Twin Cities campus
 
Twin Cities Campus

Aerospace Engineering and Mechanics Minor

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)
  • Program Type: Graduate minor related to major
  • Requirements for this program are current for Spring 2022
  • Length of program in credits (master's): 6
  • Length of program in credits (doctoral): 12
  • This program does not require summer semesters for timely completion.
The graduate program emphasizes engineering sciences that are 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
Special Application Requirements:
Students interested in the minor are strongly encouraged to confer with their major field advisor and director of graduate studies, and the Aerospace Engineering and Mechanics director of graduate studies regarding feasibility and requirements.
For an online application or for more information about graduate education admissions, see the General Information section of this website.
Program Requirements
Use of 4xxx courses towards program requirements is not permitted.
Courses must be taken under the AEM course designator to be counted towards a minor. Courses must be taken on the A-F grade basis, unless only offered S/N. The minimum cumulative GPA for the minor is 3.00.
Coursework (6 to 12 credits)
Master's students select 6 credits, and doctoral students select 12 credits from the following in consultation with the Aerospace Engineering and Mechanics director of graduate studies. Other courses can be applied to the minor with approval by the Aerospace Engineering and Mechanics director of graduate studies.
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 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 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)
Program Sub-plans
Students are required to complete one of the following sub-plans.
Students may not complete the program with more than one sub-plan.
Masters
Doctoral
 
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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 Odd 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 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 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]