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 the direction of a member of the graduate faculty. TUT. Prerequisite: Permission of instructor and approval of the department chair.**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. LEC.**MAE 507 Engineering Analysis I**

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 II**

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 fundamental 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 from instructor.**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. LEC.

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.**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. LEC.**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 Musculoskeletal Biomechanics**

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.**MAE 521 Sustainable Manufacturing**

The course is designed for engineering undergraduate/graduate students who are interested in furthering their knowledge in green engineering techniques. The approaches presented in this class are from the levels of manufacturing, machine and systems, as well as the overall product lifecycle and supply chain perspective. The main goal of this course is to help students understand the importance of green and sustainable manufacturing. The course will discuss some practical aspects of sustainability and green engineering with students and encourage them to look at the processes and systems around them more carefully and think about opportunities to improve, reuse, replacement and reduction of the environmental impacts of the processes, systems, and behaviors. LEC.**MAE 524 Elasticity 1**

Introduction to Cartesian tensors; deformation, stress, constitutive relations for linear elasticity; formulation of boundary value problems; variational principles; torsion and bending of rods; plane problems. 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. LEC.**MAE 526 Orbital Mechanics**

This course covers the fundamentals of orbital mechanics, focusing on the positional motion of spacecraft. Topics include: review of the two-body problem, Kepler’s problem, Lambert’s problem, orbit in space, orbital transfers, interplanetary trajectories, the three-body problem, and orbital perturbations. Applications and advanced topics will be also discussed. The course presents and tackles problems both in analytical and numerical ways. LEC.**MAE 528 Decision-Based System Design**

The course is designed for engineering graduate students who are interested in furthering their knowledge in decision making methods during engineering design process. This course emphasizes on the role of uncertainty in engineering design and reviews different approaches to decision-based design through discussing the strengths and weaknesses of each approach. Various topics including Robust Design, Suhs Design Axioms, Multi-Attribute Utility Theory, Discrete Choice Analysis, Simulation-based Approaches, and Analytical Techniques for Modeling Consumer Preferences and Choices will be discussed in this course. Moreover, this course discusses the challenges that decision makers irrationalities and cognitive biases can bring into the design process. LEC.**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 Renewable and Alternative Energy**

To understand the renewable and alternative energy resources, and their sustainable usage. We will apply the basic energy laws to evaluate various renewable and alternative energy, and sustainability, including renewable energy: solar, wind, hydrothermal, ocean, biomass, etc. LEC.**MAE 532 Advanced Thermodynamics**

This course is a continuation of thermodynamic theories with applications in energy systems. Included are fundamental concepts on exergy, mixtures, psychrometry and thermochemistry. Analyses and applications will include vapor and gas power systems, refrigeration, air conditioning, and combustion processes. This course is dual-listed with MAE 432. LEC.**MAE 533 Heating, Ventilation, and Air Conditioning Theory and Design**

The objective of this course is to provide technological background and design skills in heating, ventilating and air-conditioning (HVAC). Included are fundamentals of refrigeration, psychrometrics, air conditioning processes, building load calculations, design and analysis of HVAC systems, equipment selections, air handling. This course is dual listed with MAE 433. LEC.**MAE 534 Combustion 1**

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 of 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. This course covers the principles of material design, with emphasis on the interplay among processing, structure, properties and applications. The design is illustrated with materials that are relevant to applications. LEC.**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 537 Modal Analysis****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 Computational Fluid Dynamics 1**

This course is intended for seniors and beginning graduate students interested in computer based analysis of engineering problems in fluid mechanics and heat transfer. Students need not have a graduate level background in fluid mechanics or heat transfer, however, an undergraduate level is necessary. The general governing equations of fluid mechanics and heat transfer and methods to solve them, that will mainly focus on finite-difference and finite-volume methods. Topics on the classification and analysis of these methods are examined with application to conduction heat transfer, convection and laminar mixing problems. The overall objective of this course is to provide the student with a firm understanding of the fundamentals of CFD employed in many commercial packages and an introduction to computer tools for analysis and graphical representation of results. LEC.**MAE 540 Computational Fluid Dynamics 2**

In many areas of fluid/thermal sciences the use of computational fluid dynamics (CFD) has become an essential tool for both fundamental understanding and design of complex engineered systems. It is beneficial if the student complete an introductory course on CFD (such as MAE 539). The general governing equations of fluid mechanics and heat transfer and methods to solve them, will be presented. Topics on the classification and analysis of these methods are examined with application to conduction heat transfer, convection and laminar mixing problems. The overall objective of this course is to provide the student with a firm understanding of the fundamentals of CFD techniques. LEC.**MAE 541 Topics Finite Element**

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. LEC.

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/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 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. LEC.**MAE 550 Optimization in Engineering Design**

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. LEC.**MAE 551 Advanced Design Theory****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. 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. LEC.**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. LEC.**MAE 556 Numerical Modeling of Moving Interfaces**

An applied numerical methods to model systems with moving interface, such as multiphase fluid problems, image sementation, path planning, and self-assembly. LEC.**MAE 557 Introduction to Combustion Diagnostics and Spectroscopy**

This course aims to provide fundamental understanding of spectroscopy and laser diagnostics for combustion application. The course will also cover introductory physical gas dynamics to familiarize you to the concept of statistical mechanics. LEC.**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 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. LLB.

Prerequisite: MAE 477 or equivalent, background in manufacturing.**MAE 565 Acoustics & Wave Propagation**

This course introduces fundamental concepts of engineering acoustics and reviews acoustic wave equations, the dynamics of acoustic resonators, and wave propagation phenomena including radiation, absorption, and transmission of sound from and through simple structures. Acoustic measurement techniques, prediction methods, and design tools for noise control and acoustical system design in practice will be presented. The course also reviews wave dispersion and elastic wave propagation in 1D structures, with applications to phononic systems and acoustic metamaterials. LEC.**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. LEC.**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. For students who did not take vibrations as an undergraduate. LEC.**MAE 568 Vibration and Shock 2**

Continuation of MAE 565. Vibration of distributed parameter and parameter systems; modal testing; nonlinear systems; finite elements. LEC.**MAE 569 Flow Estimation and Control**

This course introduces methods for low-order and reduced-order modeling of fluid flows for the purposes of estimation and control. Basic estimation theory as well as linear control methods are presented are presented for estimation and interaction with the flows through sensor and actuator models. Relevant systems theory tools such observability and controllability aid in optimal and actuator placement. Examples are drawn from aerodynamic applications; however, the conceptual tools are directly applicable across other fluid-flow systems, including internal and external flows in various flow regimes, as well as physical length scales. LEC.**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**

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.**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. LEC.

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. LEC.

Pre-Requisite: MAE 570 or permissions of instructor.**MAE 576 Mechatronics**

Studies the theory and practice of hardware and software interfacing of microprocessors with analog and digital sensor/actuators to realize mechatronic systems. Coverage includes microprocessor architectures, programming, digital and analog circuits, sensors, actuators, communication protocols, and real-time and operator interface issues as applicable to the design and implementation of simple mechatronic subsystems.**MAE 577 CAD Applications**

This course will cover basic concepts and building blocks of geometric transformations and modeling theory that underlie many CAD software tools and computational geometry-related problems. LLB.**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 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**MAE 582 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.**MAE 584 Principles and Materials for (bio) Micro-Electro-Mechanical Systems (MEMS)**

Introduces advanced technologies that enable integration of micro-sensors and micromechanical components on the same chip to produce miniature devices called micro electromechanical systems (MEMS). The course covers physical principles and design rules that govern the performance of a device at small length scales. Discuss a large set of microfabrication techniques including photolithography, material removal processes, and additive technologies. Discuss the applications of MEMS devices in automotive, communication, energy, and BioMEMS in 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. LEC.**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 589 Materials Experimental Methods**

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. This course is dual-listed with MAE 489. LEC.**MAE 593 Robotics I**

The objective of this course is to provide working knowledge required to formulate and analyze problems in robotic systems design. This course will also provide methodologies for solutions to such formulated problems. Comprehensive skill level will be reached through basic topics such as: a) Kinematics, b) Inverse Kinematics, c) Computation of the Manipulator’s Jacobian, d) Newton-Euler Formulation of Equations of Motion,e) Lagrange’s Formulation of Equations of Motion and f) Control. This course is dual-listed with MAE 493. LEC.**MAE 594 Robotics II: Collaborative Robotics**

The objective of this course is to provide working knowledge required to formulate and analyze problems related to the application of collaborative robots. This course will also provide methodologies for solutions to such formulated problems. This course is dual-listed with MAE 490. LEC.

Pre-Requisite: MAE 593.**MAE 598 Graduate Internship**

For use by graduate students requiring academic credit for practical training. TUT.**MAE 601 Individual Problems (1-12 credits)**

For Doctor of Philosophy candidates. Individual problems/research on topics as determined by students working individually with a faculty member. See department and/or advisor for additional information. TUT.**MAE 607 Biomaterials Science Cell-Surface**

LEC.**MAE 608 Polymeric Biomaterials**

LEC.**MAE 609 High Performance Computing I**

The first semester of a two-semester course sequence that will introduce students to the fundamental concepts of scientific computing, with particular attention given to algorithms that are well-suited to high performance computer architectures. The first semester will concentrate on computational linear algebra, including iterative and direct methods for solving linear systems and for eigenvalue problems, and the use of BLAS and other public domain libraries. This course is equivalent to CDA 609, CSE 547, CE 620, MTH 667, PHY 515, and GLY 609. LEC.**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**MAE 618 Biotransport and Biofluid Mechanics**

Transport processes in microscopic living systems are often characterized by low Reynolds and low Peclet numbers, which differ significantly from how we perceive and experience in our daily lives. This course aims to provide a fundamental understanding of how diffusion and viscous effects influence ways in which various biological systems operate, e.g., how microorganisms move around, how they sense their surroundings, how they uptake nutrients, and how they encounter prey/predator. The emphasis of the course will be on the application of physical and fluid dynamical principles to life at the microscale, in particular to aquatic systems. Topics include diffusion, receptors, bacterial random walk, chemotaxis, Stokes flow, hydrodynamic dispersion, hydrodynamic sensing, flagellar propulsion, and resistive force theory. LEC.**MAE 631 Advanced Gas Dynamics**

Kinetic theory; 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. LEC.

Prerequisites: MAE 515.**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 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.**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.**MAE 673 Vibration Control of 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 676 Data Assimilation**

The Data assimilation (DA) course is an advanced level graduate course with focus on forecasting for large scale dynamical systems such as weather, tsunamis, epidemics, etc. i.e., any spatio-temporally varying dynamical system. The objectives are to develop a fundamental understanding of integrating measurement data with model data accounting for uncertainties in both the sources of data. Topics included in this course include: Review of linear and non-linear least squares; Tikhnov regularization and systematic approaches for the selection of the regularization parameter such as the L-curve and Mazarov’s approach; Total least squares, variable projection least squares, adjoint approach for determining gradients for optimization; 3Dvar, Kalman Filter, Extended Kalman Filter, Reduced Rank Filters such as Ensemble Kalman Filter, and Local Ensemble Kalman Filter. LEC.

Pre-Requisite: MAE 571.**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. LEC.**MAE 698 Random Matrix Theory - Applications Mechanics**

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). LEC.

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