Syllabus for MATH 602

Title: Methods and Applications of Partial Differential Equations

Prerequisites: MATH 601 or 308, 405 and 407

Courses Topics:

This is a one semester course on solving problems in physics and engineering by partialdifferential equations. The course emphasizes the basic equations in engineering such asvibration of thin elastic membranes and strings, heat flow in finite and infinite bars, fluid flow inporous media, convection-diffusion processes and potential theory. The course introduces basicmethods for solving partial differential equations including:

I. Introduction and derivation of basic partial differential equations in applied mechanics; (6hours)

II. the method of characteristics for first order equations and systems;(6 hours)III. separation of variables.(9 hours)IV. Green's functions;(6 hours)V. Fourier series and Fourier integrals; (6 hours)VI. orthogonal functions and orthogonal polynomials;(6 hours)VII. special functions and Sturm-Liouville theory;(6 hours)

Suggested Text:

Basic Partial Differential Equations, by D. Bleecker & G. Csordas