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AMS 501 Differential Equations and Boundary Value Problems I 
Examples of initial and boundary value problems in which differential equations arise. Existence and uniqueness of solutions, systems of linear differential equations, and the fundamental solution matrix. Power series solutions, Sturm-Louisville theory, eigenfunction expansion, Green's functions. 
Spring, 3 credits, ABCF grading 
AMS 501 Webpage 

AMS 502 Differential Equations and Boundary Value Problems II 
Analytic solution techniques for, and properties of solutions of, partial differential equations, with concentration on second order PDEs. Techniques covered include: method of characteristics, separation of variables, eigenfunction expansions, spherical means, GreenÕs functions and fundamental solutions, and Fourier transforms. Solution properties include: energy conservation, dispersion, dissipation, existence and uniqueness, maximum and mean value principles. 
Prerequisite: AMS 501 
Fall, 3 credits, ABCF grading 
AMS 502 webpage 

AMS 503 Applications of Complex Analysis 
A study of those concepts and techniques in complex function theory that are of interest for their applications. Pertinent material is selected from the following topics: harmonic functions, calculus of residues, conformal mapping, and the argument principle. Application is made to problems in heat conduction, potential theory, fluid dynamics, and feedback systems. 
Spring, 3 credits, ABCF grading 
AMS 503 webpage 

AMS 510 Analytical Methods for Applied Mathematics and Statistics 
Review of techniques of multivariate calculus, convergence and limits, matrix analysis, vector space basics, and Lagrange multipliers. 
Fall, 3 credits, ABCF grading
AMS 510 webpage 

AMS 526 Numerical Analysis I 
Direct and indirect methods for solving simultaneous linear equations and matrix inversion, conditioning, and round-off errors. Computation of eigenvalues and eigenvectors. 
Co-requisite: AMS 505
Fall, 3 credits, ABCF grading
AMS 526 webpage 

AMS 527 Numerical Analysis II 
Numerical methods based upon functional approximation: polynomial interpolation and approximation; and numerical differentiation and integration. Solution methods for ordinary differential equations. AMS 527 may be taken whether or not the student has completed AMS 526. 
Spring, 3 credits, ABCF grading 
AMS 527 webpage

AMS 528 Numerical Analysis III 
An introduction to scientific computation, this course considers the basic numerical techniques designed to solve problems of physical and engineering interest. Finite difference methods are covered for the three major classes of partial differential equations: parabolic, elliptic, and hyperbolic. Practical implementation will be discussed. The student is also introduced to the important packages of scientific software algorithms. AMS 528 may be taken whether or not the student has completed AMS 526 or AMS 527. 
Spring, 3 credits, ABCF grading 
AMS 528 webpage 

AMS 530 Principles in Parallel Computing 
This course is designed for both academic and industrial scientists interested in parallel computing and its applications to large-scale scientific and engineering problems. It focuses on the three main issues in parallel computing: analysis of parallel hardware and software systems, design and implementation of parallel algorithms, and applications of parallel computing to selected problems in physical science and engineering. The course emphasizes hands-on practice and understanding of algorithmic concepts of parallel computing.
AMS 530 webpage

AMS 565 Wave Propagation 
Theory of propagation of vector and scalar waves in bounded and unbounded regions. Development of methods of geometrical optics. Propagation in homogeneous and anisotropic media. 
Fall, 3 credits, ABCF grading 
AMS 565 webpage 

AMS 566 Compressible Fluid Dynamics 
Physical, mathematical, and computational description in compressible fluid flows. Integral and differential forms of the conservation equations, one-dimensional flow, shocks and expansion waves in two and three dimensions, quasi-one-dimensional flow, transient flow, numerical methods for steady supersonic flow, numerical methods for transient flow. 
Spring, 3 credits, ABCF grading 
AMS 566 webpage

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