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. A list of regularly scheduled classes can be found in the appendix A of the Graduate Manual.

**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 departmentchair.**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. SEM.**MAE 505 SP TP: Probability Essentials and Applications**

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 sampling.

Pre-requisites for this course are working knowledge of multivariate calculus, basic knowledge of optimization theory, and programming skills**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. LEC.**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 fluid mechanics.**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, and turbines.**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 determination.**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 composition. LEC.**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 Dynamics**

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. LEC.**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 Dynamics**

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 required.**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.

No prerequisite.**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. LEC.

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 prerequisite.**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. LEC.**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 performance.**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 formulations. LEC.**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. LEC.**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 product development.

Prerequisite: MAE 477 or equivalent, background in manufacturing.**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. LEC.

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 filters.

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 elements. LEC.

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. LEC**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. LEC.

Prerequisite: First undergraduate courses in fluid and solid mechanics.**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. LEC.

Prerequisite: First undergraduate courses in fluid and solid mechanics.**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 Materials**

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 methods.**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. LEC.

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 Engineering**

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 instructor.**MAE 592 Experimental Methods for Composite Materials**

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 years)**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 systems).**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 codes.**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 methods. LEC.

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 attractors. LEC

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 friction. LEC.**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 detail. LEC.**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 equation.**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 time permits).

Pre-requisite is the course on "Probability Essentials and Applications" described earlier.