# Viterbi School of Engineering

## Aerospace and Mechanical Engineering

### Courses of Instruction

###### Aerospace and Mechanical Engineering (AME)

The terms indicated are *expected* but are not *guaranteed*. For the courses offered during any given term, consult the *Schedule of Classes*.

**AME 101L Introduction to Mechanical Engineering and Graphics (3, Fa)** Gateway to the bachelor of science degree in mechanical engineering. Introduction to mechanical engineering disciplines and practice; graphical communication and layout of machine parts; introduction to computer-aided drafting and drawing.

**AME 105 Introduction to Aerospace Engineering (4, Fa)** Gateway to the Aerospace Engineering major. Introduction to flight vehicle performance and propulsion. Elements of the physics of gases. Laboratory: computers and graphics; model rocket and glider test flights.

**AME 150L Introduction to Computational Methods (4, Sp)** Computer programming; organization of problems for computational solution; introduction to software for computation and graphics; applications to engineering problems. *Corequisite: *MATH 125.

**AME 201 Statics (3, FaSp)** Analysis of forces acting on particles and rigid bodies in static equilibrium; equivalent systems of forces; friction; centroids and moments of inertia; introduction to energy methods. *Prerequisite: *MATH 125; *recommended preparation:* AME 101, PHYS 151*L*.

**AME 204 Strength of Materials (3, FaSp)** Stress, strain and deflection of mechanical elements due to tension, shear, bending, or torsion; combined loads; energy methods, statically indeterminate structures; strength-based design. *Prerequisite: *AME 201 or CE 205.

**AME 222 Fundamentals of Audio Engineering (3, Fa)** (Enroll in EE 222)

**AME 231L Mechanical Behavior of Materials (3, Sp)** Material properties of metals, ceramics, and composites; stress-strain relationships; microstructural characteristics; fracture, fatigue, and creep; effects of processing. *Corequisite:* AME 204.

**AME 261 Basic Flight Mechanics (4, Sp)** Performance of flight vehicles; maximum speed, rate-of-climb, range, and endurance; basic stability and control, weight, and balance; computer exercises. *Recommended preparation:* AME 150*L*.

**AME 291 Undergraduate Design Projects I (1, max 4, FaSp)** Analysis, design, fabrication, and evaluation of devices intended for entry in local and national design competitions. Intended for lower division students or those with little prior project experience. Graded CR/NC.

**AME 301 Dynamics (3, FaSp)** 2-D and 3-D kinematics and dynamics of particles and rigid bodies; systems of particles and rigid bodies; coupled rigid bodies; introduction to vibrations. *Prerequisite: *AME 201 or CE 205; *recommended preparation:* PHYS 151*L*.

**AME 302 Dynamic Systems (3, FaSp)** Modeling of lumped parameter elements and systems; free and forced response of first and second order systems; design oriented approach to dynamic systems. *Prerequisite:* MATH 245; *recommended preparation:* AME 309 or CE 309; AME 301 or CE 325.

**AME 303 Dynamics of Machinery (3, FaSpSm)** Kinematics and dynamics of machines; balancing of rotating and reciprocating machinery; gyroscopic effects; critical speeds; energy variation in machinery; introduction to mechanism design. *Prerequisite: *AME 301 or CE 235.

**AME 305 Mechanical Design (3, Fa)** Design and analysis of mechanical elements including shafts, bearings, springs, screws, belts and gears; strength, fatigue and deflection considerations in machine design. *Prerequisite: *AME 204 or CE 225.

**AME 308 Computer-Aided Analyses for Aero-Mechanical Design (3, FaSpSm)** Introduction to the finite element method; practical application of computer analysis tools for structural analysis and design. *Prerequisite:* AME 204; *corequisite:* AME 301.

**AME 309 Dynamics of Fluids (4, FaSp)** Fluid statics; conservation of mass, momentum, and energy in integral and differential form; applications. Laminar and turbulent pipe flow; compressible flow; potential flow over bodies. *Recommended preparation: *AME 310.

**AME 310 Engineering Thermodynamics I (3, FaSp)** Fundamental laws of thermodynamics applied to actual and perfect gases and vapors; energy concepts, processes, and applications. *Prerequisite:* MATH 226; *recommended preparation: *PHYS 151*L, *high-level programming language.

**AME 312 Engineering Thermodynamics II (3, Sp)** Application of thermodynamic principles to fluid flow, power cycles, and refrigeration. *Prerequisite: *AME 310; *recommended preparation: *high-level programming language.

**AME 331 Heat Transfer (3, Sp)** General principles underlying heat transfer by conduction, convection, and radiation; steady and transient conditions; heat exchangers. *Prerequisite:* AME 310; *corequisite:* AME 309 or CE 309.

**AME 341abL Mechoptronics Laboratory I and II (3-3, FaSp)** A coordinated laboratory and lecture sequence on aeromechanical instrumentation and device control stressing the symbiotic integration of mechanical, optical and electronic components. *Prerequisite: *PHYS 152*L*, MATH 126.

**AME 353 Aerospace Structures I (3, Irregular)** Shear and bending in symmetrical and unsymmetrical sections; torsion, column, and thin sheet analysis and design, including plastic failures and open section crippling.

**AME 390 Special Problems (1-4)** Supervised, individual studies. No more than one registration permitted. Enrollment by petition only.

**AME 403 Stress Analysis (3, Sp)** Theories of failure, shear center, unsymmetrical bending, curved beams, torsion of non-circular sections; cylinders, rotating discs, thermal stresses, inelastic strains, energy methods. *Prerequisite: *AME 204.

**AME 404 Computational Solutions to Engineering Problems (3, Fa)** Mathematical aspects of the solutions to typical advanced mechanical engineering problems. Modeling, simulation, computational aspects, computer solutions, and computational tools. *Recommended preparation: *FORTRAN, MATLAB and Maple.

**AME 408 Computer-Aided Design of Mechanical Systems (3, FaSp)** Design of mechanical systems using advanced graphics techniques; computer-aided drafting, design optimization, elements of computer graphics, solids modeling; introduction to computer-aided manufacturing. *Prerequisite:* AME 204 or CE 225; *recommended preparation:* AME 308.

**AME 409 Senior Design Project (4, Sp)** Modeling, analysis, integration, layout and performance analysis of a mechanical system to meet specified design requirements. *Prerequisite: *senior standing.

**AME 410 Engineering Design Theory and Methodology (3, Fa)** Product planning and task clarification, voice of customers, quality function deployment, conceptual and embodiment design, axiomatic theory of design, product quality and manufacturability, design decision-making. Junior standing. *Recommended preparation: *AME 305.

**AME 412 Molecular Theory of Gases (3, Irregular)** Molecular structure; intermolecular potentials; molecular processes in gases; molecular interpretation of concepts of classical thermodynamics; radiative transport phenomena in gases. *Prerequisite: *AME 310.

**AME 415 Turbine Design and Analysis (3, Fa)** Physics of turbine operation; design and analysis for the development of turbine hardware for propulsion and power generation. *Recommended preparation:* familiarity with Matlab.

**AME 420 Engineering Vibrations I (3, Fa)** Theory of free and forced vibrations with and without damping; systems of single and multiple degrees of freedom; iteration; methods; vibration isolation; instrumentation. *Prerequisite: *MATH 245.

**AME 423L Loudspeaker and Sound-System Design (3, Sp)** (Enroll in EE 423*L*)

**AME 428 Mechanics of Materials (3)** (Enroll in CE 428)

**AME 430 Thermal Systems Design (3, Fa)** Design methodology for thermal systems; boilers, condensers, air conditioning, power generation, air pollution control, combustion and alternative fuels. *Prerequisite:* AME 331; *recommended preparation:* AME 312.

**AME 436 Energy and Propulsion (3, Fa)** Performance and analysis of reciprocating, jet, rocket engines, and hybrid systems. Characteristics of inlets, compressors, combustors, turbines, nozzles and engine systems. Energy and environmental problems. *Prerequisite: *AME 310; AME 309 or CE 309.

**AME 441abL Senior Projects Laboratory (3-3, FaSp)** Individual engineering projects designed and constructed to model and test a physical principle or system. *Prerequisite:* AME 341*bL*.

**AME 443 Control Systems Laboratory (3, Sp)** Vibration measurement and analysis; simulation, design, and experimental verification of mechanical control systems; identification of system parameters, implementation of controllers, verification of closed-loop performance via experimentation and stimulation. (Duplicates credit in former AME 442*bL*.) *Prerequisite:* AME 420 or AME 451 or EE 482.

**AME 451 Linear Control Systems I (3, FaSp)** Transform methods, block diagrams; transfer functions; stability; root-locus and frequency domain analysis and design; state space and multiloop systems. *Prerequisite: *MATH 245.

**AME 453 Engineering Dynamics (3, Sp)** Principles of dynamics applied to mechanical and aerospace problems. Introduction to gyroscopic motion and rigid body dynamics. *Prerequisite: *MATH 245.

**AME 455 Introduction to MEMS (3, Sp)** Introduction to micro-electro-opto-mechanical systems; scaling effects on material properties, fluid flows, dynamical behavior; fabrication methods; design considerations for MEMS sensors and actuators. *Recommended preparation:* AME 301, AME 309 and AME 310.

**AME 457 Engineering Fluid Dynamics (3, Fa)** Laminar and turbulent boundary layer flow with and without heat transfer; boundary layer separation, stability, transition and control; introduction to compressible fluid flow. *Prerequisite: *AME 310; AME 309 or CE 309.

**AME 458 Theory of Structures II (3)** (Enroll in CE 458)

**AME 459 Flight Mechanics (3, Fa)** Applications of basic aerodynamics to aircraft and missile performance, power and thrust, stability and control, compressibility effects. *Recommended preparation: *AME 309.

**AME 460 Aerodynamic Theory (3)** Basic relations describing the inviscid flow field about bodies and wings moving at subsonic and supersonic speeds. *Prerequisite:* AME 309.

**AME 461 Formation Evaluation (3)** (Enroll in PTE 461)

**AME 462 Economic, Risk and Formation Productivity Analysis (4)** (Enroll in PTE 462)

**AME 463L Introduction to Transport Processing in Porous Media (3)** (Enroll in PTE 463*L*)

**AME 464L Petroleum Reservoir Engineering (3)** (Enroll in PTE 464*L*)

**AME 465L Drilling Technology and Subsurface Methods (3)** (Enroll in PTE 465*L*)

**AME 481 Aircraft Design (4, Sp)** Aircraft design and analysis, design requirements and specifications; integration of structure, propulsion, control system, and aerodynamic configuration; performance analysis and prediction. *Recommended preparation: *AME 309, AME 353.

**AME 490x Directed Research (1-8, max 12)** Individual research and readings. Not available for graduate credit.

**AME 491 Undergraduate Design Projects II (1, max 4, FaSp)** Analysis, design, fabrication, and evaluation of devices intended for entry in local and national design competitions. Intended for students with prior project experience. Upper division standing. Graded CR/NC.

**AME 499 Special Topics (2-4, max 8, FaSpx)** Course content to be selected each semester from recent developments in mechanical engineering and related fields.

**AME 502 Modern Topics in Aerospace Design (3, Fa)** Current topics in Aerospace Engineering are addressed by a number of industry panelists. Students, under panelists’ supervision and guidance, complete independent research reports and briefings. *Recommended preparation:* AME 261, AME 441, AME 481 or equivalents. Genuine interest in design of flight vehicles. Open only to Senior, Master, and Doctoral students.

**AME 503 Advanced Mechanical Design (3, Fa)** Specific problems and methods of analysis in mechanical systems design.

**AME 505 Engineering Information Modeling (3, Sp)** Symbolic and object-oriented modeling, product and process modeling for design and manufacturing, information models for computer integrated and collaborative engineering, information modeling for life-cycle engineering.

**AME 507 Mechanics of Solids I (3)** (Enroll in CE 507)

**AME 509 Applied Elasticity (3, Sp)** Condensed treatment dealing with engineering applications of the principles of elasticity, using the theories of elasticity, elastic stability, and plates and shells. *Prerequisite: *AME 403.

**AME 511 Compressible Gas Dynamics (3, Sp)** Thermodynamics, kinetic theory, compressible flow equations, shock and expansion waves, similarity, shock-expansion techniques and linearized flow applied to bodies, characteristics, theory of boundary layers.

**AME 513 Principles of Combustion (3, Fa)** Thermochemistry, equilibrium, chemical kinetics, flame temperature, flame velocity, flame stability, diffusion flames spray combustion, detonation. Equations of motion including reaction, heat transfer, and diffusion.

**AME 514 Applications of Combustion and Reacting Flows (3, Sp)** Advanced topics and modern developments in combustion and reacting flows including ignition and extinction, pollutant formation, microscale and microgravity combustion, turbulent combustion and hypersonic propulsion. *Recommended preparation: *AME 513.

**AME 515 Advanced Problems in Heat Conduction (3, Sp)** Review of analytical methods in heat conduction; moving boundaries melting and freezing; sources and sinks, anisotropic and composite media; numerical methods for steady and unsteady problems. *Recommended preparation: *AME 331, AME 526.

**AME 516 Convection Processes (3, Sp)** Analysis of isothermal and nonisothermal boundary layers. Exact and approximate solutions of laminar and turbulent flows. Variable-property and high-speed effects; dimensional analysis. *Prerequisite:* AME 457; *recommended preparation:* AME 526, AME 331.

**AME 517 Radiation Heat Transfer (3, Fa)** Radiation properties; black body radiation; shape factors of radiation network analogy and solar radiation. *Prerequisite: *AME 331; *corequisite:* AME 525 or AME 526.

**AME 520 Modeling of Bio-Systems (3, Sp)** Interacting population dynamics, Cheyne-Stokes respiration, reaction kinetics, biological switches, neuronal models, BZ reaction, phase locking, reaction diffusion, chemotaxis, biological waves, and animal coat patterns. *Recommended preparation:* MATH 245.

**AME 521 Engineering Vibrations II (3, Fa)** Multi-degree of freedom systems; modal analysis. Rayleigh’s quotient. Continuous systems; modal analysis. Beams, rods, membranes. Colocations, Galerkin, Rayleigh Ritz methods; finite elements. *Prerequisite: *AME 420.

**AME 522 Nonlinear Dynamical Systems, Vibrations, and Chaos (3, Fa)** Lagrange equations; nonlinear maps and differential equations; fixed points; periodic motion; qualitative/quantitative and local/global analysis; higher order systems; stability; bifurcations; chaos; fractals.

**AME 523 Random Vibrations (3, Irregular)** Random processes, ergodic theory. Ito calculus. Linear systems under stationary and nonstationary excitations. Fokker-Planck equations. Failure analysis and first passage problems. *Prerequisite: *AME 420, basic probability (or MATH 407), AME 451 recommended.

**AME 524 Advanced Engineering Dynamics (3, Fa)** Principle of virtual work, constraints, Lagrange’s equations, Gibbs-Appell equations, Gauss’s Principle, Theory of Rotations, dynamics of rigid bodies, Hamiltonian mechanics, Hamilton-Jacobi equation. *Recommended preparation: *AME 521, AME 525.

**AME 525 Engineering Analysis (3, FaSpSm)** Typical engineering problems discussed on a physical basis. Vector analysis; functions of complex variables, infinite series, residues.

**AME 526 Engineering Analytical Methods (3, FaSpSm)** Typical engineering problems discussed on a physical basis. Fourier series; Fourier integrals; Laplace transform; partial differential equations; Bessel function.

**AME 527 Elements of Vehicle and Energy Systems Design (3, Irregular)** Design synthesis of aero/hydro/mechanical systems; techniques of design; conceptual thinking; problem definition, configurational development, analytic engineering approximation, oral briefings and group problem solving. Graduate standing.

**AME 529 Aircraft Structures Analysis (3, Sp)** The direct stiffness (finite element) method for analysis of semimonocoque structures; energy methods; elasticity, plates and shells, vibration, and stability; system identification.

**AME 530ab Dynamics of Incompressible Fluids (3-3, FaSp)** A unified discussion of low-speed fluid mechanics including exact solutions; approximation techniques for low and high Reynolds numbers; inviscid flows; surface waves; dynamic stability; turbulence.

**AME 532ab Flight Vehicle Stability and Control (3-3, FaSp)** Response of flight to linear, nonlinear, and randomly defined disturbances. Generation and measurement of error signals in navigational systems. Stability and control techniques. *Recommended preparation:* AME 459.

**AME 533 Multi-Phase Flows (3, Sp)** Physics of the interaction between phases, empirical and analytical methods of solution to relevant technological problems. *Prerequisite: *AME 457.

**AME 534 Nuclear Thermal-Hydraulics (3, Fa)** Thermal-fluid phenomena for nuclear power stations. Heat generation by nuclear reactions, conduction in fuel rods, and transport of generated heat by convection, boiling, and condensation. Open only to master’s and doctoral students. *Prerequisite: *AME 457 or AME 530*a*; and AME 526 and AME 581; *recommended preparation*: undergraduate degree in engineering.

**AME 535ab Introduction to Computational Fluid Mechanics (3-3, FaSp)** *a:* Convergence, consistency, stability: finite difference, finite element, and spectral methods; direct and iterative procedures for steady problems; linear diffusion and advection problems; non-linear advection problems. *Recommended preparation: *AME 526. *b:* Generalized curvilinear coordinates; grid generation; numerical techniques for transonic and supersonic inviscid flows; boundary layer flows; reduced Navier-Stokes equations; compressible and incompressible viscous flows. *Recommended preparation:* AME 511 or AME 530*a*, AME 535*a*.

**AME 537 Microfluidics (3, Fa)** Introduction to fluid dynamics in the microscale. Scaling parameters, dynamic, thermodynamic, electroosmotic and electrochemical forces. Flow in microdevices, external flow measurement and control, microvalves and micropumps. Limited to students with graduate standing. *Recommended preparation: *AME 309, MATH 445.

**AME 539 Multi-body Dynamics (3, Sp)** Kinematics and kinetics of rigid body motion, quaternions; elastic vibrations of continua; geometric and material nonlinearities; Galerkin methods; meshless finite elements; complex dynamical systems; computational methods.

**AME 541 Linear Control Systems II (3, Fa)** State space representation, linearization, solution of state equations; controllability and observability; state feedback, state observers; optimal control; output feedback. *Prerequisite: *AME 451.

**AME 542 Theory of Plates (3)** (Enroll in CE 542)

**AME 543 Stability of Structures (3)** (Enroll in CE 543)

**AME 544 Computer Control of Mechanical Systems (3, Sp)** Computer control as applied to machine tools, mechanical manipulators, and other mechanical machinery; discrete time controller design; microprocessor implementation of motion and force control servos. *Prerequisite: *AME 451.

**AME 545 Modeling and Control of Distributed Dynamic Systems (3, Sp)** Modeling and analysis of complex flexible mechanical systems; distributed transfer function synthesis; frequency-domain control methods; smart structure design; applications in vibration and noise control. *Prerequisite: *AME 521 and AME 541.

**AME 548 Analytical Methods in Robotics (3, Irregular)** Homogeneous transformations; formal description of robot manipulators; kinematic equations and their solution; differential relationships; dynamics; control; static forces; compliance. *Prerequisite: *EE 545; EE 482 or AME 451; knowledge of linear algebra.

**AME 549 Systems Architecting (3, FaSm)** (Enroll in SAE 549)

**AME 550ab Seminar in Aerospace and Mechanical Engineering (1-1, FaSp)** Recent developments and research in aerospace and mechanical engineering and related fields. Oral and written reports. Graded CR/NC. Open only to AME graduate students.

**AME 551 Mechanical Behavior of Engineering Materials (3)** (Enroll in MASC 551)

**AME 552 Nonlinear Control Systems (3, Sp)** Phase plane, describing functions, applications to mechanical and aerospace systems. Lyapunov direct and indirect methods, applications; Popov circle criteria applications. *Prerequisite: *AME 541.

**AME 553abL Digital Control Systems (3-1)** (Enroll in EE 543*abL*)

**AME 559 Creep (3, Fa)** Behavior of engineering materials at elevated temperatures; thermal stresses; creep mechanisms; interpretation of creep data; methods of predicting long-term strains.

**AME 560 Fatigue and Fracture (3, Sp)** Behavior of materials under cyclic and static fatigue; plastic instability; life-time predictions; brittle and ductile fracture; crack propagation and plastic blunting.

**AME 561 Dislocation Theory and Applications (3)** (Enroll in MASC 561)

**AME 567 Collaborative Engineering Principles and Practice (3, Sp)** (Enroll in ISE 567)

**AME 572L Experimental Engineering Projects (3)** Experimental methods appropriate to engineering research, emphasizing interdisciplinary investigations. Individual projects.

**AME 573 Aerosol Physics and Chemistry (3, Sp)** Examination of the fundamentals of aerosol formation and evolution, aerosol effects on health and climate, and the principles of aerosol measurement. Open only to master’s and doctoral students.

**AME 575 Advanced Engineering Analysis (3, Fa)** Solution of engineering problems by methods of calculus variations, integral equations, asymptotic expansions. *Prerequisite: *CE 525*ab* or AME 525 and AME 526.

**AME 576 Advanced Engineering Analytical Methods (3, Sp)** Solution of engineering problems by methods of linear and nonlinear partial differential equations of first and second order; perturbations. *Prerequisite:* AME 525 or AME 526 or CE 525 or CE 526.

**AME 577 Survey of Energy and Power for a Sustainable Future (3, FaSp)** Power production includes conventional fossil fuels, synthetic fuels, hydroelectric, solar, wind, geothermal, biomass and nuclear. The environmental consequences of various energy sources are discussed. (Duplicates credit in CHE 510.)

**AME 578 Modern Alternative Energy Conversion Devices (3, FaSp)** Alternative energy/power conversion including fuel cells, photovoltaic, batteries, and biologically inspired energy processes; biomass conversion and utilization; Environmental implications of alternative energy processes.

**AME 579 Combustion Chemistry and Physics (3, Sp)** Thermodynamics of combustion processes. Reaction mechanisms of hydrocarbon combustion. Pollutant formation. Theories and application of thermochemical kinetics and reaction rate theories. Transport in reacting flows.

**AME 581 Introduction to Nuclear Engineering (3, Fa)** Review of basic nuclear physics, binding energy, reactor kinetics, thermal transport in reactor systems, radioactivity, shielding, reactor safety and health effects of radiation, risk assessment. Open only to graduate students. *Recommended preparation: *Undergraduate degree in engineering; AME 310, MATH 245, PHYS 153*L*.

**AME 582 Nuclear Reactor Physics (3, Sp)** Neutron-induced fission chain reactions, reactor criticality. Neutron transport and diffusion in nuclear reactors. Mathematical/computational foundation for diffusion theory and transport calculations for fission reactor design/analysis. Open only to master’s and doctoral students. *Prerequisite: *AME 526 and AME 581; *recommended preparation:* undergraduate degree in engineering and PHYS 153*L*.

**AME 583 Effects of Radiation on Health (3, Sp)** Nuclear physics relevant to human health. Biological effects of radiation, quantification and measurement of different types of radiation affecting living tissue, radiation protection, nuclear accidents. Open only to master’s and doctoral students. *Prerequisite: *AME 526 and AME 581;* recommended preparation:* undergraduate degree in engineering and PHYS 153*L*.

**AME 584 Fracture Mechanics and Mechanisms (3, Fa)** Failure modes, stress concentrations, complex stress analysis, linear elastic fracture mechanics, yielding fracture mechanics, experimental methods, environmental assisted fracture and fatigue. *Prerequisite: *AME 403.

**AME 588 Materials Selection (3, Sp)** Materials selection in relationship to design and fabrication, economic considerations, methodology of selection, performance parameter; case studies.

**AME 590 Directed Research (1-12)** Research leading to the master’s degree. Maximum units which may be applied to the degree to be determined by the department. Graded CR/NC.

**AME 594abz Master’s Thesis (2-2-0)** Credit on acceptance of thesis. Graded IP/CR/NC.

**AME 599 Special Topics (2-4, max 9, FaSp)** Course content will be selected each semester to reflect current trends and developments in the field of mechanical engineering.

**AME 620 Aero and Hydrodynamic Wave Theory (3)** Linear and nonlinear wave motion in fluids: group velocity, dispersion, wave action, wave patterns, evolution equations, solitons and solitary waves, resonance phenomena. *Recommended preparation: *AME 526 and CE 309.

**AME 621 Stability of Fluids (3)** Linear and nonlinear stability analysis applied to free shear layers, boundary layers and jets; Rayleigh-Benard convective instabilities and centrifugal instability of rotating flows. *Recommended preparation: *AME 530*b*.

**AME 623 Dynamics of Stratified and Rotating Flows (3)** Fluid motions in which density gradients and/or rotation are important, including internal wave motions with rotation, flow past obstacles, viscous effects, singular perturbations. *Recommended preparation:* AME 530*b*.

**AME 624 The Fluid Dynamics of Natural Phenomena (3)** Application of the basic concepts of rotating, stratified fluid motion to problems in meteorology, oceanography, geophysics and astrophysics.

**AME 626 Singular Perturbation Methods (3)** Asymptotic series, W.K.B. approximation, method of steepest descent, stationary phase; matched asymptotic expansions and method of multiple scales applied to ordinary and partial differential equations. *Recommended preparation: *AME 526.

**AME 630 Transition to Chaos in Dynamical Systems (3)** Bifurcation theory and universal routes to chaos in deterministic systems; application to maps and differential flows; characterization of strange attractors. *Recommended preparation: *AME 526.

**AME 640 Advanced Theory of Elasticity (3)** (Enroll in CE 640)

**AME 645 Uncertainty Modeling and Stochastic Organization (3)** (Enroll in CE 645)

**AME 647 Multiscale Methods in Mechanics (3)** (Enroll in CE 647)

**AME 651 Statistical Theories of Turbulence (3)** Stationary stochastic processes. Isotropic turbulence; governing equations for the velocity correlation and spectrum functions. Turbulent diffusion. Scalar fluctuations in a turbulent field. *Recommended preparation: *AME 530*b*.

**AME 652 Turbulent Shear Flows (3)** Free shear layers. Turbulent flows in pipes and channels. Turbulent boundary layers. Effects of compressibility. Sound radiation by turbulence. *Recommended preparation: *AME 530*b*.

**AME 690 Directed Research (1-4, max 8)** Laboratory study of specific problems by candidates for the degree Engineer in Mechanical Engineering. Graded CR/NC.

**AME 694abz Thesis (2-2-0)** Required for the degree Engineer in Aerospace Engineering. Credit on acceptance of thesis. Graded IP/CR/NC.

**AME 790 Research (1-12)** Research leading to the doctorate. Maximum units which may be applied to the degree to be determined by the department. Graded CR/NC.

**AME 794abcdz Doctoral Dissertation (2-2-2-2-0)** Credit on acceptance of dissertation. Graded IP/CR/NC.