GOAL: This is an introductory course
on linear PDEs at the senior undergraduate level;

the intended audience are students
in mathematics, physics and engineering. I will

emphasize analytical methods (kernel
functions, Fourier series) and applications to the

classical PDEs of mathematical
physics. The prerequisite for this course is a working

knowledge of multivariable
calculus.

TIME/PLACE: Tuesday/Thursday, 5:05-6:20, Ayres 125

TEXT: Walter A. Strauss, Partial Differential Equations, J.Wiley (1992)

GRADING: Based on weekly homework
assignments (20%), two in-class exams( 25% each)

and a comprehensive final exam
(30%)

EXAM DATES: 9/28, 11/9; FINAL EXAM: 12/9, 5-7 p.m.

HOMEWORK- I will post on this web
site a list of problems from the

text for each section covered;
some of these will be solved in class. The remaining problems

from the list will be collected
each Thursday (at the beginning of class) and graded.

DUE DATE: the problems due
each Thursday are those in sections covered on the preceding

Tuesday and Thursday (usually 6
to 8 problems each week).

COURSE OUTLINE

PART I- Solution of the Cauchy problem

Ch. 2: wave equation and heat equation in 1D

Ch. 3: reflections and sources (non-homogeneous problems)

Ch.9: wave and heat equation in 2D and 3D; Schroedinger equation

Ch.7: Green's identitites, Green's functions, Poisson kernel

PART II- Boundary-value problems

Ch.5: Fourier series

Ch.4 Boundary-value problems in 1D

Ch. 11: Eigenvalues of bounded domains in 2D and 3D

Ch. 10: problems with circular, spherical or cylindrical symmetry

PART III- Special topics and applications

Ch.13: Some PDEs of mathematical physics

14.1: nonlinear equations: shock waves, weak solutions

updated 8/22/00