Concentration areas

Course offerings are categorized according to the three concentration areas below. The first two concentration areas comprise courses joint listed with supporting graduate programs from the Colleges of Engineering and of Natural Sciences.

Area A: Applicable Mathematics

CAM 381D, Complex Analysis
CAM 681E, Real and Abstract Analysis
CAM 381M, Methods of Mathematical Physics
CAM 381N, Methods of Mathematical Physics
CAM 684C, Theory of Probability
CAM 684D, Mathematical Statistics
CAM 386M,Functional Analysis in Theoretical Mechanics
CAM 386N, Qualitative Methods in Nonlinear Mechanics
CAM 391, Introductory Dynamical Systems
CAM 391C, Topics in Analysis
- Fourier Analysis
- Wavelets
- Advanced Dynamical Systems
CAM 393C, Topics in Applied Mathematics
- Methods of Applied Mathematics
- Approximation Theory
- Introduction to Partial Differential Equations
- Abstract Cauchy Problems and Nonlinear Partial Differential Equations
- Nonlinear Wave Equations
- Euler and Navier-Stokes Equations
- Pseudodifferential and Fourier Integral Operators
- Statistical Mechanics
- Ergodic Theory
- Quantum Mechanics
- Bifurcation Theory
CAM 394C, Topics in Probability and Statistics
- Nonparametric Statistics
- Advanced Probability

Area B: Numerical Analysis and Scientific Computation

CAM 380N, AlgorithmsforParallel and Distributed Computation
CAM 381C, Computational Physics
CAM 382L, Numerical Methods in Petroleum Engineering
CAM 383, Special Topics in Petroleum Engineering
- Numerical Solution of Time-Dependent Problems
- Topics in Computational Methods
CAM383C, NumericalAnalysis. LinearAlgebra
CAM383D, NumericalAnalysis: Interpolation,Approximation, Quadrature, and Differential Equations
CAM 384G, Computer Graphics
CAM 386K, Numerical Treatment of Differential Equations
CAM 393D, Topics in Numerical Analysis
CAM 393M, Numerical Solution of Elliptic Partial Differential Equations
CAM 393N, Numerical Methods forFlow and Transport Problems
CAM 394F, Finite Element Methods
CAM 394G, Computational Techniques in Finite Elements
CAM 394H, Advanced Theory of Finite Element Methods
CAM 195T, 295T, 395T, Topics in ComputerSciences: Parallel Cornputations
- Parallel MethodsforNumerical Algorithms
- Parallel Algorithms and Architecture Parallel Programming
CAM 397, Topics in Computational and Applied Mathematics
- Supercomputing in Computational Mechanics
- Grid Generation, Adaptive Grids, and Multigrids
- Advanced Computational Fluid Mechanics

Area C: Mathematical Modeling and Applications

Courses in mathematical modeling and applications are offered in several areas of science and engineering Four groups of courses from which this concentration area might be developed are given as examples below Other examples are fluid dynamics, control theory, semiconductors, celestial mechanics, chemistry, and the theory of relativity Concentrations in mathematical modeling and applications are also available in various departments; these may be included in computational and applied mathematics degree programs with the approval of the Graduate Studies Committee.

Solid and Continuum Mechanics

Engineering Mechanics 380, Theory of Plasticity
Engineering Mechanics 388, Solid Mechanics I
Engineering Mechanics 388F, Fracture Mechanics
Engineering Mechanics 388L, Solid Mechanics II
Engineering Mechanics 394V, Wave Propagation I
Engineering Mechanics 394W, Wave Propagation II

Fluid Mechanics

Aerospace Engineering 382Q, Fluid Mechanics
- Turbulent Fluid Mechanics
- Finite Difference Methods in Computational Fluid Dynamics
- Advanced Problems in Compressible Flow
Aerospace Engineering 382R, Aerodynamics
- Low-Speed Aerodynamics
- High-Speed Aerodynamics
- Hypersonic Aerodynamics
- Theoretical Gas Dynamics
- Advanced ComputationalAerodynamics
Chemical Engineering 381N, Fluid Flow and Heat Transfer
Engineering Mechanics 387, Foundations of Fluid Mechanics
Engineering Mechanics 393K, Advanced Fluid Mechanics I: Inviscid Flow
Mechanical Engineering 380Q, Mathematical Methods in Engineering
- Perturbation Methods
- Spectral Methods in Fl~id Dynamics
- Mechanical Engineering 381P, Dynamics of Fluids
- Incompressible Flow I: Theory
- Dynamics of Turbulent Flow
- Incompressible Flow II. Applications
- Modeling of Turbulent Flows

Nonlinear Dynamics

Aerospace Engineering 388P, Celestial Mechanics
- Hamiltonian Mechanics
- Celestial Mechanics I
- Celestial Mechanics II
- Satellite Theory
- Theory of Orbits I
- Theory of Orbits II
- Regularization
- Engineering Mechanics 381,Advanced Dynamics

System and Control Theory

Aerospace Engineering 381P, System Theory
- Linear Systems Analysis
- Multivariable Control Systems
- Optimal Control Theory I
- Optimal Control Theory II
- Statistical Estimation Theory
- Advanced Topics in Estimation Theory
- Stochastic Estimation and Control
Electrical Engineering 380K, Introduction to System Theory
Electrical Engineering 380N, Topics in System Theory
- Nonlinear Systems. Input-Output Properties
- Nonlinear Systems: Geometric Theory
- Stochastic Control Theory
- Stochastic Dynamical Systems
Mechanical Engineering 390R, Engineering Statistics and Probability
- Time-Series Analysis
- Applied Stochastic Processes
- Regression and Analysis of Variance
- Mechanical Engineering 391Q, OperationsResearch
- Nonlinear Programming
- Dynamic Programming