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).
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