Aero 215. Introduction to Solid Mechanics and Aerospace Structures
Prerequisite: Preceded or accompanied by Math 216 and Aero 245. I, II (4 credits)
An introduction to the fundamental phenomena of solid and structural mechanics in Aerospace systems. Includes analysis and numerical methods of solutions used for design of thin-walled Aerospace structures. Emphasis is placed on understanding behavior particular to thin-walled structures.

Aero 225. Introduction to Gas Dynamics
Prerequisite: Math 215, Chem 125/130, Physics 140/141. I, II (4 credits)
An introduction to gas dynamics, covering fundamental concepts in thermodynamics and fluid dynamics. Topics include molecular and continuum concepts for fluids, first and second laws of thermodynamics, conservation laws for moving fluids, one-dimensional compressible flows, shocks and expansion waves, flows in nozzles, and two- and three-dimensional compressible flows.

Aero 245. Performance of Aircraft and Spacecraft
Prerequisite: preceded by Engr 100, Engr 101, Physics 140/141, and Math 116. I, II (4 credits)
An introduction to the aerospace field. Introduces students to steady motion of aircraft and spacecraft and to methods for evaluating performance of aircraft and spacecraft systems. Students learn basic aerodynamics, propulsion, and orbital mechanics. Involves team projects that include written reports.

Aero 285. Aerospace Engineering Seminar
Prerequisite: preceded or accompanied by AE 245. I, (1 credit) 
Seminars by noted speakers, designed to acquaint undergraduates with contemporary technologies and broader issues in the global aerospace enterprise. Involves writing assignments pertinent to seminar topics. 

Aero 290. Directed Study
Prerequisite: permission of instructor (1-3 credits) 
Study aspects of aerospace engineering that are not suitable for technical elective credit. May be used for student team projects, pilot ground school, UROP, or other academic studies that are directed by an Aerospace Engineering faculty member. The student will submit a final report.   

Aero 305. Aerospace Engineering Laboratory I
Prerequisite: preceded or accompanied by EECS 206 or 215 or EECS 314. Preceded by Aero 225 and Aero 215. I, II (4 credits)
First course of a two-semester sequence covering fundamentals of instrumentation and measurement and their application in engineering testing and experimentation. Includes principles of analog and digital data acquisition, analysis of discrete measurement data, statistical assessment of hypotheses, design of experiments, and similarity scaling of data. Emphasized development of skills for written communication and for working effectively in a team environment.

Aero 315. Aircraft and Spacecraft Structures
Prerequisite: preceded by Aero 215 and Math 216. I, II (4 credits)
Concepts of displacement, strain, stress, compatibility, equilibrium, and constitutive equations as used in solid mechanics. Emphasis is on boundary-value problem formulation via simple examples, followed by the use of the finite-element method for solving problems in vehicle design.

Aero 325. Aerodynamics
Prerequisite: preceded by Math 216 and Aero 225. I, II (4 credits)
Fundamental concepts in aerodynamics. Students learn how airfoils produce lift and how the pressure distribution about an airfoil can be calculated. Introduces the boundary-layer concept, how boundary layers lead to drag, and what makes them prone to instability and turbulence or separation. Effects of the wing planform shape on lift and drag. Introduction to airfoil design, high-lift devices and high-speed aerodynamics.

Aero 335. Aircraft and Spacecraft Propulsion
Prerequisite: preceded by Aero 225 and Math 216. I, II (4 credits)
Airbreathing propulsion, rocket propulsion, and an introduction to modern advanced propulsion concepts. Includes thermodynamic cycles as related to propulsion and the chemistry and thermodynamics of combustion. Students analyze turbojets, turbofans and other air-breathing propulsion systems. Introduces liquid- and solid-propellant rockets and advanced propulsion concepts such as Hall thrusters and pulsed plasma thrusters. Students also learn about the environmental impact of propulsion systems and work in teams to design a jet engine.

Aero 345. Flight Dynamics and Control
Prerequisite: preceded by Math 216, Aero 245, and ME 240. I, II (4 credits)
An introduction to dynamics and control of aircraft. Introduces concepts from linear systems theory (state equations, transfer functions, stability, time and frequency response). Aircraft longitudinal and lateral flight dynamics and control systems. 

Aero 384. Introduction to Solid Modeling and CAD
Prerequisite: preceded or accompanied by Aero 245 and Aero 215. I (3 credits)
Design process including specifications, configurations, trades, and design drivers. Introduction to solid visualization and modeling through an integrated CAD/CAE/CAM/PDM software package in the context of the design process. The role of CAD in analysis, manufacturing, and product management. Flight vehicle related projects.

Aero 390. Directed Study
Prerequisite: permission of instructor (1-3 credits) 
Study specialized aspects of aerospace engineering. May be used for student team projects, pilot certification, or other academic studies that are directed by an Aerospace Engineering faculty member. The student will submit a final report.

Aero 405. Aerospace Laboratory II
Prerequisite: preceded by Aero 305. Preceded or accompanied by Aero 315 and Aero 325. I, II (4 credits)
Second course of a two-semester sequence covering fundamentals of instrumentation and measurement and their application in engineering testing and experimentation. Focuses primarily on application of the fundamental principles learned in Aero 305 to more advanced test and measurement applications. Involves instructor-designed experiments and one major project conceived, designed, conducted, analyzed, and reported by student teams. Emphasizes development of skills for written communication and for working effectively in a team environment.

Aero 416 (NA 416). Theory of Plates and Shells 
Prerequisite: Aero 315. II alternate years (3 credits)
Linear elastic plates. Membrane and bending theory of axisymmetric and non-axisymmetric shells.
Variational formulation of governing equations boundary conditions. Finite element techniques for plate and shell problems.

Aero 421. Engineering Aerodynamics 
Prerequisite: Aero 325. II alternate years (3 credits)
This course teaches contemporary aerodynamic analysis and design of aerospace vehicles and other systems.  Topics include: review of theoretical concepts and methods, computer-based CFD tools, experimental methods and wind tunnel testing.  Case studies are discussed to illustrate the combined use of advanced aerodynamic design methods. A team project is required.

Aero 445. Flight Dynamics of Aerospace Vehicles
Prerequisite: Aero 345. II (3 credits)
Flight-oriented models of aerospace vehicles. Analytical modeling principles for analysis and control. Computer-based simulation, performance evaluation, and model validation. Flight properties of various aerospace vehicles, such as fixed-wing aircraft, rotorcraft, launch and reentry vehicles, orbiters, and interplanetary vehicles.

Aero 447. Flight Testing
Prerequisite: Aero 305 and Aero 345. II (3 credits)
Theory and practice of obtaining flight-test data on performance and stability of airplanes from actual flight tests. Modern electronic flight test instrumentation, collection of flight test data, calibration procedures for air data sensors, estimation of stability derivatives from flight test data. Lectures and laboratory.

Aero 450. Flight Software Systems 
Prerequisite: Eng 101 and Aero 245. I (3 credits)
Theory and practice of embedded flight software systems. Computational theory topics include discrete mathematics, finite automata, computational complexity, and model checking. Software development concepts include object oriented programming, networks, multi-threaded software, real-time scheduling, and sensor/actuator interface protocols. Emphasis placed on C/C++ development in Linux with guidance, navigational control applications.  Lectures and laboratory.

Aero 464 (AOSS 464) (ENSCEN 464). The Space Environment
Prerequisite: senior or graduate standing in a physical science or engineering. I (3 credits)
An introduction to physical and aeronomical processes in the space environment. Discussion of theoretical tools, the Sun, solar spectrum, solar wind, interplanetary magnetic field, planetary magnetosphere, ionospheres and upper atmospheres. Atmospheric processes, densities, temperatures, and wind.

Aero 481. Aircraft Design
Prerequisite: Aero 315, Aero 325, required, Aero 335 and Aero 345 can be concurrent. I (4 credits)
Multidisciplinary integration of aerodynamics, performance, stability and control, propulsion, structures and aeroelasticity in a system approach aimed at designing an aircraft for a set of specifications.  Includes weight estimates, configuration and power plant selection, tail-sizing, maneuver and gust diagrams, wing loading, structural and aeroelastic analysis.  Students work in teams on the design project.

Aero 483. Space System Design
Prerequisite: preceded by Aero 345. Preceded or accompanied by Aero 315, 325, and 335. II (4 credits)
Introduction to the engineering design process for space systems. Includes a lecture phase that covers mission planning, launch vehicle integration, propulsion, power systems, communications, budgeting, and reliability. Subsequently, students experience the latest practices in space-systems engineering by forming into mission-component teams and collectively designing a space mission. Effective team and communication skills are emphasized. Report writing and presentations are required throughout, culminating in the final report and public presentation.

Aero 484. Computer Aided Design
Prerequisite: preceded by Aero 315, Aero 325, Aero 335, and Aero 345. I (4 credits)
Advanced computer-aided design. Students learn about computer generation of geometric models, calculation of design parameters, trade-off diagrams, and finite-element modeling and analysis. Each student carries out a structural component design using industry-standard software. The course includes individual and team assignments.

Aero 490. Directed Study 
Prerequisite: permission of instructor (1-3 credits)
Study of advanced aspects of aerospace engineering directed by an Aerospace faculty member. The student will submit a final report.

Aero 495. Special Topics in Aerospace Engineering
Prerequisite: permission of instructor. (1-4 credits)
Specific aerospace engineering topics that are not treated in the regular Aerospace Engineering undergraduate curriculum.

Aero 510. Finite Elements in Mechanical and Structural Analysis I
Prerequisite: Aero 315. I (3 credits)
Introductory level. Finite element solutions for structural dynamics and nonlinear problems. Normal modes, forced vibrations, Euler buckling (bifurcations), large deflections, nonlinear elasticity, transient heat conduction. Computer laboratory based on a general purpose finite element code.

Aero 511. Finite Elements in Mechanical and Structural Analysis II
Prerequisite: Aero 510 or ME 505. II (3 credits)
Intermediate level. Finite element solutions for structural dynamics and nonlinear problems. Normal modes, forced vibration, Euler buckling (bifurcation), large deflections, nonlinear elasticity, transient heat conduction. Computer laboratory based on a general purpose finite element code.

Aero 512. Experimental Solid Mechanics
Prerequisite: Aero 305, Aero 315 or equivalents. II (3 credits)
Lectures and experiments that demonstrate historical and contemporary methods of measurement in solid mechanics. A review of classical experiments that substantiate many typical assumptions (e.g., material linearity or Hooke's Law) concerning the response of solids. An introduction to contemporary techniques of process measurement involving piezoresistivity.

Aero 513. Foundations of Solid and Structural Mechanics I
Prerequisite: Aero 315, ME 311 or equivalent. I (3 credits)
Introduction to linear continuum and structural mechanics. Three-dimensional analysis of stress and infinitesimal strain, including transformation of tensors, equations of motion, and kinematic compatibility. Boundary value problem formation. Constitutive relations for isotropic and anisotropic linear elastic materials. Introduction to variational calculus and energy methods. Applications to thin-walled and slender aerospace structures.

Aero 514. Foundations of Solid and Structural Mechanics II
Prerequisite: Aero 315 or equivalent. II (3 credits)
Introduction to nonlinear continuum and structural mechanics. Elements of tensor calculus, basic kinematics, conservation laws (mass, linear and angular momentum, energy, etc.), constitutive equations in continual applications in hyperelastic solids, numerical (f.e.m.) methods for the corresponding nonlinear boundary value problems, derivation of nonlinear shell theories from 3-D considerations.

Aero 515. Mechanics of Composite and Microstructured Media
Prerequisite: Aero 514 or equivalent. I (3 credits)
An introduction to the mechanics of composite (more than one phase) solids with an emphasis on the derivation of macroscopical constitutive laws based on the microstructure. Eshelby transformation theory, self consistent methods, homogenization theory for periodic media, bounding properties for effective moduli of composites. Applications of aerospace interest.

Aero 516. Mechanics of Fibrous Composites
Prerequisite: Aero 315 or ME 412. I (3 credits)
Effective stiffness properties of composites. Constitutive description of laminated plates. Laminated plate theory. Edge effects in laminates. Nonlinear theory of generally laminated plates. Governing equations in the Von Karman sense. Laminated plates with moderately large deflections. Postbuckling and nonlinear vibration of laminated plates. Failure theories and experimental results for laminates.

Aero 518. Theory of Elastic Stability I
Prerequisite: Aero 315 or ME 412 or the equivalent. II (3 credits)
Concepts of stability and bifurcation. Simple examples to illustrate buckling and instability mechanisms in structures. Both equilibrium and time dependent problems discussed. General theory for stability in continuum, conservative elastic solids. Applications to bars, rings, plates and shells.

Aero 520. Compressible Flow I
Prerequisite: Aero 325. I (3 credits)
Elements of inviscid compressible-flow theory: review of thermodynamics; equations of frictionless flow; analysis of unsteady one-dimensional and steady supersonic two-dimensional flows; including the method of characteristics; small-disturbance theory with applications to supersonic thin-airfoil theory.

Aero 521. Experimental Methods in Fluid Mechanics
Prerequisite: Aero 405 or Grad standing. II (3 credits)
Fundamental principles and practice of  non-intrusive measurement techniques for compressible and incompressible flows.  Review of geometric and Gaussian beam optics; Laser Doppler Velocimentry; quantitative flow field measurement techniques including interferometry, Laser induced Fluorescence and Particle Image Velocimetry.  Advanced data processing techniques for turbulent flow. Error estimation. Lecture and laboratory.

Aero 522. Viscous Flow
Prerequisite: Aero 325. I (3 credits)
The Navier-Stokes equations, including elementary discussion of tensors; exact solutions. Laminar boundary-layer theory; three-dimensional and compressible boundary layers. Laminar-flow instability theory; transition. Introduction to the mechanics of turbulence; turbulent free shear flows and boundary layers.

Aero 523 (ME 523). Computational Fluid Dynamics I
Prerequisite: Aero 325 or preceded or accompanied by ME 520. I (3 credits)
Physical and mathematical foundations of computational fluid mechanics with emphasis on applications. Solution methods for model equations and the Euler and the Navier-Stokes equations. The finite volume formulation of the equations. Classification of partial differential equations and solution techniques. Truncation errors, stability, conservation, and monotonicity. Computer projects and homework.

Aero 524. Aerodynamics II
Prerequisite: Aero 325. II (3 credits)
Two- and three-dimensional potential flow about wings and bodies; complex-variable methods; singularity distributions; numerical solution using panel methods. Unsteady aerodynamics; slender-body theory. Viscous effects: airfoil stall, high-lift systems, boundary-layer control. Wings and bodies at transonic and supersonic speeds; numerical methods.

Aero 525. Introduction to Turbulent Flows
Prerequisite: Aero 522. II (3 credits)
Mathematical description of turbulent flow phenomena. Flow equations, vorticity dynamics, Reynolds-averaged equations, engineering turbulence models. Theory of homogeneous turbulence, spectral dynamics. Shear flow turbulence, mean and fluctuating structure of free and wall-bounded turbulent flows.

Aero 526. Hypersonic Aerothermodynamics
Prerequisite: Graduate standing or Aero 225 and Aero 325. I (3 credits)  
Hypersonic vehicles offer rapid air transportation and access to space. This course provides an introduction to the aerothermodynamics of hypersonic vehicles. Topics covered include: vehicle types (missiles, space planes, air-breathers); flight dynamics (trajectory, range, stability); aerothermodynamics (fluid dynamics, thermodynamics, aerodynamics, heating); and propulsion systems (scramjets, combined cycles).

Aero 530. Gas-Turbine Propulsion
Prerequisite: Aero 335 II (3 credits)
Advanced analysis of turbojet engines: effect of altitude parameters on engine performance; off-design equilibrium running of a turbojet engine; dynamics of engine considered as a quasi-static system; fluid mechanics of a rotating axial blade row; centrifugal compressors; transonic flow problems.

Aero 532. Molecular Gas Dynamics
Prerequisite: permission of instructor. II (3 credits)
Analysis of basic gas properties at the molecular level. Kinetic theory: molecular collisions, the Boltzmann equation. Maxwellian distribution function. Quantum mechanics: the Schrodinger equation, quantum energy states for translation, rotation, vibration, and electronic models of atoms and molecules. Statistical mechanics: the Boltzmann relation, the Boltzmann energy distribution, partition functions. These ideas are combined for the analysis of a chemically reacting gas at the molecular level.

Aero 533 (ENSCEN 533). Combustion Processes
Prerequisite: Aero 225. (3 credits)
This course covers the fundamentals of combustion systems, and fire and explosion phenomena. Topics covered include thermochemistry, chemical kinetics, laminar flame propagation, detonations and explosions, flammability and ignition, spray combustion, and the use of computer techniques in combustion problems.

Aero 535. Rocket Propulsion
Prerequisite: Aero 335. I (3 credits)
Analysis of liquid and solid propellant rocket powerplants; propellant thermochemistry, heat transfer, system considerations. Low-thrust rockets, multi-stage rockets, trajectories in powered flight, electric propulsion.

Aero 536. Electric Propulsion
Prerequisite: Aero 335, senior standing. I (3 credits)
Introduction to electric propulsion with an overview of electricity and magnetism, atomic physics, non-equilibrium flows and electrothermal, electromagnetic, and electrostatic electric propulsion systems.

Aero 540 (ME 540). Intermediate Dynamics
Prerequisite: ME 240. I (3 credits)
Newton/Euler and Lagrangian formulations for three dimensional motion of particles and rigid bodies. Principles of dynamics applied to various rigid-body and multi-body dynamics problems that arise in aerospace and mechanical engineering.

Aero 543. Structural Dynamics
Prerequisite: Aero 315 or Aero 540. (3 credits)
Natural frequencies and mode shapes of elastic bodies. Nonconservative elastic systems. Structural and viscous damping. Influence coefficient methods for typical flight structures. Response of structures to random and shock loads. Lab demonstration.

Aero 544. Aeroelasticity
Prerequisite: Aero 315 or Aero 540. (3 credits)
Introduction to aeroelasticity. Vibration and flutter of elastic bodies exposed to fluid flow. Static divergence and flutter of airplane wings. Flutter of flat plates and thin walled cylinders at supersonic speeds. Oscillations of structures due to vortex shedding.

Aero 545. Principles of Helicopter and  V/STOL Flight
Prerequisite: preceded or accompanied by Aero 325. I (3 credits)
Introduction to helicopter performance, aerodynamics, stability and control, vibration and flutter. Other V/STOL concepts of current interest.

Aero 548. Astrodynamics
Prerequisite: Aero 345. II (3 credits)
Review of two-body problem for spacecraft: orbital trajectories, transfers, targeting, and time of flight. Orbit perturbation formulations and analysis. Restricted 3-body problem and applications.

Aero 549. Orbital Analysis and Determination
Prerequisite: Either Aero 548, Aero 540, or Aero 573 - Permission of Instructor. II (3 credits)
The analysis, characterization and determination of space trajectories from a dynamical systems viewpoint. The general formulation and solution of the spacecraft trajectory design and navigation problems. Computation of periodic orbits and their stability. Estimation of model parameters from spacecraft tracking data (e.g., gravity field estimation). Elements of precision modeling and precision orbit determination. 

Aero 550 (EECS 560) (ME 564). Linear Systems Theory
Prerequisite: graduate standing. I (4 credits)
Linear spaces and linear operators. Bases, subspaces, eigenvalues and eigenvectors, canonical forms. Linear differential and difference equations. Mathematical representations: state equations, transfer functions, impulse response, matrix fraction and polynomial descriptions. System-theoretic concepts: causality, controllability, observability, realizations, canonical decomposition, stability.

Aero 551 (EECS 562). Nonlinear Systems and Control
Prerequisite: graduate standing. II (3 credits)
Introduction to the analysis and design of nonlinear systems and nonlinear control systems. Stability analysis using Liapunov, input-output and asymptotic methods. Design of stabilizing controllers using a variety of methods: linearization, absolute stability theory, vibrational control, sliding modes and feedback linearization.

Aero 565. Optimal Structural Design
Prerequisite: Aero 315, a course in advanced calculus. II (3 credits)
Optimal design of structural elements (bars, trusses, frames, plates, sheets) and systems; variational formulation for discrete and distributed parameter structures; sensitivity analysis; optimal material distribution and layout; design for criteria of stiffness, strength, buckling, and dynamic response.

Aero 566. Data Analysis and System Identification
Prerequisite: Graduate standing  (3 credits)
Methods of data analysis and empirical modeling. Sensors and measurement concepts. Time and frequency data analysis; statistical and spectral concepts. Linear regression and identifications of time-series models. Parameter estimation using optimization. Basis-function expansions and non-linear time-series identification. Eigensystem realization and subspace identification. Non-linear  state space identification.  

Aero 573. Dynamics and Control of Spacecraft
Prerequisite: Aero 345. I (3 credits)
Introduction to spacecraft dynamics and control. Spacecraft orbit and attitude representations, kinematics, dynamics. Perturbation equations for near circular orbits. Spacecraft maneuvers formulated and solved as control problems.

Aero 575. Flight and Trajectory Optimization
Prerequisite: Aero 345. I (3 credits)
Formulation and solution of optimization problems for atmospheric flight vehicles and space flight vehicles. Optimality criteria, constraints, vehicle dynamics. Flight and trajectory optimization as problems of nonlinear programming, calculus of variations, and optimal control. Algorithms and software for solution of flight and trajectory optimization problems.

Aero 579. Control of Structures and Fluids
Prerequisite: Aero 345. II (3 credits)
Stabilization and vibration suppression for structures and fluids. Control-oriented modeling of structural and acoustic dynamics. Fixed-gain and adaptive control methods. Control-oriented fluid dynamics for compressible and incompressible fluids. Feedback stabilization of laminar flow, rotating surge and stall.

Aero 580 (EECS 565). Linear Feedback Control Systems
Prerequisite: EECS 460 or Aero 345 or ME 461 and Aero 550 (EECS 560). II (3 credits)
Control design concepts for linear multivariable systems. Review of single variable systems and extensions to multivariable systems. Purpose of feedback. Sensitivity, robustness, and design trade-offs. Design formulations using both frequency domain and state space descriptions. Pole placement/observer design. Linear quadratic Gaussian based design methods. Design problems unique to multivariable systems.

Aero 581 (AOSS 581). Space System Management
Prerequisite: graduate standing. I (3 credits)
The first part of the course will offer a comprehensive introduction to modern management methods used in large projects. The second part will concentrate on successful management examples of complex space projects. This course will usually be taught by adjunct faculty with extensive experience in successful management of large space projects.

Aero 582 (AOSS 582). Spacecraft Technology
Prerequisite: Graduate standing. I (4 credits)
Systematic and comprehensive review of spacecraft and space mission
design and  key technologies for space missions. Discussions on project
management and the economic and political factors that affect space
missions.  Specific space mission designs are developed in teams.
Students of AERO 483/583  choose their projects based on these designs.

Aero 583. Management of Space Systems Design
Prerequisite: graduate standing. II (4 credits)
Meets with Aero 483 (Space System Design), or other senior design course when appropriate topic is chosen. Students in this course lead teams in high level project design of a space system. Modern methods of concurrent engineering manufacturing, marketing and finance, etc., are incorporated.

Aero 584. Avionics, Navigation and Guidance of Aerospace Vehicles
Prerequisite: Aero 345. II (3 credits)
Principles of avionics, navigation and guidance. Deterministic and stochastic linear perturbation theory. Position fixing and celestial navigation with redundant measurements. Recursive navigation and Kalman filtering. Pursuit guidance, proportional navigation, ballistic guidance and velocity-to-be-gained guidance. Hardware mechanization.

Aero 585. Aerospace Engineering Seminar
Prerequisite: Aero 385 or senior standing. (1 credit)
A series of seminars by noted speakers designed to acquaint graduate and undergraduate students with contemporary research and technological issues in the aerospace industry. Involves a short term paper pertinent to one of the seminar topics.

Aero 590. Directed Study
Prerequisite: graduate standing and permission of  instructor. (1-6 credits)
Study of advanced aspects of aerospace engineering directed by an Aerospace faculty member.  Primarily for graduates. The student will submit a final report. 

Aero 597 (AOSS 597). Fundamentals of Space Plasma Physics
Prerequisite: senior-level statistical physics course. II (3 credits)
Basic plasma concepts, Boltzmann equation, higher order moments equations, MHD equations, double adiabatic theory. Plasma expansion to vacuum, transonic flows, solar wind, polar wind. Collisionless shocks, propagating and planetary shocks. Fokker-Planck equation, quasilinear theory, velocity diffusion, cosmic ray transport, shock acceleration. Spacecraft charging, mass loading.

Aero 611. Advanced Topics in Finite Element Structural Analysis
Prerequisite: Aero 511 or ME 605. I (3 credits)
Cyclic symmetry, design sensitivities and optimization. Applications to stress analysis, vibration, heat conduction, centrifugal effects, buckling. Introduction to high-level matrix-oriented programming languages (e.g., Direct Matrix Abstraction Program). Use of a large, general purpose finite element code as a research tool.

Aero 614. Advanced Theory of Plates and Shells
Prerequisite: Aero 416. II alternate years (3 credits)
Differential geometry of surfaces. Linear and nonlinear plate and shell theories in curvilinear coordinates. Anisotropic and laminated shells. Stability and post-buckling behavior. Finite element techniques, including special considerations for collapse analysis.

Aero 615 (CEE 617) (ME 649). Random Vibrations
Prerequisite: Math 425 or equivalent, CEE 513 or ME 541 or Aero 543 or equivalent. II alternate years (3 credits)
Introduction to concepts of random vibration with applications in civil, mechanical, and aerospace engineering. Topics include: characterization of random processes and random fields, calculus of random processes, applications of random vibrations to linear dynamical systems, brief discussion on applications to nonlinear dynamical systems.

Aero 618. Theory of Elastic Stability II
Prerequisite: Aero 518 or equivalent and graduate standing. II (3 credits)
Koiter's theory for buckling, post-buckling, mode interaction and imperfection sensitivity behavior in nonlinear solids. Applications to thin-walled beams, cylindrical and spherical shells as well as to 3-D hyperelastic solids. Loss of ellipticity in finitely strained solids. Hill's theory on bifurcation, uniqueness and post-bifurcation analysis in elastic-plastic solids with applications.

Aero 623. Computational Fluid Dynamics II
Prerequisite: Aero 523 or equivalent, substantial computer programming experience, and Aero 520. II (3 credits)
Advanced mathematical and physical concepts in computational fluid dynamics, with applications to one- and two-dimensional compressible flow. Euler and Navier-Stokes equations, numerical flux functions, boundary conditions, monotonicity, marching in time, marching to a steady state, grid generation.

Aero 625. Advanced Topics in Turbulent Flow
Prerequisite: Aero 525. II (3 credits)
Fundamentals of turbulent shear flows, with emphasis on dimensional reasoning and similarity scaling. Development of laminar shear flows, instability and transition to turbulent flow, kinetic and scalar energy transport mechanisms in turbulent shear flows, critical examination of numerical methods for turbulent flows, comparisons with experiments.

Aero 627. Advanced Gas Dynamics
Prerequisite: Aero 520, Aero 522. I (3 credits)
Linear and nonlinear surface waves. Flow instabilities; nonlinear stability analysis. Vorticity dynamics: vortex motions, instabilities, and breakdown. Boundary layers: steady and unsteady interactions; nonlinear instability.

Aero 633. Advanced Combustion
Prerequisite: Aero 533. II (3 credits)
Thermodynamics of gas mixtures, chemical kinetics, conservation equations for multi-component reacting gas mixtures, deflagration and detonation waves. Nozzle flows and boundary layers with reaction and diffusion.

Aero 714. Special Topics in Structural Mechanics
Prerequisite: permission of instructor. Term offered depends on special topic (to be arranged)

Aero 729. Special Topics in Gas Dynamics
Prerequisite: permission of instructor (to be arranged)
Advanced topics of current interest.

Aero 740. Special Topics in Flight Dynamics and Control Systems
(to be arranged)

Aero 800. Seminar

Aero 810. Seminar in Structures
(to be arranged)

Aero 820. Seminar in Aerodynamics
(to be arranged)

Aero 830. Seminar in Propulsion
(to be arranged)

Aero 840. Dynamics and Control Systems
(to be arranged)

Aero 990. Dissertation/Pre-Candidate
I, II (2-8 credits); IIIa, IIIb (1-4 credits)
Dissertation work by doctoral student not yet admitted to status as candidate. The defense of the dissertation, that is, the final oral examination, must be held under a full-term candidacy enrollment.

Aero 995. Dissertation/Candidate
Prerequisite: Graduate School authorization for admission as a doctoral candidate. I, II (8 credits); IIIa, IIIb (4 credits)
Election for dissertation work by a doctoral student who has been admitted to candidate status. The defense of the dissertation, that is, the final oral examination, must be held under a full-term candidacy enrollment.