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Twin Cities Campus

Aerospace Engineering and Mechanics Ph.D.

Aerospace Engineering & Mechanics
College of Science and Engineering
Link to a list of faculty for this program.
Contact Information
Director of Graduate Studies, Department of Aerospace Engineering and Mechanics, University of Minnesota, 107 Akerman Hall, 110 Union Street S.E., Minneapolis, MN 55455 (612-625-8000; fax: 612-626-1558)
Email: aem-dgs@umn.edu
Website: https://cse.umn.edu/aem
  • Program Type: Doctorate
  • Requirements for this program are current for Fall 2021
  • Length of program in credits: 66
  • This program does not require summer semesters for timely completion.
  • Degree: Doctor of Philosophy
Along with the program-specific requirements listed below, please read the General Information section of this website for requirements that apply to all major fields.
The Department of Aerospace Engineering and Mechanics offers a PhD degree program which emphasizes engineering sciences basic to fluid mechanics, aerospace systems, and solid mechanics. Theoretical, analytical, experimental, and computational aspects of these fields are covered by the courses and research opportunities offered by the department.
Program Delivery
  • via classroom (the majority of instruction is face-to-face)
Prerequisites for Admission
The preferred undergraduate GPA for admittance to the program is 3.20.
A four-year BS degree in an engineering, basic science, or mathematics program is required.
Other requirements to be completed before admission:
Admission depends primarily on the applicant's undergraduate record, personal statement, and letters of recommendation.
Special Application Requirements:
Students are admitted fall semester only, with exceptions made only in unusual circumstances. The application deadline to be considered for financial aid via the department is December 15.
International applicants must submit score(s) from one of the following tests:
  • TOEFL
    • Internet Based - Total Score: 79
    • Internet Based - Writing Score: 21
    • Internet Based - Reading Score: 19
  • IELTS
    • Total Score: 6.5
  • MELAB
    • Final score: 80
Key to test abbreviations (TOEFL, IELTS, MELAB).
For an online application or for more information about graduate education admissions, see the General Information section of this website.
Program Requirements
12 to 30 credits are required in the major.
12 to 30 credits are required outside the major.
24 thesis credits are required.
This program may be completed with a minor.
Use of 4xxx courses toward program requirements is permitted under certain conditions with adviser approval.
A minimum GPA of 3.00 is required for students to remain in good standing.
Students can apply a maximum of 8 4-level course credits and 13 S/N-graded course credits to degree requirements. A maximum of 6 semester credits, no more than 4 from AEM 8000, can be applied to degree requirements.
Required Courses (4 credits)
Take 4 credits of the following in consultation with the advisor:
AEM 8000 - Seminar: Aerospace Engineering and Mechanics (1.0 cr)
Major Coursework (8 to 26 credits)
Select at least 8 credits in consultation with the advisor to meet the 12-credit minimum for the major field. Additional credits can be applied to the major with advisor approval.
AEM 4305 - Spacecraft Attitude Dynamics and Control (3.0 cr)
AEM 4321 - Automatic Control Systems (3.0 cr)
AEM 5247 - Hypersonic Aerodynamics (3.0 cr)
AEM 5253 - Computational Fluid Mechanics (3.0 cr)
AEM 5321 - Modern Feedback Control (3.0 cr)
AEM 5333 - Design-to-Flight: Small Uninhabited Aerial Vehicles (3.0 cr)
AEM 5401 - Intermediate Dynamics (3.0 cr)
AEM 5451 - Optimal Estimation (3.0 cr)
AEM 5501 - Continuum Mechanics (3.0 cr)
AEM 5503 - Theory of Elasticity (3.0 cr)
AEM 5581 - Mechanics of Solids (3.0 cr)
AEM 5651 - Aeroelasticity (3.0 cr)
AEM 8201 - Fluid Mechanics I (3.0 cr)
AEM 8202 - Fluid Mechanics II (3.0 cr)
AEM 8203 - Fluid Mechanics III (3.0 cr)
AEM 8207 - Hydrodynamic Stability (3.0 cr)
AEM 8211 - Theory of Turbulence I (3.0 cr)
AEM 8212 - Theory of Turbulence II (3.0 cr)
AEM 8213 - Turbulent Shear Flows (3.0 cr)
AEM 8221 - Rheological Fluid Mechanics (3.0 cr)
AEM 8231 - Molecular Gas Dynamics (3.0 cr)
AEM 8232 - Physical Gas Dynamics and Molecular Simulation (3.0 cr)
AEM 8241 - Perturbation Methods in Fluid Mechanics (3.0 cr)
AEM 8251 - Finite-Volume Methods in Computational Fluid Dynamics (3.0 cr)
AEM 8253 - Computational Methods in Fluid Mechanics (3.0 cr)
AEM 8261 - Nonlinear Waves in Mechanics (3.0 cr)
AEM 8271 - Experimental Methods in Fluid Mechanics (3.0 cr)
AEM 8400 - Seminar: Aerospace Systems (1.0 cr)
AEM 8411 - Advanced Dynamics (3.0 cr)
AEM 8421 - Robust Multivariable Control Design (3.0 cr)
AEM 8423 - Convex Optimization Methods in Control (3.0 cr)
AEM 8426 - Optimization and System Sciences (3.0 cr)
AEM 8442 - Aerospace Positioning, Navigation and Timing (3.0 cr)
AEM 8451 - System Identification: Theory and Applications (3.0 cr)
AEM 8453 - Model Reduction and Approximation of Dynamical Systems (3.0 cr)
AEM 8500 - Research Seminar in Mechanics of Materials (1.0 cr)
AEM 8523 - Elastodynamics (3.0 cr)
AEM 8525 - Elastic Stability of Materials (3.0 cr)
AEM 8527 - Pattern Formation and Bifurcation in Materials (3.0 cr)
AEM 8531 - Fracture Mechanics (3.0 cr)
AEM 8533 - Theory of Plasticity (3.0 cr)
AEM 8541 - Mechanics of Crystalline Solids (3.0 cr)
AEM 8551 - Multiscale Methods for Bridging Length and Time Scales (3.0 cr)
Outside Coursework (12 to 30 credits)
Select credits from the following in consultation with the advisor to meet the 12-credit minimum, and additional credits as needed to complete the 42 course credits required. Other courses may be chosen with advisor approval.
BMEN 5321 - Microfluidics in Biology and Medicine (3.0 cr)
BMEN 8101 - Biomedical Digital Signal Processing (3.0 cr)
CEGE 8401 - Fundamentals of Finite Element Method (3.0 cr)
CEGE 8521 - The Atmospheric Boundary Layer (4.0 cr)
CHEM 8541 - Dynamics (4.0 cr)
CHEM 8565 - Chemical Reaction Dynamics (2.0 cr)
CSCI 4041 - Algorithms and Data Structures (4.0 cr)
CSCI 5304 - Computational Aspects of Matrix Theory (3.0 cr)
CSCI 5451 - Introduction to Parallel Computing: Architectures, Algorithms, and Programming (3.0 cr)
CSCI 5512 - Artificial Intelligence II (3.0 cr)
CSCI 5521 - Machine Learning Fundamentals (3.0 cr)
CSCI 5525 - Machine Learning: Analysis and Methods (3.0 cr)
CSCI 5551 - Introduction to Intelligent Robotic Systems (3.0 cr)
CSCI 5552 - Sensing and Estimation in Robotics (3.0 cr)
CSCI 8314 - Sparse Matrix Computations (3.0 cr)
EE 5231 - Linear Systems and Control (3.0 cr)
EE 5235 - Robust Control System Design (3.0 cr)
EE 5239 - Introduction to Nonlinear Optimization (3.0 cr)
EE 5531 - Probability and Stochastic Processes (3.0 cr)
EE 8215 - Nonlinear Systems (3.0 cr)
EE 5571 - Statistical Learning and Inference (3.0 cr)
MATH 4242 - Applied Linear Algebra (4.0 cr)
MATH 5587 - Elementary Partial Differential Equations I (4.0 cr)
MATH 5651 - Basic Theory of Probability and Statistics (4.0 cr)
MATH 8401 - Mathematical Modeling and Methods of Applied Mathematics (3.0 cr)
MATH 8402 - Mathematical Modeling and Methods of Applied Mathematics (3.0 cr)
MATH 8431 - Mathematical Fluid Mechanics (3.0 cr)
MATH 8441 - Numerical Analysis and Scientific Computing (3.0 cr)
MATH 8442 - Numerical Analysis and Scientific Computing (3.0 cr)
MATH 8445 - Numerical Analysis of Differential Equations (3.0 cr)
MATH 8446 - Numerical Analysis of Differential Equations (3.0 cr)
MATH 8601 - Real Analysis (3.0 cr)
ME 8285 - Control Systems for Intelligent Vehicle Applications (3.0 cr)
ME 8361 - Molecular Gas Dynamics (3.0 cr)
ME 8446 - Advanced Combustion (3.0 cr)
Thesis Credits (24 credits)
Take 24 doctoral thesis credits after passing preliminary oral exam.
AEM 8888 - Thesis Credit: Doctoral (1.0-24.0 cr)
 
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AEM 8000 - Seminar: Aerospace Engineering and Mechanics
Credits: 1.0 [max 4.0]
Grading Basis: S-N or Aud
Typically offered: Every Fall & Spring
To be determined prereq: DGS consent
AEM 4305 - Spacecraft Attitude Dynamics and Control
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Every Spring
Kinematics/dynamics for six-degree of freedom rigid body motions. Euler's angles/equations. Torque free motion, spin stabilization, dual-spin spacecraft, nutation damping, gyroscopic attitude control, gravity gradient stabilization. Linear systems analysis, Laplace transforms, transfer functions. Linear control theory. PID controllers. prereq: [4301, [3101 or ME 3281 or EE 3015], CSE upper div] or grad student
AEM 4321 - Automatic Control Systems
Credits: 3.0 [max 3.0]
Course Equivalencies: AEM 4321/EE 4231
Grading Basis: A-F or Aud
Typically offered: Every Fall
Modeling, characteristics, and performance of feedback control systems. Stability, root locus, and frequency response methods. Nyquist and Bode diagrams. Lead-lag and PID compensators. Digital implementation and hardware considerations. prereq: CSE upper div or grad student
AEM 5247 - Hypersonic Aerodynamics
Credits: 3.0 [max 3.0]
Course Equivalencies: AEM 4247/AEM 5247
Grading Basis: A-F or Aud
Typically offered: Spring Even Year
Importance/properties of hypersonic flow. Hypersonic shock and expansion-wave relations. Local surface inclination methods. Approximate/exact methods for hypersonic inviscid flow fields. Viscous flow: boundary layers, aerodynamic heating, hypersonic viscous interactions, computational methods. Hypersonic propulsion and vehicle design. prereq: 4202 or equiv, CSE grad student
AEM 5253 - Computational Fluid Mechanics
Credits: 3.0 [max 3.0]
Course Equivalencies: AEM 4253/AEM 5253
Prerequisites: [4201 or equiv], [CSci 1113 or equiv], CSE grad student
Grading Basis: A-F or Aud
Typically offered: Every Fall
Introductory concepts in finite difference and finite volume methods as applied to various ordinary/partial differential model equations in fluid mechanics. Fundamentals of spatial discretization and numerical integration. Numerical linear algebra. Introduction to engineering and scientific computing environment. Advanced topics may include finite element methods, spectral methods, grid generation, turbulence modeling. prereq: [4201 or equiv], [CSci 1113 or equiv], CSE grad student
AEM 5321 - Modern Feedback Control
Credits: 3.0 [max 3.0]
Course Equivalencies: AEM 5321/EE 5231
Typically offered: Every Fall
State space theory for multiple-input-multiple-output aerospace systems. Singular value decomposition technique, applications to performance/robustness. Linear quadratic gaussian and eigenstructure assignment design methods. Topics in H[infinity symbol]. Applications. prereq: 4321 or EE 4231 or ME 5281 or equiv
AEM 5333 - Design-to-Flight: Small Uninhabited Aerial Vehicles
Credits: 3.0 [max 3.0]
Grading Basis: A-F only
Typically offered: Periodic Spring
Designing, assembling, modeling, simulating, testing/flying of uninhabited aerial vehicles. Rapid prototyping software tools for vehicle modeling. Guidance, navigation, flight control, real-time implementations, hardware-in-the-loop simulations, flight tests. prereq: [[4202, concurrent registration is required (or allowed) in 4303W, 4601] or equiv], instr consent
AEM 5401 - Intermediate Dynamics
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall
Three-dimensional Newtonian mechanics, kinematics of rigid bodies, dynamics of rigid bodies, generalized coordinates, holonomic constraints, Lagrange equations, applications. prereq: CSE upper div or grad, 2012, Math 2243
AEM 5451 - Optimal Estimation
Credits: 3.0 [max 3.0]
Course Equivalencies: AEM 5451/EE 5251
Typically offered: Fall Even Year
Basic probability theory. Batch/recursive least squares estimation. Filtering of linear/non-linear systems using Kalman and extended Kalman filters. Applications to sensor fusion, fault detection, and system identification. prereq: [[MATH 2243 or STAT 3021 or equiv], [4321 or EE 4231 or ME 5281 or equiv]] or instr consent
AEM 5501 - Continuum Mechanics
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
Concepts common to all continuous media; elements of tensor analysis; motion, deformation, vorticity; material derivatives; mass, continuity equation; balance of linear, angular momentum; geometric characterization of stress; constitutive equations. prereq: CSE upper div or grad, 3031, Math 2243 or equiv or instr consent
AEM 5503 - Theory of Elasticity
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Every Spring
Introduction to the theory of elasticity, with emphasis on linear elasticity. Linear and nonlinear strain measures, boundary-value problem for linear elasticity, plane problems in linear elasticity, three dimensional problems in linear elasticity. Topics from nonlinear elasticity, micromechanics, contact problems, fracture mechanics. prereq: 4501 or equiv, Math 2263 or equiv or instr consent
AEM 5581 - Mechanics of Solids
Credits: 3.0 [max 3.0]
Course Equivalencies: AEM 4581/AEM 5581
Typically offered: Fall Odd Year
Continuum mechanics in one dimension: kinematics; mass, momentum/energy, constitutive theory. Wave propagation, heat conduction. Strings. Euler-Bernoulli theory. 3-D deformations/stress. Topics from fracture mechanics, structural stability, vibrations, thin films, layered media, smart materials, phase transformations, 3-D elastic wave propagation. Elasticity, viscoelasticity, plasticity. prereq: 3031 or equiv, [Math 2373 or equiv], [Math 2374 or equiv], [CSE grad student]
AEM 5651 - Aeroelasticity
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall
Static aeroelastic phenomena, torsional divergence of a lifting surface, control surface reversal. Aeroelastic flutter, unsteady aerodynamics. Problems of gust response, buffeting. Design project. prereq: 4202, 4301, [grad student or CSE upper div]
AEM 8201 - Fluid Mechanics I
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
Mathematical and physical principles governing the motion of fluids. Kinematic, dynamic, and thermodynamic properties of fluids; stress and deformation; equations of motion; analysis of rotational and irrotational inviscid incompressible flow; two-dimensional and three-dimensional potential flow. prereq: 4201 or equiv, Math 2263 or equiv
AEM 8202 - Fluid Mechanics II
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
Analysis of incompressible viscous flow; creeping flows; boundary layer flow. prereq: 8201
AEM 8203 - Fluid Mechanics III
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
Analysis of compressible flow and shock waves; method of characteristics for one-dimensional unsteady flow and for two-dimensional steady flow. prereq: 8202
AEM 8207 - Hydrodynamic Stability
Credits: 3.0 [max 4.0]
Typically offered: Periodic Fall
Theory of hydrodynamic stability. Stability of shear flows, rotating flows, boundary layer, two fluid flows, fingering flows, Rayleigh-Taylor instability, Kelvin Helmholtz instability, capillary instability, convective/absolute stability. Methods of linear stability, normal modes, energy theory of stability, nonlinear perturbation, bifurcation theory, transition to turbulence. prereq: 8201
AEM 8211 - Theory of Turbulence I
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall
Reynolds equations, methods of averaging, elements of stability theory and vortex dynamics; description of large vortical structures in mixing layers and boundary layers; horseshoe vortices; flow visualization. prereq: 8202
AEM 8212 - Theory of Turbulence II
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall
Prandtl's mixing length theory applied to classical boundary layer, pipe, jet, and wake flows; prediction methods used at Stanford Conference; law of wall; law of wake; K-epsilon method. prereq: 8211
AEM 8213 - Turbulent Shear Flows
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Periodic Fall
Equations of motion for turbulent flow. Isotropic/homogeneous turbulence. Free shear flows. Wall turbulence, elements of vortex dynamics. prereq: 8201, 8202
AEM 8221 - Rheological Fluid Mechanics
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall
Methods of solution for flows of simple fluids with general constitutive equations. Topics from viscometric flow, extensional flow, perturbations of the rest state with steady and unsteady flow, secondary flow. prereq: 8201 or 5501 or instr consent
AEM 8231 - Molecular Gas Dynamics
Credits: 3.0 [max 3.0]
Course Equivalencies: AEM 8231/ME 8361
Typically offered: Periodic Fall
Kinetic theory of gases, Boltzmann equation, Maxwell-Boltzmann distribution, collisions, transport properties. Introduction to quantum mechanics. Statistical thermodynamics, classical/quantum statistics. Partition functions and thermodynamic properties. Irreversible thermodynamics. prereq: [4201 or equiv], [4203 or equiv], [ME 3324 or equiv]
AEM 8232 - Physical Gas Dynamics and Molecular Simulation
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Periodic Spring
Molecular description of gas dynamics. Kinetic theory, transport theory, quantum mechanics for internal energy partitions, statistical thermodynamics. Finite rate chemical kinetics. Emphasis on link to continuum fluid dynamics. Overview of numerical simulation techniques for the Boltzmann equation with emphasis on direct simulation Monte Carlo. prereq: AEM 8231
AEM 8241 - Perturbation Methods in Fluid Mechanics
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall
Method of matched asymptotic expansions presented through simple examples and applied to viscous flows at high and low Reynolds numbers and other problems in fluid mechanics and applied mathematics. prereq: 8202 or instr consent
AEM 8251 - Finite-Volume Methods in Computational Fluid Dynamics
Credits: 3.0 [max 3.0]
Typically offered: Periodic Spring
Development of finite-volume computational methods for solution of compressible Navier-Stokes equations. Accuracy, consistency, and stability of numerical methods; high-resolution upwind shock-capturing schemes; treatment of boundary conditions; explicit and implicit formulations; considerations for high performance computers; recent developments and advanced topics. prereq: 4201 or 8201 or equiv, CSci 1107 or equiv
AEM 8253 - Computational Methods in Fluid Mechanics
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Periodic Fall
Spatial discretization. Spectral methods. Temporal discretization. Nonlinear sources of error. Incompressible Navier-Stokes equations. Compressible Navier-Stokes equations. prereq: 4201
AEM 8261 - Nonlinear Waves in Mechanics
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall
Theory of kinematic, hyperbolic, and dispersive waves, with application to traffic flow, gas dynamics, and water waves. prereq: 5501 or instr consent
AEM 8271 - Experimental Methods in Fluid Mechanics
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall
Overview of computer organization, including external communications and A/D, D/A conversion. Measurement techniques, such as pressure measurements and hot-wire and laser Doppler anemometry. Signal processing and uncertainty; computer control of experiments. prereq: 4201, instr consent
AEM 8400 - Seminar: Aerospace Systems
Credits: 1.0 [max 4.0]
Grading Basis: S-N or Aud
Typically offered: Every Fall & Spring
Developing program of research in aerospace Systems. Discussions of current research/topics of interest. prereq: Aerosp Eng grad student
AEM 8411 - Advanced Dynamics
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Periodic Spring
Advanced analytical mechanics and non-linear dynamical systems. Review of Lagrangian mechanics. Hamilton's equations of motion. Canonical transformations and Hamilton-Jacobi theory. Kane's equations. Analysis of differential equations and numerical methods. Phase plane, averaging, and perturbation methods. Stability/bifurcations of equilibria. prereq: 5401 or equiv
AEM 8421 - Robust Multivariable Control Design
Credits: 3.0 [max 3.0]
Typically offered: Periodic Spring
Application of robust control theory to aerospace systems. Role of model uncertainty/modeling errors in design process. Control analysis and synthesis, including H[sub2] and H[infinity symbol] optimal control design and structural singular value [Greek letter mu] techniques. prereq: 5321 or equiv
AEM 8423 - Convex Optimization Methods in Control
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Periodic Fall
Practical aspects of convex optimization methods applied to solve design/analysis problems in control theory. prereq: 5321 or EE 5231 or equiv
AEM 8426 - Optimization and System Sciences
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Periodic Fall
Review of probability concepts and random variables, nonlinear stochastic differential equations and their numerical solutions, Monte-Carlo simulations, Gauss-Markov process, stochastic dynamic programming, and optimal control of practical uncertain dynamic systems. prereq: 5321 or 5431, CSE grad student
AEM 8442 - Aerospace Positioning, Navigation and Timing
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall
Fundamental principles of navigation. Algorithms, performance analysis of navigational systems. Radio-navigation systems (DME,VOR,ILS). Satellite navigation ysstems (GPS,GLDNASS). Inertial navigation systems mechanization, error analysis. prereq: Exposure to [linear algebra, differential equations, probability, statistics]
AEM 8451 - System Identification: Theory and Applications
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Periodic Spring
Modeling methods for dynamic systems using measurement data, or in combination with first principles, based on theory of systems/signals. Primary emphasis on linear systems for control system design/simulation applications. Examples from aerospace applications. prereq: 4321 or equiv
AEM 8453 - Model Reduction and Approximation of Dynamical Systems
Credits: 3.0 [max 3.0]
Typically offered: Periodic Spring
In this course, we will study analytical and data-driven methods for model reduction and approximation of dynamical systems. The focus will be on learning the relevant mathematics and tools for obtaining ?lean? low-dimensional representations of dynamical systems, which can be used to facilitate analysis and design. Roughly half of the course will be devoted to the problem of model reduction: i.e., given a mathematical description of a system, reduce the number of degrees of freedom required to faithfully represent that system. The other half of the course will be devoted to data-driven approximation of dynamical systems: i.e., given empirical data generated by a dynamical system, determine a mathematical representation for the underlying system dynamics. Although these two general problems are distinct, they are closely related and will be studied in parallel throughout the term.
AEM 8500 - Research Seminar in Mechanics of Materials
Credits: 1.0 [max 12.0]
Grading Basis: S-N or Aud
Typically offered: Every Fall & Spring
Seminars given by students, faculty, and visitors on topics drawn from current research. prereq: instr consent
AEM 8523 - Elastodynamics
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Periodic Fall
Waves and vibrations in rods, beams, and plates; dispersion; volume and surface waves; reflection; energy theorems; vibrations of bounded media and relation to technical theories; elements of nonlinear waves, inelastic waves, and stability of motion of elastic systems. prereq: 4581 or 5501 or instr consent
AEM 8525 - Elastic Stability of Materials
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Fall Even Year
Stability/bifurcation problems. Poincare stability, Lyapunov stability, asymptotic stability. Lyapunov's general methods. Minimum potential energy criterion for elastic conservative systems. Numerical methods for continuation/branch switching. Material phase transformation, crystalline material stability, soft-phonon theory of phase transitions. Material instability problems in finite-strain elasticity. Stability of discrete/continuous structures. prereq: CSE grad student, familiarity with theory of linear algebra
AEM 8527 - Pattern Formation and Bifurcation in Materials
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Periodic Fall
This course provides an in-depth discussion of bifurcation and stability problems and pattern formation in physics, chemistry, and mechanics (Fluids, Solids, Materials Science) with an emphasis on the application of symmetry theory to such problems. This theory applies to essentially all nonlinear equilibrium problems in science and engineering, but this class has a particular focus on structural mechanics and materials applications, including buckling of: beams, honeycombs, lattice structures, and phase transforming crystals. prereq: CSE grad student or instructor consent, familiarity with linear algebra.
AEM 8531 - Fracture Mechanics
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Periodic Fall & Spring
Theories of mechanical breakdown. Kinetic rate theories and instability considerations; formation of equilibrium cracks and circular crack propagation under pulses; statistical aspects of strength and fracture of micromolecular systems; time and temperature dependency in fracture problems and instability of compressed material systems. prereq: 5503 or instr consent
AEM 8533 - Theory of Plasticity
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall
Theory of permanent deformation of ductile metals; bi-linear material models, Drucker's three bar truss, and other examples; 3-D continuum formulation, yield surfaces, hardening rules, and material stability; slip line theory, Prandtl punch solution; single crystal plasticity. prereq: 5203 or instr consent
AEM 8541 - Mechanics of Crystalline Solids
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall & Spring
Atomic theory of crystals and origins of stress in crystals. Relation between atomic and continuum description; phase transformations and analysis of microstructure; effects of shear stress, pressure, temperature, electromagnetic fields, and composition on transformation temperatures and microstructure; interfacial energy in solids. prereq: 5501 or instr consent
AEM 8551 - Multiscale Methods for Bridging Length and Time Scales
Credits: 3.0 [max 3.0]
Course Equivalencies: AEM 8551/SCIC 8551
Prerequisites: Basic knowledge of [continuum mechanics, atomic forces], familiarity with partial differential equations, grad student in [engineering or mathematics or physics]
Grading Basis: A-F or Aud
Typically offered: Periodic Spring
Classical/emerging techniques for bridging length/time scales. Nonlinear thermoelasticity, viscous fluids, and micromagnetics from macro/atomic viewpoints. Statistical mechanics, kinetic theory of gases, weak convergence methods, quasicontinuum, effective Hamiltonians, MD, new methods for bridging time scales. prereq: Basic knowledge of [continuum mechanics, atomic forces], familiarity with partial differential equations, grad student in [engineering or mathematics or physics]
BMEN 5321 - Microfluidics in Biology and Medicine
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall
Fundamentals of microfluidics. Fluid mechanics/transport phenomena in microscale systems. Pressure/surface driven flows. Capillary forces, electrokinetics, hydraulic circuit analysis. Finite element modeling for microfluidic systems. Design/fabrication methods for microfluidic devices. prereq: [3111, AEM 4201, ChEn 4005, [ME 3331 or ME 3332 or CSE grad student or instr consent]
BMEN 8101 - Biomedical Digital Signal Processing
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Every Spring
Signal processing theory for analyzing real world digital signals. Digital signal processing and mathematically derived algorithms for analysis of stochastic signals. Spectral analyses, noise cancellation, optimal filtering, blind source separation, beamforming techniques. prereq: [[MATH 2243 or MATH 2373], [MATH 2263 or MATH 2374]] or equiv
CEGE 8401 - Fundamentals of Finite Element Method
Credits: 3.0 [max 3.0]
Prerequisites: 4411 or #
Grading Basis: A-F or Aud
Typically offered: Every Spring
Elements of calculus of variations; weak and strong formulations of linear continuum and structural problems. Isoparametric elements and numerical integration. Basic concepts of error analysis and convergence. Analysis of plates and shells. Introduction to mixed methods and time dependent problems. prereq: 4411 or instr consent
CEGE 8521 - The Atmospheric Boundary Layer
Credits: 4.0 [max 4.0]
Prerequisites: CSE or COAFES grad student or #
Grading Basis: A-F or Aud
Typically offered: Periodic Summer
Land-atmosphere interactions and turbulent transport in the atmospheric boundary layer (ABL), the lowest part of the atmosphere. ABL development and dynamics. Turbulence, surface energy balance, spectral analysis, similarity theory. Flow over homogeneous and heterogeneous surfaces. Atmospheric stability, measurement, simulation of turbulent fluxes. prereq: CSE or COAFES grad student or instr consent
CHEM 8541 - Dynamics
Credits: 4.0 [max 4.0]
Course Equivalencies: Chem 5541/8541
Typically offered: Periodic Fall
Mathematical methods for physical chemistry. Classical mechanics/dynamics, normal modes of vibration. Special topics such as rotational motion, Langevin equation, Brownian motion, time correlation functions, collision theory, cross sections, energy transfer, molecular forces, potential energy surfaces, classical electrostatics, Shannon entropy. prereq: Undergrad physical chem course
CHEM 8565 - Chemical Reaction Dynamics
Credits: 2.0 [max 2.0]
Typically offered: Periodic Spring
Fundamentals of chemical reaction dynamics including potential energy surfaces, collision theory, statistical mechanical background and transition state theory, variational transition state theory, activation energy, tunneling, unimolecular reactions, energy transfer, reactions in solution, solvation free energy, potential of mean force, quasithermodynamic treatment, reactions in solution, diffusion control, Kramers’ theory, and photochemistry
CSCI 4041 - Algorithms and Data Structures
Credits: 4.0 [max 4.0]
Course Equivalencies: CSci 4041/CSci 4041H
Typically offered: Every Fall & Spring
Rigorous analysis of algorithms/implementation. Algorithm analysis, sorting algorithms, binary trees, heaps, priority queues, heapsort, balanced binary search trees, AVL trees, hash tables and hashing, graphs, graph traversal, single source shortest path, minimum cost spanning trees. prereq: [(1913 or 1933) and 2011] or instr consent; cannot be taken for grad CSci cr
CSCI 5304 - Computational Aspects of Matrix Theory
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
Perturbation theory for linear systems and eigenvalue problems. Direct/iterative solution of large linear systems. Matrix factorizations. Computation of eigenvalues/eigenvectors. Singular value decomposition. LAPACK/other software packages. Introduction to sparse matrix methods. prereq: 2031 or 2033 or instr consent
CSCI 5451 - Introduction to Parallel Computing: Architectures, Algorithms, and Programming
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
Parallel architectures design, embeddings, routing. Examples of parallel computers. Fundamental communication operations. Performance metrics. Parallel algorithms for sorting. Matrix problems, graph problems, dynamic load balancing, types of parallelisms. Parallel programming paradigms. Message passing programming in MPI. Shared-address space programming in openMP or threads. prereq: 4041 or instr consent
CSCI 5512 - Artificial Intelligence II
Credits: 3.0 [max 3.0]
Course Equivalencies: CSci 5512W/CSci 5512
Typically offered: Every Spring
Uncertainty in artificial intelligence. Probability as a model of uncertainty, methods for reasoning/learning under uncertainty, utility theory, decision-theoretic methods. prereq: [STAT 3021, 4041] or instr consent
CSCI 5521 - Machine Learning Fundamentals
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall
Problems of pattern recognition, feature selection, measurement techniques. Statistical decision theory, nonstatistical techniques. Automatic feature selection/data clustering. Syntactic pattern recognition. Mathematical pattern recognition/artificial intelligence. Prereq: [2031 or 2033], STAT 3021, and knowledge of partial derivatives
CSCI 5525 - Machine Learning: Analysis and Methods
Credits: 3.0 [max 3.0]
Typically offered: Fall Even Year
Models of learning. Supervised algorithms such as perceptrons, logistic regression, and large margin methods (SVMs, boosting). Hypothesis evaluation. Learning theory. Online algorithms such as winnow and weighted majority. Unsupervised algorithms, dimensionality reduction, spectral methods. Graphical models. prereq: Grad student or instr consent
CSCI 5551 - Introduction to Intelligent Robotic Systems
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall
Transformations, kinematics/inverse kinematics, dynamics, control. Sensing (robot vision, force control, tactile sensing), applications of sensor-based robot control, robot programming, mobile robotics, microrobotics. prereq: 2031 or 2033 or instr consent
CSCI 5552 - Sensing and Estimation in Robotics
Credits: 3.0 [max 3.0]
Typically offered: Periodic Spring
Bayesian estimation, maximum likelihood estimation, Kalman filtering, particle filtering. Sensor modeling and fusion. Mobile robot motion estimation (odometry, inertial,laser scan matching, vision-based) and path planning. Map representations, landmark-based localization, Markov localization, simultaneous localization/mapping (SLAM), multi-robot localization/mapping. prereq: [5551, Stat 3021] or instr consent
CSCI 8314 - Sparse Matrix Computations
Credits: 3.0 [max 3.0]
Typically offered: Periodic Spring
Sparsity and sparse matrices. Data structures for sparse matrices. Direct methods for sparse linear systems. Reordering techniques to reduce fill-in such as minimal degree ordering and nested dissection ordering. Iterative methods. Preconditioning algorithms. Algorithms for sparse eigenvalue problems and sparse least-squares. prereq: 5304 or numerical linear algebra course or instr consent
EE 5231 - Linear Systems and Control
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
The course studies finite-dimensional linear systems in continuous and discrete time. Such systems are described by ordinary differential and difference equations. Input-output and state-space descriptions are provided and analyzed. Introductory methods for controlling such systems are developed. prereq: [3015, CSE grad student] or instr consent
EE 5235 - Robust Control System Design
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
Development of control system design ideas; frequency response techniques in design of single-input/single-output (and MI/MO) systems. Robust control concepts. CAD tools. prereq: CSE grad, 3015, 5231 or instr consent
EE 5239 - Introduction to Nonlinear Optimization
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall & Spring
Nonlinear optimization. Analytical/computational methods. Constrained optimization methods. Convex analysis, Lagrangian relaxation, non-differentiable optimization, applications in integer programming. Optimality conditions, Lagrange multiplier theory, duality theory. Control, communications, management science applications. prereq: [3025, Math 2373, Math 2374, CSE grad student] or dept consent
EE 5531 - Probability and Stochastic Processes
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
Probability, random variables and random processes. System response to random inputs. Gaussian, Markov and other processes for modeling and engineering applications. Correlation and spectral analysis. Estimation principles. Examples from digital communications and computer networks. prereq: [3025, CSE grad student] or dept consent
EE 8215 - Nonlinear Systems
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall & Spring
Current topics in stability analysis of nonlinear systems, design of controllers for nonlinear systems, discrete-time and stochastic nonlinear systems. prereq: instr consent
EE 5571 - Statistical Learning and Inference
Credits: 3.0 [max 3.0]
Typically offered: Periodic Spring
Deterministic and random approaches to learning and inference from data, with applications to statistical models for estimation, detection, and classification. Algorithms and their performance include minimum-variance unbiased estimators, sufficient statistics, fundamental bounds, (non)linear least-squares, maximum-likelihood, expectation-maximization, nonparametric density estimators, mean-square error and Bayesian estimators, importance sampling, Kalman and particle filtering, sequential probability ratio test, bootstrap, Monte Carlo Markov Chains, and graphical models. prereq: courses in Stochastic Processes (EE 5531) and Digital Signal Processing (EE 4541)
MATH 4242 - Applied Linear Algebra
Credits: 4.0 [max 4.0]
Course Equivalencies: Math 4242/Math 4457
Typically offered: Every Fall, Spring & Summer
Systems of linear equations, vector spaces, subspaces, bases, linear transformations, matrices, determinants, eigenvalues, canonical forms, quadratic forms, applications. prereq: 2243 or 2373 or 2573
MATH 5587 - Elementary Partial Differential Equations I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Emphasizes partial differential equations w/physical applications, including heat, wave, Laplace's equations. Interpretations of boundary conditions. Characteristics, Fourier series, transforms, Green's functions, images, computational methods. Applications include wave propagation, diffusions, electrostatics, shocks. prereq: [2243 or 2373 or 2573], [2263 or 2374 or 2574]
MATH 5651 - Basic Theory of Probability and Statistics
Credits: 4.0 [max 4.0]
Course Equivalencies: Math 5651/Stat 5101
Typically offered: Every Fall & Spring
Logical development of probability, basic issues in statistics. Probability spaces, random variables, their distributions/expected values. Law of large numbers, central limit theorem, generating functions, sampling, sufficiency, estimation. prereq: [2263 or 2374 or 2573], [2243 or 2373]; [2283 or 2574 or 3283] recommended.
MATH 8401 - Mathematical Modeling and Methods of Applied Mathematics
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall
Dimension analysis, similarity solutions, linearization, stability theory, well-posedness, and characterization of type. Fourier series and integrals, wavelets, Green's functions, weak solutions and distributions. prereq: 4xxx numerical analysis and applied linear algebra or instr consent
MATH 8402 - Mathematical Modeling and Methods of Applied Mathematics
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Every Spring
Calculus of variations, integral equations, eigenvalue problems, spectral theory. Perturbation, asymptotic methods. Artificial boundary conditions, conformal mapping, coordinate transformations. Applications to specific modeling problems. prereq: 8401 or instr consent
MATH 8431 - Mathematical Fluid Mechanics
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Periodic Fall
Equations of continuity/motion. Kinematics. Bernoulli's theorem, stream function, velocity potential. Applications of conformal mapping. prereq: 5xxx numerical analysis of partial differential equations or instr consent
MATH 8441 - Numerical Analysis and Scientific Computing
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
Approximation of functions, numerical integration. Numerical methods for elliptic partial differential equations, including finite element methods, finite difference methods, and spectral methods. Grid generation. prereq: [4xxx analysis, 4xxx applied linear algebra] or instr consent
MATH 8442 - Numerical Analysis and Scientific Computing
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
Numerical methods for integral equations, parabolic partial differential equations, hyperbolic partial differential equations. Monte Carlo methods. prereq: 8441 or instr consent; 5477-5478 recommended for engineering and science grad students
MATH 8445 - Numerical Analysis of Differential Equations
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall
Finite element and finite difference methods for elliptic boundary value problems (e.g., Laplace's equation) and solution of resulting linear systems by direct and iterative methods. prereq: 4xxx numerical analysis, 4xxx partial differential equations or instr consent
MATH 8446 - Numerical Analysis of Differential Equations
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Every Spring
Numerical methods for parabolic equations (e.g., heat equations). Methods for elasticity, fluid mechanics, electromagnetics. Applications to specific computations. prereq: 8445 or instr consent
MATH 8601 - Real Analysis
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall
Set theory/fundamentals. Axiom of choice, measures, measure spaces, Borel/Lebesgue measure, integration, fundamental convergence theorems, Riesz representation. prereq: 5616 or instr consent
ME 8285 - Control Systems for Intelligent Vehicle Applications
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall
This course focuses on a study of several advanced control design techniques and their applications to smart vehicles. The control system topics studied include lead and lag compensator design, loop shaping, analysis of system norms, H2-optimal control, feedback linearization, sliding surface control, and observer design. The vehicle application topics studied include cruise control, adaptive cruise control, automated lane keeping, automated highway systems, yaw stability control, active rollover prevention, engine control, and active and semi-active suspensions. In each application, a dynamic model is first developed that is simple enough for control system design, but at the same time, rich enough for capturing the essential features of the dynamics. The control design for each application is studied in-depth during lecture and further analyzed during hands-on homework. prereq: 5281 or EE 5231 or equiv
ME 8361 - Molecular Gas Dynamics
Credits: 3.0 [max 3.0]
Course Equivalencies: AEM 8231/ME 8361
Grading Basis: A-F or Aud
Typically offered: Periodic Fall
Kinetic theory of gases, Boltzmann equation, Maxwell-Boltzmann distribution, collisions, transport properties. Introduction to quantum mechanics. Statistical thermodynamics, classical/quantum statistics. partition functions and thermodynamic properties. Irreversible thermodynamics. prereq: CSE grad student
ME 8446 - Advanced Combustion
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Periodic Fall
Fundamental understanding of linkage between thermodynamics, chemical kinetics, and transport phenomena in combustion systems. Heat release rate, flame stability, and emissions. How those issues arise in furnaces, internal combustion engines, and rockets. prereq: Undergrad courses in thermodynamics, fluid mechanics, heat transfer, IT grad student; 5446 or 8641 highly recommended
AEM 8888 - Thesis Credit: Doctoral
Credits: 1.0 -24.0 [max 100.0]
Grading Basis: No Grade
Typically offered: Every Fall, Spring & Summer
(No description) prereq: Max 18 cr per semester or summer; 24 cr required