Math 224B: Mathematical Methods for the Physical Sciences, Spring 2006
Lecture: MWF 10-11 AM, 39 Evans
Instructor: Jon Wilkening,
wilken@math.berkeley.edu
Course webpage:
/~wilken/224B.S06
Office: 1091 Evans, (510) 643-7990 or (510) 486-7006.
Office hours: Monday 11-12, Wednesday 2-3
Course Description
Prerequisites: Advanced Calculus, Complex Analysis, some
experience with Partial Differential Equations.
(224A is not a prerequisite)
Required Text:
Ivar Stakgold, Green's Functions and Boundary Value Problems
Related Texts:
Coddington and Levinson, Theory of Ordinary Differential Equations
M. A. Naimark, Linear Differential Operators, Part I
Courant and Hilbert, Methods of Mathematical Physics, Volume I
Gerald Folland, Introduction to Partial Differential Equations
N. I. Muskhelishvili, Singular Integral Equations
C. Pozrikidis, Boundary integral and singularity methods for linearized
viscous flow
Grading:
The grade will be based entirely on homework,
which will be assigned every two weeks.
(7 assignments)
Content:
In this course, we will study classical boundary
value problems in one and several dimensions using Green's functions,
spectral theory, layer potentials and Cauchy integrals. A rough plan
for the course is as follows:
- weeks 1-3: Green's functions in 1d, maximum
principles, generalized functions
- weeks 4-5: boundary value problems in 1d, characteristic and
associated functions
- weeks 6-7: intro to functional analysis, operators on a
Hilbert space, spectral theory
- weeks 8-9: eigenfunction expansions; Bessel,
Hermite and Legendre equations
- weeks 10-11: Fredholm integral equations, potential theory
(following Folland)
- weeks 12-13: complex variable methods in elasticity, rigid stamps,
contact problems (following Muskhelishvili)
- weeks 14-15: boundary integral methods for the Stokes equations
(following Pozrikidis)
I'll hand out copies of the relevant background material from
the texts other than Stakgold.