16:650:504 Mathematical Methods in Engineering: Advanced Controls I (3) An entry-level graduate course in linear control system design. Selected topics in both input/output and state space representation of linear systems including equilibrium and stability theory for linear systems, state feedback control system design, observability and controllability of linear systems, linear quadratic (LQ) optimal control, and the Kalman filter.� Extensive use of the MATLAB/Simulink will be expected.

16:650:505 Mathematical Methods in Engineering (3) Review of matrix algebra; numerical methods for inversion; ordinary differential equations; functions of a complex variable; calculus of variations; partial differential equations and their classification; Fourier methods; asymptotic and perturbation methods. Prerequisites: Undergraduate calculus and differential equations.

16:650:510 (F) Computer-Aided Design (3) Broad introduction to computer-aided design and modeling. Mathematical representations of curves, surfaces, and solids. Two- and three-dimensional computer graphics. Programming required for design projects. Prerequisite: Permission of instructor.

16:650:512 Robotics and Mechatronics (3) Introduction to robotics and mechatronics, including mechanisms and control theories as well as applications; manipulator mechanics; design considerations; control fundamentals; model and sensor-based control algorithm development; walking robots; medical and space robotics; experimental mechatronics. Prerequisites: Undergraduate vibrations, controls, and dynamics.

16:650:514 Design of Mechanisms (3) Complete mechanism design cycle: synthesis, analysis, and redesign; analytical, numerical, and visualization techniques applied to mechanism synthesis (type, number, and dimensional) and analysis; application of optimization methods in the design cycle; planar and spatial mechanisms. Prerequisite: Undergraduate kinematics of mechanisms or equivalent.

16:650:522 (S) Analytical Dynamics (3) Newtonian mechanics, rotating frames, variational principles, Lagrange's equations, Hamilton's equations, Euler angles, Euler equations, and gyroscopic motion. Prerequisite: Graduate standing in mechanical/aerospace engineering.

16:650:524 Optimal Design in Mechanical Engineering (3) Formulation and solution of engineering optimal design problems in mechanical engineering. Introduction to algorithms for constrained and unconstrained searching. Application to optimal design of mechanical and structural components. Use of discretization techniques; shape optimization problem.

16:650:530 Fluid Mechanics I (3) Physical properties of fluids; basic equations of motion; kinematics; exact solutions of the Euler and Navier-Stokes equations; incompressible boundary-layer equations and applications; flow past bodies, jets, and wakes; introduction to turbulent flows. Prerequisite: Undergraduate fluid mechanics.

16:650:532 Experimental Methods in Fluid Mechanics (3) Experimental and analytical data tools needed by fluid experimentalists, data acquisition, measurements, model building, optical diagnostics, and visualization. Prerequisite: Undergraduate fluid mechanics.

16:650:534 Computational Fluid Mechanics (3) Development and application of computational methods for fluid mechanics based on the incompressible and compressible Navier-Stokes equations, boundary-layer equations, and Euler equations. Selected algorithms, including finite difference, finite volume, and special techniques. Applications chosen from incompressible and compressible flows. Prerequisites: Undergraduate fluid mechanics and thermodynamics.

16:650:550 Mechanics of Materials (3) Theories and methods for evaluating stresses and deformations of mechanical components and structures under static and dynamic loading. Prerequisite: Undergraduate solid mechanics.

16:650:554 Mechanics of Continuua (Solid Mechanics I) (3) Introduction to the fundamental concepts of continuum mechanics, including stress and strain, kinematics, balance laws, and material symmetry. Theories of elasticity, plasticity, fracture, viscoelasticity, and classical fluid dynamics. Prerequisites: Undergraduate mechanics and engineering mathematics.

16:650:556 Theory of Elasticity (Solid Mechanics II) (3) Classical theory of linear elasticity. Equations of equilibrium; plane stress; plane strain; Airy stress function; torsion; energy theorems; solutions of selected classical problems. Prerequisite: 16:642:527 or equivalent. Corequisite: 16:642:528.

16:650:570 Conduction Heat Transfer (3) Analytical methods in steady and transient heat conduction in solids; finite difference methods in heat conduction. Prerequisite: Undergraduate heat transfer.

16:650:574 Thermodynamic Theory (3) Principles and methods of thermodynamics, including classical, statistical, and irreversible thermodynamics. Prerequisite: Undergraduate thermodynamics.

16:650:578 Convection Heat Transfer (3) Forced and free convection in laminar and turbulent flows; mass transfer; applications. Prerequisites: Undergraduate heat transfer; 16:650:530 or equivalent.

16:650:582 Computational Heat Transfer (3) Development and application of computational methods for conduction; natural, forced, and mixed convection; radiation; traditional and recent conjugate heat transfer; and mass transfer. Selected algorithms include finite difference, finite volume, finite element, and spectral techniques. Applications chosen from thermal energy systems, environmental heat transfer, microelectronics packaging, materials processing, and other areas. Prerequisites: Undergraduate fluid mechanics and thermodynamics.

16:650:601,602 Independent Study (3,3) Independent studies or investigations in a selected area of mechanical and aerospace engineering. The instructor prepares a syllabus on the subject being studied for the student's file. Prerequisites: Permission of instructor and graduate program director.

16:650:606 (S) Renewable Energy: Solar, Wind, Fuel Cell, and Gas-Fired Systems (3) Fundamentals of renewable, gas-fired, and alternative energy systems. Cook-Chennault

16:650:608 Mechanical Engineering Colloquium (1) Lectures by invited speakers on current research topics in mechanical and aerospace engineering. Prerequisite (for credit): Ph.D. candidacy in mechanical and aerospace engineering.

16:650:618 Special Applications in Control (3) Introduction to recently developed concepts in control theory and their application in real-life problems. Topics include robust and optimal control (H2, H-infinity, and advanced LQR control techniques), neural networks, and system identification. Prerequisites: Graduate background in mechanical control systems and vibration and 16:650:504.

16:650:630 Fluid Mechanics II (3) Vortex dynamics of incompressible inviscid and low-viscosity fluids. One-, two-, and three-dimensional compressible flows. Linear, nonlinear, acoustic, and gravity waves; shock waves using shock polars. Stability of viscous and inviscid vortex, wave, and boundary-layer flows. Special topics include accelerated flows: Rayleigh-Taylor and Richtmeyer-Meshkov for supersonic combustion and inertial confinement fusion; visualization and quantification of evolving flows; and turbulent scaling laws. Prerequisite: 16:650:530 or equivalent or permission of instructor.

16:650:631 Fluid Mechanics III (3) Waves, low Reynolds number flows, stratified and inviscid flows. Prerequisite: 16:650:630.

16:650:634 Compressible Flows (3) Linear and nonlinear theory of one-dimensional inviscid unsteady motion, compression and expansion waves, shock-tube and wave interactions; two-dimensional inviscid steady motions, including linearized subsonic and supersonic flows; boundary-layer theory of compressible fluids. Prerequisite: 16:650:630 or equivalent.

16:650:652 Composite Materials, Fracture Mechanics, and Thermoelasticity (Solid Mechanics IV) (3) Composite materials: anisotropy, elastic constants, stress-strain averages, energy principles, bounds, and micromechanics models. Basic principles of fracture mechanics: mechanisms of fracture and crack growth, energy-release rates, complex stress functions, stress intensity, fracture criteria, mixed-mode fracture, and dynamic fracture. Thermoelasticity: linear-coupled theory, uncoupled theory, solution of selected applied problems involving heat and deformation, and application to composite and advanced materials. Prerequisites: 16:650:554, 556.

16:650:654 Dynamics of Solids and Structures (Solid Mechanics VI) (3) Review of multidegree of freedom vibration. Vibration of continuous systems: strings, beams, membranes, and plates. Vibration and waves. Waves in beams and plates. Bulk elastic waves. Reflection and transmission, Rayleigh surface waves, and ultrasonics. Additional topics, such as random vibration, as time permits. Prerequisites: Undergraduate course in mechanical vibration and 16:650:550, 554, and 556.

16:650:660 Computational Solid Mechanics (3) General theory, application of finite element methods to the solutions of the equations of elasticity, viscoelasticity, and plasticity. Two- and three-dimensional linear and nonlinear, static, and dynamic problems. Working computer programs. Prerequisite: 16:650:554.

16:650:670 Combustion (3) Fundamentals of combustion processes; premixed flames, diffusion flames, one-dimensional gas dynamics, and thermal explosion theory. Prerequisites: Undergraduate thermodynamics and fluid mechanics.

16:650:674 Radiation Heat Transfer (3) Theory of radiant heat transfer; characteristics of ideal and real systems; radiant energy exchange with and without a participating medium; analytical numerical experimental techniques; gray and nongray system analysis. Prerequisite: Undergraduate heat transfer.

16:650:692 Seminar in Mechanical and Aerospace Engineering (1)

16:650:699 Nonthesis Study (N1)

16:650:701,702 Research in Mechanical and Aerospace Engineering (BA,BA) By arrangement with adviser.