Graduate Courses

The faculty has approval to offer the following courses in the academic years 2019–2020 and 2020–2021; however, not all courses are taught each semester or summer session. Students should consult the Course Schedule to determine which courses and topics will be offered during a particular semester or summer session. The Course Schedule may also reflect changes made to the course inventory after the publication of this catalog.

Please see the General Information Catalog for an updated list of courses effective fall 2020.¹

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1	Added fall 2020.

Aerospace Engineering: ASE

ASE 380P. Mathematical Analysis for Aerospace Engineers.

Three lecture hours a week for one semester. May be repeated for credit when the topics vary. Prerequisite: Graduate standing and consent of instructor.

Topic 1: Analytical Methods I. Introduction to modern mathematics, real analysis of functions of one variable, linear algebra, elements of real analysis of functions of many variables, calculus of variations. Aerospace Engineering 380P (Topic 1) and Engineering Mechanics 386K may not both be counted.
Topic 2: Analytical Methods II. Elements of complex analysis, Fourier and Laplace transforms, ordinary and partial differential equations, perturbation methods. Only one of the following may be counted: Aerospace Engineering 380P (Topic 2), Computational Science, Engineering, and Mathematics 386L, Engineering Mechanics 386L.

ASE 381P. System Theory.

Three lecture hours a week for one semester. May be repeated for credit when the topics vary. Prerequisite: Graduate standing and consent of instructor.

Topic 1: Linear Systems Analysis. Linear dynamical systems; controllability and observability; stability; realization theory; state-feedback and observers.
Topic 2: Multivariable Control Systems. Multivariable feedback systems; factorizations and controller parameterization; limitations and trade-offs of feedback; robust stability and performance; robust H2 and H-infinity control methods. Additional prerequisite: Aerospace Engineering 381P (Topic 1) or the equivalent.
Topic 3: Optimal Control Theory. Unconstrained and constrained finite-dimensional optimization, introduction to calculus of variations and optimal control, necessary and sufficient conditions for optimality, Pontryagin's Maximum Principle, minimum-time control, linear quadratic optimal control theory, introduction to dynamic programming, Hamilton-Jacobi-Bellman equation.
Topic 4: Numerical Methods in Optimization. Numerical methods for solving parameter optimization, suboptimal control, and optimal control problems.
Topic 6: Statistical Estimation Theory. Modeling static and dynamic systems, linear and nonlinear estimation, Bayesian estimation, batch least squares, Kalman filtering, square-root and information filtering, introduction to advanced estimation methods.
Topic 7: Advanced Topics in Estimation Theory. Estimation in the presence of unmodeled accelerations; nonlinear estimators; continuous estimation methods. Additional prerequisite: Aerospace Engineering 381P (Topic 6).
Topic 11: Nonlinear Dynamics and Control. Analysis and synthesis of nonlinear control systems. Stability theory, Center manifold analysis, feedback linearization, backstepping, time-scale separations, nonlinear observers, Aeromechanical system applications. Aerospace Engineering 381P (Topic 11) and 396 (Topic: Nonlinear Dynamics and Control) may not both be counted. Additional prerequisite: Aerospace Engineering 381P (Topic 1) or the equivalent, and consent of instructor.
Topic 13: Decision and Control of Human-Centered Robots. Oriented towards graduate students in control and robotics who are interested in end-to-end performance of real-world human-centered robotic systems. Control theory for robotics; socio cognitive modeling of human activity; behavior intervention via optimal control; Kinodynamic motion planning; temporal logics and their application to human-centered robots; whole-Body Dynamic Locomotion Controllers; intelligent Collision Management for human-centered robots. Explores theory and application from state-of-the-art papers from venues such as IEEE CSS American Control Conference, Robotics Science and Systems, The International Workshop on the Algorithmic Foundation of Robotics, Dynamic Walking, and IEEE-RAS International Conference on Humanoid Robots. Aerospace Engineering 381P (Topic 13) and Mechanical Engineering 396D may not both be counted. Additional prerequisite: Consent of graduate adviser.
Topic 14: System ID and Adaptive Control. System identification, persistence of excitation, model reference adaptive control, projection operators, immersion and invariance techniques, applications to aeromechanical systems. Aerospace Engineering 381P (Topic 14) and 396 (Topic: System ID and Adaptive Control) may not both be counted. Additional prerequisite: Aerospace Engineering 381P (Topic 1) or the equivalent.

ASE 382Q. Fluid Mechanics.

Three lecture hours a week for one semester. May be repeated for credit when the topics vary. Prerequisite: Graduate standing and consent of instructor.

Topic 1: Foundations of Fluid Mechanics. Fundamental equations; constitutive equations for Newtonian fluids; inviscid, incompressible potential flow; viscous flow including exact solutions and boundary layer theory; compressible flow.
Topic 7: Advanced Problems in Compressible Flow. Physics and modeling of compressible fluids; types and structure of shock waves; heat conduction and secondary viscosity effects; exact nonlinear flow models.
Topic 8: Lagrangian Methods in Computational Fluid Dynamics. Particle-based methods of computational fluid dynamics: molecular dynamics, direct simulation Monte Carlo, cellular automata, lattice Boltzmann, particle in cell, point vortex, immersed boundary.
Topic 9: Turbulent Mixing. Fundamentals of turbulent scalar mixing relevant to turbulent combustion. Includes governing equations, mass diffusion, scalar transport, kinematics, chaotic advection, vortex dynamics, small-scale structure of vorticity and dissipative fields, scalar dissipation rate, scaling laws for canonical flows, heat release effects, and turbulent jet flame structure.
Topic 10: Plasmas and Reactive Flows. Fundamental description of plasmas and reactive flows. Includes derivation of common governing transport equations for a broad class of electrically conducting and nonconducting reactive gases, and electromagnetic field interactions with gases, gas-phase and surface kinetics, transport properties, and applications.
Topic 11: Foundations of Computational Fluid Dynamics. Higher-order numerical methods for solving partial differential equations and ordinary differential equations. Focus on the numerical computation of fluid flows, with a variety of scientific applications. Aerospace Engineering 382Q (Topic 11) and Aerospace Engineering 396 (Topic: Foundations of Computational Fluid Dynamics) may not both be counted.

ASE 382R. Aerodynamics.

Three lecture hours a week for one semester. May be repeated for credit when the topics vary. Prerequisite: Graduate standing and consent of instructor.

Topic 3: Hypersonic Aerodynamics. Characteristics and assumptions of hypersonic flow; hypersonic similitude; Newtonian theory; constant density solutions.
Topic 5: Advanced Computational Methods. Development and implementation of numerical methods for solution of transport equations; computational grid generation; applications to fluid flows, including shock waves.
Topic 6: Molecular Gas Dynamics. Same as Mechanical Engineering 381Q (Topic 4). Kinetic theory, chemical thermodynamics, statistical mechanics. Applications: equilibrium gas properties, chemical kinetics, interaction of matter with radiation, rarefied gas dynamics. Additional prerequisite: Consent of instructor
Topic 7: Optical Diagnostics for Gas Flows. Fundamentals of nonintrusive flowfield diagnostics for aerodynamics and combustion. Basics of lasers and optical detectors; interferometric methods; Rayleigh, Raman, and Mie scattering; absorption spectroscopy; laser-induced fluorescence.

ASE 384P. Structural and Solid Mechanics.

Three lecture hours or two lecture hours and three laboratory hours a week for one semester, depending on the topic. May be repeated for credit when the topics vary. Prerequisite: Graduate standing and consent of instructor.

Topic 1: Solid Mechanics I. Same as Engineering Mechanics 388. Mathematical description of stress, deformation, and constitutive equations of solid mechanics; boundary value problems of elasticity. Three lecture hours a week for one semester.
Topic 2: Solid Mechanics II. Same as Engineering Mechanics 388L. Continuation of Engineering Mechanics 388. Additional topics in elasticity, plasticity, viscoelasticity, variational methods, and other areas of solid mechanics. Three lecture hours a week for one semester. Prerequisite: Graduate standing, Engineering Mechanics 388 or Aerospace Engineering 384P (Topic 1), and consent of instructor.
Topic 3: Structural Dynamics. Same as Engineering Mechanics 384L. Free and forced vibration of single-degree-of-freedom, multiple-degree-of-freedom, and continuous systems. Lagrange's equations and Hamilton's principle; discretization of continuous systems; numerical methods for response and algebraic eigenvalue problems. Three lecture hours a week for one semester.
Topic 4: Finite Element Methods. Same as Computational Science, Engineering, and Mathematics 393F and Engineering Mechanics 394F. Derivation and implementation of the finite element method; basic coding techniques; application to problems of stress and diffusion. Three lecture hours a week for one semester. Only one of the following may be counted: Aerospace Engineering 384P (Topic 4), Computational Science, Engineering, and Mathematics 393F, Engineering Mechanics 394F. Additional prerequisite: Graduate standing and consent of instructor.
Topic 6: Advanced Structural Dynamics. Analysis of complex flexible systems; discretization of complex structures by the finite element method; advanced computational methods for large finite element models. Three lecture hours a week for one semester. Additional prerequisite: Aerospace Engineering 384P (Topic 3) or Engineering Mechanics 384L or the equivalent.
Topic 8: Selected Topics in Aeroelasticity. Classical and contemporary topics in aeroelasticity; general introduction to aeroelastic phenomena, including flutter, divergence, control reversal, and flexibility effects on stability and control; aeroelastic tailoring; active control concepts; unsteady aerodynamic theories for lifting surfaces and bodies; aeroelastic system identification, including nonlinear systems (theory and laboratory applications). Three lecture hours a week for one semester.
Topic 11: Mechanics of Composite Materials. Constitutive equations; micromechanical and macromechanical behavior of lamina; strength and stiffness in tension and compression, theory of laminated plates; strength of laminates; delamination. Three lecture hours a week for one semester.

ASE 387P. Flight Mechanics, Guidance, Navigation, and Control.

Three lecture hours a week for one semester. May be repeated for credit when the topics vary. Prerequisite: Graduate standing and consent of instructor.

Topic 2: Mission Analysis and Design. Mission design and mission constraints, launch windows; rendezvous analysis; orbital design interactions with thermal and structural analysis; design of a typical mission.
Topic 6: Optimal Spacecraft Trajectories. Optimal control of spacecraft; primer vector theory; impulsive maneuvers; finite burn high/low thrust maneuvers; solar sails; numerical methods; applications to contemporary trajectory problems using single or multiple spacecraft.
Topic 7: Sensors and Actuators. Students use LabVIEW to study aerospace devices such as inertial navigation systems, control-moment gyroscopes, optical navigation systems, torque coils and magnetometers, robots, and integrated satellites.

ASE 388P. Celestial Mechanics.

Three lecture hours a week for one semester. May be repeated for credit when the topics vary. Prerequisite: Graduate standing and consent of instructor.

Topic 2: Celestial Mechanics I. N-body problem; three-body problem; restricted three-body problem; Jacobian integral; zero-velocity curves; equilibrium points; stability; linearized solutions; variational equations; periodic orbits; the two-body problem; variation of parameters; Lagrange's planetary equations; applications to near-earth and deep-space trajectories; numerical methods.
Topic 3: Celestial Mechanics II. Hamiltonian mechanics; dynamical systems; canonical transformations; invariant manifolds; Poincare surfaces of section; applications to restricted n-body problems; applications to sun-earth-moon or sun-planet-moon particle trajectory problems. Additional prerequisite: Aerospace Engineering 388P (Topic 2).

ASE 189, 289, 389, 489, 589, 689. Topics in Aerospace Engineering.

For each semester hour of credit earned, one lecture hour a week for one semester. May be repeated for credit when the topics vary. Prerequisite: Graduate standing and consent of instructor.

ASE 389P. Satellite Applications.

Three lecture hours a week for one semester. May be repeated for credit when the topics vary. Prerequisite: Graduate standing and consent of instructor.

Topic 1: Determination of Time. Concepts of time; fundamental reference system; polar motion; practical methods in time determination and dissemination; historical and present-day time scales; atomic clocks; time transfer via satellite.
Topic 2: Satellite Geodesy. Explore theory of the gravitational potential, including its time-variations; spherical harmonics and other representations; space-based remote sensing of the geopotential and its gradients; mass flux variability and its applications.
Topic 4: Methods in Orbit Determination. Variational methods of the orbit determination, Orbit parameter estimation, satellite tracking techniques and observables, modern precision orbit determination. Three lecture hours a week for one semester. Aerospace engineering 389P (Topic 4) and 396 (Topic: Orbit Determination) may not both be counted. Additional prerequisite: Aerospace Engineering 381P (Topic 6) or equivalent.
Topic 7: Global Navigation Satellite System Signal Processing. Comprehensive review of the theory and applications of the Global Positioning System (GPS), including the space segment, the control segment, the user segment, dilution of precision, GPS time, antispoofing, selected availability, differential/kinematic/dynamic techniques, field procedures, and GPS data collection and analysis. Applications of ground-based, aircraft-based, and satellite-based GPS receivers.
Topic 8: Satellite Control Systems. Spacecraft equations of motion; linearization and stability, classical control methods; digital and sampled data systems; multivariable control; attitude determination and control; momentum management; coupled modes; and case studies in satellite control.
Topic 9: Synthetic Aperture Radar: Principles and Applications. Synthetic Aperture Radar (SAR) imaging for Earth remote sensing, including image formation concepts and interpretation, radar interferometry processing and strategies, surface deformation, topographic mapping, and polarimetric applications.
Topic 10: Fundamentals and Geophysical Application of Imaging Radar Systems. Exploration of how radar images are formed and manipulated, as well as applications of the systems to problems such as measurement of the Earth crustal deformation. Focus on radar as a signal processing problem, radar image formation, polarimetric radars, and radar interferometry. Subjects include system design, scattering from natural surfaces, range and azimuth processing algorithms, and processor design. Additional prerequisite: Knowledge of Fourier Transform and at least one programming language (MATLAB, C or Fortran).
Topic 11: Advanced Satellite Geodesy. Examine kinematics and dynamics of displacement and Earth orientation. Investigate the determination of time and reference frames. Explore deformations of the Earth due to tides and mass loading. Study modern space geodetic applications. Additional prerequisite: Aerospace Engineering 389P (Topic 2).

ASE 397. Graduate Seminar.

Student, faculty, and visitor presentations of current research topics. Three lecture hours a week for one semester. May be repeated for credit. Offered on the credit/no credit basis only. Prerequisite: Graduate standing.

ASE 197R, 297R, 397R, 497R, 597R, 697R. Research in Aerospace Engineering.

For each semester hour of credit earned, the equivalent of one lecture hour a week for one semester. May be repeated for credit. Offered on the credit/no credit basis only. Prerequisite: Graduate standing and consent of instructor.

ASE 698. Thesis.

The equivalent of three lecture hours a week for two semesters. Offered on the credit/no credit basis only. Prerequisite: For 698A, graduate standing in aerospace engineering and consent of the graduate adviser; for 698B, Aerospace Engineering 698A.

ASE 398R. Master's Report.

Preparation of a report to fulfill the requirement for the master's degree under the report option. The equivalent of three lecture hours a week for one semester. Offered on the credit/no credit basis only. Prerequisite: Graduate standing in aerospace engineering and consent of the graduate adviser.

ASE 398T. Supervised Teaching in Aerospace Engineering.

Teaching methods and objectives, criteria for evaluating teaching effectiveness, procedural rules and regulations, laboratory teaching. Three lecture hours a week for one semester. Offered on the credit/no credit basis only. Prerequisite: Graduate standing and appointment as a teaching assistant.

ASE 399W, 699W, 999W. Dissertation.

May be repeated for credit. Offered on the credit/no credit basis only. Prerequisite: Admission to candidacy for the doctoral degree.