MATHEMATICS / 209


 GRADUATE COURSES

MS 601-MATHEMATICAL METHODS OF PHYSICS AND ENGINEERING. 3 credits
 Prerequisites: MS 501, MS 502, MS 503, MS 505, or the equivalent. Ortho-
gonal functions; integral transforms; theory of distributions; integral equations;
eigenfunctions and Green's functions; special functions; boundary and initial
value problems, with emphasis on potential theory (Laplace and Poisson equa-
tions), the wave equation, and the diffusion equation.
MS 602-MATHEMATICAL METHODS OF PHYSICS AND ENGINEERING 2.
 3 credits
 Prerequisite: MS 601. Continuation of MS 601.
MS 603-MATHEMATICAL METHODS OF PHYSICS AND ENGINEERING 3.
 3 credits
 Prerequisite: MS 602. Continuation of MS 602.
MS 607-FOURIER SERIES 1. 3 credits
 Prerequisite: MS 601. Fundamental theorems on convergence, differentiation, and
integration. Applications to boundary value problems.
MS 608-FOURIER SERIES 2. 3 credits
 Prerequisite: MS 607. A continuation of MS 607.
MS 609-INTRODUCTION TO CALCULUS OF VARIATIONS FOR ENGINEERS AND
 PHYSICAL SCIENTISTS. 3 credits
 Prerequisite: MS 601. Extremals for integrals with fixed endpoints, effect of
varying endpoints, transversality condition, direct methods.
MS 610-TENSOR ANALYSIS. 3 credits
 Prerequisites: MS 502, MS 601. The calculus of tensors with special attention
to its application to differential geometry, problems from physics, and n-dimensional
spaces.
MS 611-APPLICATIONS OF GROUP THEORY IN THE PHYSICAL SCIENCES.
 3 credits
 Prerequisite: PS 647. Group theory, the theory of representations of groups
and their relationship to the problems of physics.
MS 614-NUMERICAL ANALYSIS. 3 credits
 Prerequisites: MS 411; MS 543 or MS 446. Designed to acquaint research
students with numerical analysis, error analysis of differential equations, integral
equations, eigenvalue, and matrix problems with study of errors.
MS 615-PARTIAL DIFFERENTIAL EQUATIONS 1. 3 credits
 Prerequisites: MS 505; MS 543 or MS 603. Cauchy-Kowalewski theorem, first
 order equations, classification of equations, hyperbolic equations, elliptic equations,
 parabolic equations, hyperbolic systems, nonlinear hyperbolic systems, existence
 theory based on functional analysis. Applications to partial differential equations
 arising from physical sciences.
 MS 616-PARTIAL DIFFERENTIAL EQUATIONS 2. 3 credits
 Continuation of MS 615.
 MS 617-PARTIAL DIFFERENTIAL EQUATIONS 3. 3 credits
 Continuation of MS 616.
MS 631-ALGEBRA 1. 3 credits
 Prerequisite: MS 533. Sylow theorems, solvable and nilpotent groups, Jordan-
 Holder theorem, abelian groups, Jacobson radical, Jacobson density theorem,
 Wedderburn-Artin theorem.