The University of Texas Rio Grande Valley

MATH 6361 Partial Differential Equations

This course considers waves and diffusion, initial value problems for hyperbolic and parabolic equations, boundary value problems for elliptic equations. Topics include: first-order equations: characteristic ODEs, local existence of smooth solutions, conservation law equations, shocks, rarefaction, integral solutions; second-order partial differentail equations and clssification; Wave equation: fundamental solutions in one, two and three dimensions, Duhamel's principle, energy methods, finite propagation speed; Laplace equation: mean-value property, smoothness, maximum principle, uniqueness of solutions, Hamack inequality, Liouville theorem; Poisson Equation: fundamental solution, Greens functions, energy methods. Heat Equation: fundamental solution, maximum principle, uniqueness of solutions on a bounded domain, energy methods.

Credits

3

Prerequisite

MATH 3341 Differential Equations with a grade of ?C? or higher, or consent of instructor.

Schedule Type

Lecture

Grading Basis

Standard Letter (A-F)

Administrative Unit

School of Mathematical & Stat

Offered

As scheduled