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Partial list of mathematics graduate courses
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MATH 505, Mathematical Fluid Mechanics
Kinematics, balance laws, constitutive equations; ideal fluids, viscous flows, boundary layers, lubrication; gas dynamics.
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MATH 513, Partial Differential Equations I
First order equations, the Cauchy problem, Cauchy-Kowalevski theorem, Laplace equation, wave equation, heat equation.
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MATH 514, Partial Differential Equations II
Sobolev spaces and Elliptic boundary value problems, Schauder estimates. Quasilinear symmetric hyperbolic systems, conservation laws.
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MATH 523, Numerical Analysis I
Approximation and interpolation, numerical quadrature, direct methods of numerical linear algebra, numerical solutions of nonlinear systems and optimization.
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MATH 524, Numerical Analysis II
Iterative methods in linear algebra, numerical solution of ordinary and partial differential equations.
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MATH 550 (CSE 550), Numerical Linear Algebra
Solution of linear systems, sparse matrix techniques, linear least squares, singular value decomposition, numerical computation of eigenvalues and eigenvectors.
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MATH 555 (CSE 555), Numerical Optimization Techniques
Unconstrained and constrained optimization methods, linear and quadratic programming, software issues, ellipsoid and Karmarkar's algorithm, global optimization, parallelism in optimization.
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MATH 556 (CSE 556), Finite Element Methods
Sobolev spaces, variational formulations of boundary value problems; piecewise polynomial approximation theory, convergence and stability, special methods and applications.
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MATH 597D, Multiscale Modeling & Analysis
Formal courses given on a topical or special interest subject which may be offered infrequently; several different topics may be taught in one year or term.
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MATH 597B
Course contents vary from year to year: recent seminars include Multigrid and Adaptive Methods and Computability and Randomness.
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More courses in CSE, Physics, and Engineering
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ELCHE,
Electrochemical Engineering Minor
The electrochemical engineering minor is designed to equip students with
the knowledge necessary to become valuable contributors in addressing society’s
clean energy needs and demands especially in the electrochemical power generation sector.
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ACS 513, Digital Signal Processing
Discrete linear systems, transforms, digital filter design and applications, discrete fourier transforms, spectrum analysis
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AERSP 508, Foundations of Fluid Mechanics (3)
Mathematical review, fluid properties, kinematics, conservation laws, constitutive relations, similarity principles, the boundary layer, inviscid flow, vorticity dynamics and wave motion.
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AERSP 571, Foundations of Structural Dynamics and Vibration
Modeling approaches and analysis methods of structural dynamics and vibration.
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E E 556, Graphs, Algorithms, and Neural Networks
Examine neural networks by exploiting graph theory for offering alternate solutions to classical problems in signal processing and control.
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E E 560, Probability, Random Variables, and Stochastic Processes
Review of probability theory and random variables; mathematical description of random signals; linear system response; Wiener, Kalman, and other filtering.
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E MCH 500, Solid Mechanics
Introduction to continuum mechanics, variational methods, and finite element formulations; application to bars, beams, cylinders, disks, and plates.
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E MCH 461, Finite Elements in Engineering
Computer modeling and fundamental analysis of solid, fluid, and heat flow problems using existing computer codes.
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I E 505, Linear Programming
An accelerated treatment of the main theorems of linear programming and duality structures plus introduction to numerical and computational aspects of solving large-scale problems.
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M E 523, Numerical Solutions Applied to Heat Transfer and Fluid Mechanics Problems
Application of finite difference methods to the study of potential and viscous flows and conduction and convection heat transfer.
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M E 526 (AERSP 526), Computational Methods for Shear Layers
Study of numerical solution methods for steady and unsteady laminar or turbulent boundary-layer equations in two and three dimensions.
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M E 527 (AERSP 527), Computational Methods in Transonic Flow
Numerical solution of partial differential equations of mixed type, with emphasis on transonic flows and separating boundary layers.
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M E 561, Structural Optimization Using Variational and Numerical Methods
Shape and size optimization of elastic structures, continuous and discrete solution methods and numerical algorithms, design of compliant mechanisms.
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M E 565, Optimal Design of Mechanical and Structural Systems
Application of numerical optimization techniques to design mechanical and structural systems; design sensitivity analysis.
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STAT 515, Stochastic Processes I
Conditional probability and expectation, Markov chains, the exponential distribution and Poisson processes.
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STAT 517, Probability Theory
Measure theoretic foundation of probability, distribution functions and laws, types of convergence, central limit problem, conditional probability, special topics.
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