. Euler's equations of motion. Application to gyroscopic
motion. Introduction to Hamilton's equations of motion. The
linearized theory of small oscillations and associated matrix
MAE 563 Plasticity
Review of basic experiments in solid mechanics, stress, strain,
stress/strain relationships. Plastic behavior. Yield criteria. Flow
law. Limit analysis. Applications to simple structures relevant to
mechanical and aerospace engineering. Extrusion. Metal forming.
MAE 564 Manufacturing Automation
Rapid growth of automation has been a strong motivation for
engineers to acquire skills in the area of Computer Aided
Manufacturing and Design. This course will serve as an introduction
to the theory of automation as related to manufacturing and design
integration. We will look at various hardware, software and
algorithm issues involved in fast and flexible product development
cycles. Following strategies of automated manufacturing systems
will be covered: CAD-CAM: integration, programming and simulation;
Robotics: applications in welding, material handling and human
intensive processes; Reverse Engineering: modeling product from
laser and CMM data of parts; Virtual Environments: industrial
applications of virtual reality and prototyping; Intelligent
Diagnostics: sensor fusion for machine tool monitoring; Automated
Inspection: computer vision and methods of automated quality
control; Design for Manufacturing: issues involved in concurrent
Prerequisite: MAE 477 or equivalent, background in
MAE 565 Environmental Acoustics
Introductory course in acoustics and acoustical phenomena.
Fundamentals of vibration (wave motion), general treatment of
string and diaphragm motion, acoustic plane and spherical waves,
transmission and absorption, resonators and filters, speech,
hearing and noise ("noise pollution"), aircraft noise, traffic
noise, effects on man. Laboratory work will consist of individual
experiments, demonstration experiments, and field measurements.
Prerequisite: Permission of instructor.
MAE 566 System Identification
This course covers fundamental systems identification techniques.
Topics covered include: introduction to the identification process;
brief review of mathematical topics necessary for the course;
time-domain approach for identification of linear time-invariant
systems. This will include continuous and discrete time models,
Markov parameters, ARX, ARMA, ARMAX and other models; frequency
domain method; Eigensystem Realization Algorithm; and Kalman
Prerequisite: MAE 571
MAE 568 Vibration and Shock 2
Continuation of MAE 565. Vibration of distributed parameter and
parameter systems; modal testing; nonlinear systems; finite
Prerequisite: MAE 565.
MAE 567 Vibration and Shock 1
Introduction to topics in the analysis of vibrating systems of
lumped parameters. Modal analysis and synthesis. Matrix and
computer procedures. Single degree of freedom free and forced
response. Absorber and isolator design. LEC.
For students who did not take vibrations as an undergraduate.
MAE 570 Thermodynamics of Materials
Review of Classical Thermodynamics using the formalism based on the
Entropy Maximum Postulates; and, an introduction to Statistical
Thermodynamics. Application of the basic principles to the
determination of properties of single and multicomponent systems.
Physical models of atomic and molecular behavior (gas, liquid and
solid states), and electric, magnetic and electromagnetic
phenomena. Stability, phase transitions and critical points.
Chemical reactions, structural changes and surface phenomena.
MAE 571 Systems Analysis 1
Development of mathematical techniques for the analysis of systems
in the time domain. Introduction to state space concepts. Review of
matrices and vectors. Vector spaces. Coordinate transformation.
Jordan canonical form. State-space representation of control
systems. Solutions of state space equations. Controllability and
observability. Feedback control structures. LEC.
Prerequisite: Graduate standing.
MAE 572 Guidance, Navigation and Control
This course introduces the concepts of guidance, navigation and
control (GN&C) of dynamical vehicles. Guidance equipment and
software is first used to compute the vehicle location required to
satisfy mission requirements, navigation then tracks the vehicle's
actual location, and control then transports the vehicle to the
required location. Theoretical foundations are introduced to
perform basic GN&C operations. Topics include: review of
rotational kinematics and dynamics, orbital mechanics, Kalman
filtering, GPS tracking and navigation, attitude and orbit
determination, and advanced GN&C techniques. Examples are given
using spacecraft, aircraft, launch and missile vehicles.
MAE 573 Graphics in Computer-Aided Design
A course emphasizing the basics of computer-aided design (CAD) for
mechanical engineers. Interactive computing in the design process.
The role of graphics in CAD. Two-dimensional graphics; computer
graphic operations, including curve generation and splines.
Three-dimensional graphics, including data structures, rotation,
translation, reflection, isometric and perspective projection,
hidden line removal, shading, surface generation, solid modeling
concepts, object-oriented programming. LEC/LAB.
Computer programming projects in C and C++.
MAE 574 Virtual Reality Applications and Research
Virtual reality refers to techniques used to synthesize real world
by recreating its physical, visual and audio models and
representations. In this course we will study this field and review
various applications and research issues extensively. We will also
learn interactive computer graphics programming techniques using
OpenGL which is a preferred graphics programming API environment.
The following broadly describes the topics: concepts in interactive
computer graphics, programming in OpenGL/GLUT, intro to world tool
kit libraries, virtual reality hardware and software and
application and research in virtual reality.
Prerequisite: MAE 473/573 or equivalent. Students are required to
have good programming knowledge in C or C++. NOTE: This is not an
introductory course in computer graphics.
MAE 575 Kinetics of Materials
The topics to be treated are: diffusion of atoms and molecules in
solids and liquids; motion of dislocations and interfaces;
morphological evolution and phase transformation. Emphasis will be
on kinetic phenomena in crystalline and poly-crystalline materials
driven by gradients of one or more potential (e.g., chemical,
electrical, magnetic, thermal, curvature, etc.). Several atomic
models for diffusion will be considered such as thermally activated
jumping, random walks, and fast diffusion along grain boundaries.
Also to be discussed is the evolution of surface shape under the
influences of capillary and mechanical surface forces
MAE 576 Mechatronic Design
Mechatronic Design will emphasize the theory and practice of
hardware and software interfacing of microprocessors with analog
and digital sensor/actuators. The goal of this course is to enable
the students to learn the theoretical and practical
aspects of hardware and software interfacing of microprocessors
with external devices (circuits/actuators/sensors/ other
microprocessors) to realize mechatronic systems.
MAE 577 Computer-Aided Design Applications
Engineering design and analysis using state-of-the-art computer
software tools. Emphasis on the overall product development cycle
and simultaneous engineering, including conceptual design,
variational geometry, representation, creation and manipulation of
solid models, assembly design integrated kinematic and finite
element analyses, re-design, geometric dimensioning and
tolerancing, and NC programming. LEC/Software component is a part
of this course.
Prerequisite: Permission of instructor.
MAE 578 Cardiovascular Biomechanics
Introduction of the mechanical behavior of the cardiovascular
system; basic physiology; application of engineering fundamentals
to obtain quantitative descriptions; major topics include rheology
of blood, blood flow in arteries and veins, mechanics of cardiac
muscle, contraction of the heart, and control of the circulation.
Prerequisite: First undergraduate courses in fluid and solid
MAE 579 Cerebrovascular Hemodynamics
Introduction to the mechanical behavior of the cerebrovascular
system; application of engineering fundamentals and tools to obtain
quantitative descriptions; major topics include cerebrovascular
anatomy, structure and mechanics, cerebrovascular pathology,
cerebrovascular autoregulation, MRI (brain imaging) MRA (vascular
imaging), and MR Flow measurements. Transcranial Doppler (TCD),
Ultrafast CT, Ultrafast Spiral CT and novel flow measurements.
Intracranial & vascular pressure measurements.
Prerequisite: MAE 478/578
MAE 580 Pulmonary Biomechanics
Introduction of the mechanical behavior of the pulmonary system:
basic physiology; application of engineering fundamentals to obtain
quantitative descriptions; major topics include mechanics of
breathing, air flow in the lung, alveolar ventilation, pulmonary
circulation, alveolar gas exchange, control of respiration.
Prerequisite: First undergraduate courses in fluid and solid
MAE 581 Advanced Materials Science
Crystal structure: lattice and basis, types of lattice, reciprocal
lattice, index system for crystals, polytypism. Crystal binding:
Van der Waals, Covalent, ionic, and metallic, equilibrium lattice
constants. Deviation from ideal crystal structure: point, line and
planar defects, point defects in ionic crystals, equilibrium point
defect density. Effect of defects on material properties: structure
sensitivity. Phases in a n-component system: phase and phase
diagrams for a n-component systems, phase equilibrium, phase rule,
ideal and non-ideal solid solutions and derivation of their free
energy, level rule, ordered and disordered phases, superlattices.
Nucleation and growth: embryo and nucleus during phase growth and
resulting microstructure. Phase transition: first and second order
phase transition, diffusionless and diffusion-assisted phase
transitions. Concept of degenerate variants: twins as domains in a
phase transition and their effect on mechanical properties,
twin-equivalent phase inferromagnetic and ferroelectric phases,
domains as basis for functional materials. LEC
Prerequisites: MAE 381, or equivalent.
MAE 582 Introduction to Composite Materials
Provide a basic understanding of polymeric, metallic, and ceramic
composite materials - manufacturing and mechanical properties.
Behavior of unidirectional and short fiber composites; analysis of
laminated composites; performance of composites including fracture,
fatigue and creep under various conditions; fracture modes of
composites; manufacturing considerations; microstructural modeling;
experimental characterization. LEC-Fall.
MAE 583 Mechanics and Design Using Composite
An advanced level of structural analysis and design, with an
emphasis on composite materials; general anisotropic
stiffness/compliance relations, their transformations and
symmetries; effective properties for sheet/injection molded
composites; lamination theory; simplified plate and beam equations,
with solutions for deformation and stress; strength, fracture and
reliability; joining; other topics as time permits. A limited
review of materials concepts is given as needed. Includes use of
available computer methods. LEC
MAE 584 Principles and Materials for
Micro-Electro-Mechanical Systems (MEMS)
Current interest in micro-electro-mechanical systems of MEMS is
driven by the need to provide a physical window to the
micro-electronics systems, allowing them to sense and control
motion, light, sound, heat, and other physical forces. Such
micro-systems that integrate micro-electronics and sensing elements
on the same chip presents an interesting engineering problem in
terms of their design, fabrication, and choice of materials. This
course will address the design, fabrication, and materials issues
involving MEMS. These issues will be addressed within the context
of MEMS for mechanical sensing and actuation, magnetic devices,
thermal devices, automotive applications, and Bio-MEMS for
biomedical applications. LEC
MAE 585 Mechanical Properties of Materials
Relationship between the microstructure of materials and their
macroscopic properties; topics include strength and modulus,
hardness, fatigue, creep and plasticity, abrasion, impact,
elasticity, thermal stresses, strengthening mechanism, and testing
MAE 586 Fatigue and Fracture Mechanics
Failure by fatigue or brittle fracture of such important structures
as bridges, aircraft, ships, pressure vessels, etc., is of grave
consequence. Many design codes require safety against such
failures. Topics include fatigue strength of plain or notched
specimens and factors affecting it; low cycle fatigue; fatigue
under variable amplitude loading; fatigue of welded structures;
linear elastic stress analysis of cracks; fatigue crack growth
under constant or variable amplitude loading. Introduction to
elastic-plastic fracture mechanics. Also listed as CIE 586.
Prerequisite: MAE 311.
MAE 587 Modern Theory of Materials
Fundamentals of modern theories of solids are developed. Topics
include reciprocal lattices, diffraction theory, electron energy
bands and phonon dispersion. LEC.
MAE 588 Materials Applications
This course covers structural, electronic, thermal, electrochemical
and other applications of materials in a cross-disciplinary
fashion, due to the multifunctionality of many materials and the
breadth of industrial needs. The materials include metals,
ceramics, polymers, cement, carbon and composite materials. The
topics are scientifically rich and technologically relevant. Each
topic is covered in a tutorial and up-to-date manner.
Prerequisite: MAE 381.
MAE 589 Experimental Methods in Materials Science and
This lecture course will cover experimental methods in materials
science and engineering. These methods will relate to the
characterization of material structures (using spectroscopy,
microscopy and diffraction techniques), material properties
(mechanical, thermal, electrical, electrochemical, etc.) and
material processes (phase transformations, reactions, diffusion,
etc.). Illustrations will be made using materials including metals,
ceramics, polymers, carbons, semiconductors and composites.
MAE 590 High Temperature Materials
Ceramics, carbons, metals and composite materials for high
temperature applications (including aerospace applications) will be
covered, with emphasis on ceramics and the relationships among
processing, structure, properties and applications. LEC.
Prerequisite: MAE 381 or CE 433/534 or permission of
MAE 592 Experimental Methods for Composite
Brief review of appropriate analytical methods for thermoelastic
and strength properties of laminated and short fiber composites;
experimental evaluation of these properties, emphasizing the
methods unique to composites; specimen preparation and testing
using suitable fixtures, mechanical testing machine, and data
acquisition system. LEC/LAB.
Prerequisite: Permission of instructor; Spring (odd-numbered
MAE 593 Mathematical Methods in Robotics
This course introduces students to the basic mathematical and
computational tools for modeling, analysis and control of different
types of robotic systems. The course examines both the creation of
a sound theoretical framework rooted in rich traditions of
mechanics and geometry and application of this framework in the
context of serial-chain and parallel-chain manipulators, and
wheeled mobile robots (and hybrid combinations of these
MAE 595 Frontiers of Engineering Materials
Designed to provide the students with a broad perspective in the
frontiers of engineering materials. Each engineering material (or
class of materials) covered is at the frontier of technology.
Selections include metals, ceramics, polymers and composite
materials. The processing, structure, properties and applications
of each material are addressed. LEC
MAE 601-602 Individual Problems (1-12 credits)
For Doctor of Philosophy candidates. TUT.
MAE 609 High Performance Computing I
This course will introduce students to the fundamental ideas of
scientific computing on high performance architectures. The
principal objective of this course is to enable students to use
high performance computers in all aspects of scientific computing
to support research activities. At the end of the class, you should
be able to: design and implement efficient algorithms for high
performance computing related to a variety of research areas, use
MPI, OpenMP and other special tools used to program larg e
multi-processor computers, understand the basic operating
principles of these machines, and, analyze the performance of your
MAE 610 High Performance Computing II
Introduction to fundamental ideas of scientific computing, with
particular attention given to algorithms that are well-suited to
high performance computer architectures. Concentration on
scientific computing in applications, including stochastic methods,
FFTs, and finite element and finite difference methods. LEC
Prerequisite: MAE 609
MAE 617 Inviscid Incompressible Flow
Kinematics of fluid motion, stream function. Irrotational flow,
velocity potential. Rotational flow, vortex motion. Kinematics of
fluid flow, equations of motion, Bernoulli's theorem. Boundary
conditions. Momentum integral and energy integral methods. Fluid
forces, Blasius theorem, virtual mass. Method of singularities,
images, analytical solutions, conformal transformation, approximate
Prerequisite: MAE 515 and 516
MAE 618 Viscous Flow
Review of Navier-Stokes equations, classical solutions. Stokes flow
over spheres, bodies of arbitrary shape. Singularity Methods,
effects of Brownian motion. Unsteady viscous flows, acoustic
streaming. Stability of viscous flows. Triple-deck structur e,
transformation methods for boundary-layer flows. LEC.
Prerequisite: MAE 515 and 516
MAE 630 Finite Element Vibration Analysis
This course is designed for advanced graduate students with
interest in the field of vibration analysis and finite element (FE)
method. The main focus of this course is FE modeling and analysis
of vibrating systems, and checking the accuracy and validity of FE
results. Topics include brief review of vibration analysis,
Hamilton's principle and Lagrange's equations of motion, element
energy functions, FE analysis for basic structural elements (axial
vibration of rod, torsional vibration of shaft, and bending
vibration of beams), in-plane vibration of plates, flexural
vibration of plates, reduced order system (Guyan-Irons reduction,
component mode synthesis), damping (viscous damping, structural
damping, proportional damping, non-proportional damping), and
numerical solution procedures.
Pre-requisites for this course are the sound knowledge of stress,
deformation, strain, elastic constitutive equations, formulation
and solution of static boundary value problems including axial,
bending, torsion, plane strain and plane stress. Familiarity with
single- and multi-degree of freedom systems for dynamic problems
will also be very useful.
MAE 631 Compressible Flow
Governing equations for inviscid compressible flow of perfect
gases; wave phenomena in one-dimensional unsteady flows; basic
approximations and applications for steady flows in the subsonic,
transonic, supersonic, and hypersonic regimes, including flow
similitudes, imperfect gas effects at hypersonic speeds; viscous
and aerodynamic heating effects, including compressible laminar
boundary layers and shock-wave boundary layer interactions.
Prerequisites: MAE 516 and PHD status.
MAE 660 Dissertation (1-12 credits)
For Doctor of Philosophy candidates. TUT
MAE 670 Nonlinear Control
The focus of this course is on nonlinear system analysis, and
synthesis of nonlinear controllers. This includes: phase plane
analysis for second order systems, Lyapunov direct method to
analyze autonomous and non-autonomous systems, describing function
method to analyze nonlinear systems. The design of controllers
robust to structured and unstructured uncertainties include:
sliding mode controller adaptive controllers, and feedback
linearization control. LEC
MAE 672 Optimal Control Systems
Parametric optimization. Variational methods in system
optimization. Hamiltonian function. Dynamic programming. Pontryagin
Maximum Principle. Synthesis of linear optimum control systems.
Nonlinear optimum control systems. LEC.
Prerequisite: MAE 571.
MAE 671 Nonlinear Systems
A first course in the theory of nonlinear dynamical systems. Topics
included are: point attractors, limit cycles, linear and nonlinear
resonance, Poincare map, self exciting system, chaotic attractors
in forced oscillators, stability and bifurcations, Liapunov
stability and structural stability, center manifold theorem, local
bifurcations, incipient instability, iterated maps and their
stabilities, the geometry of recurrence, the Lorenz system, Lorenz
attractor, transition to chaos, Rossler's band, Smale's horseshoe
map, homoclinical trajectories, bifurcations and chaotic
Prerequisite: Graduate standing.
MAE 673 Vibration Control of Slewing Structures
Review of modeling of lumped parameter systems,
eigenvalue/eigenvector analysis, response of underdamped systems.
Prefilter design for vibration control of point-to-point motion of
vibratory systems. Introduction to the concept of sensitivity and
robust prefilter design. Minimax prefilter design for robust
vibration control. Review of LQR for vibratory systems. Review of
optimal control and its application to the design of time-optimal,
fuel/time optimal, jerk limited time-optimal controllers for
rest-to-rest maneuvers of flexible structures. Design of robust LQR
controller. Numerical techniques for prefilter design. Design of
rest-to-rest motion controllers for vibratory systems subject to
MAE 674 Optimal Estimation Methods
Introduction to linear and nonlinear estimation methods with
emphasis on both theory and implementation. Batch and sequential
strategies, real-time and post-experiment estimation are covered.
Includes both parameter estimation and state estimation. LEC
Prerequisite: Some exposure to linear systems, probability, and
optimization is helpful, or permission of instructor.
MAE 675 Multi-Resolution Approximation Methods
An advanced level course on mathematical modeling of dynamical
systems: multi-resolution analysis, local vs. global approximation,
curse of dimensionality, polynomial approximants; partition of
unity; finite element methods; radial basis functions; and their
applications in dynamical system identification, motion planning
and modern control. The emphasis of this course will be on an
intuitive understanding of the subject and practical applications
of various approximation methods so that students should be able to
apply the discussed methods to real engineering problems with the
awareness of potential difficulties that might arise in practice.
This course would cover topics from basic polynomial approximations
to wavelet analysis to adaptive control to neural network to
recently developed partition of unity approximation algorithms at a
level of detail compatible with the design and implementation of
modern control systems. These diverse topics will be covered in an
integrated fashion, using a framework derived from dynamical
systems, estimation, optimization, and approximation theory. The
formulation and case studies in this course will focus on
demonstrating, through analysis, simulation, and design, the
applicability and feasibility of a substantial set of recent
developed approximation ideas to a rich set of examples. The
reliability and limitations of the approximation methods discussed
will be assessed by considering various academic and engineering
problems. Issues related to modeling of large-scale dynamical
systems like dimensionality, quality of the measurement data,
offline or online learning, approximation accuracy, the computation
time associated with the model, complexity of the mathematical
model and efficiency of the learning algorithm will be discussed in
MAE 680 Stochastic Filtering & Control
This is an advanced level graduate course with emphasis on theory
of stochastic processes and its applications in engineering,
finance and statistics. The objectives are to develop a fundamental
understanding of stochastic processes and its applications in the
area of filtering and control of dynamical systems, to develop an
appreciation for the strengths and limitations of state-of-the-art
numerical techniques for nonlinear filtering and control problems,
to reinforce knowledge in stochastic systems with particular
emphasis on nonlinear and dynamic problems, and to learn to utilize
stochastic system analysis methods as research tools. Topics
include continuous and discrete time random processes; spectral
representation; Karhunen-Lo eve Expansion, Martingales, Poisson
Processes, Markov processes; It^o calculus; Stratonovich Integral;
Kolmogorov equation; linear and nonlinear filtering methods;
stochastic optimal control and Hamilton-Jacobi-Bellman
MAE 698 Random Matrix Theory and Its Applications
Random matrix theory (RMT) has been successfully used in a diverse
field of applications leading to many new modeling concepts and
novel parameter estimation techniques. This helps better
characterization of uncertainty in complex systems. The course is
designed for advanced graduate students and will start by briefly
reviewing the measure-theoretic probability covering random
variable (RV), random vector, and simulation of RV. It will then
focus on the main topics of the course that includes Jaynes'
maximum entropy (MaxEnt) principle, solving MaxEnt optimization
problem, concept of random matrix, Gaussian
orthogonal/unitary/symplectic ensembles, matrix-variate normal
distribution, Wishart distribution, matrix-variate beta
distribution, matrix-variate Kummer-beta distribution, simulation
of random matrix, and application to some problems of interest (if
Pre-requisite is the course on "Probability Essentials and
Applications" described earlier.