Math 224B - Mathematical Methods for the Physical Sciences

Instructor: Jon Wilkening

Lectures: MWF 10:10-11:00, Room 81 Evans

Office: 1051 Evans

Office Hours: Mon 11:10-11:55, Wed 2:15-3:30

Prerequisites: Undergraduate Analysis (104), Complex Analysis (185), and Linear Algebra (110). (224A is not a prerequisite.)

Required Text: I will post excerpts from the following books and papers on bCourses.

Recommended Reading:
1. G. B. Whitham, Linear and Nonlinear Waves
2. Novikov, Manakov, Pitaevskii, Zakharov, Theory of Solitons, The Inverse Scattering Method
3. G. B. Folland, Partial Differential Equations
4. R. Kress, Linear Integral Equations
5. R. S. Johnson, A Modern Introduction to the Mathematical Theory of Water Waves
6. Dyachenko, Kuznetsov, Spector, Zakharov, Analytic description of the free surface dynamics of an ideal fluid, Phys. Lett. A, 221:73-79, 1996.
7. L. C. Evans Partial Differential Equations
8. D. Braess, Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics
9. Robert Richtmyer, Principles of Advanced Mathematical Physics, Volume I
10. F. Otto, The Geometry of Dissipative Evolution Equations: the Porous Medium Equation , Comm. Partial Diff. Eq., 26, 101-174, (2001).
11. F. W. J. Olver, Asymptotics and Special Functions
12. C. Bender and S. Orszag, Advanced Mathematical Methods for Scientists and Engineers
13. Kozlov, Maz'ya, Rossmann, Elliptic Boundary Value Problems in Domains with Point Singularities
14. Kevorkian and Cole, Multiple Scale and Singular Perturbation Methods
15. J. Neu, Singular Perturbation Theory (unpublished notes)

Syllabus: The course will survey basic theory and practical methods for solving the fundamental problems of mathematical physics. It is intended for graduate students in applied mathematics, physics, engineering or other mathematical sciences. The overall purpose of the course will be to develop non-numerical tools for understanding and approximating solutions of differential equations. A rough outline for 224B is:

Course Material: I will post handouts, assignments and solutions on bCourses. Please e-mail me if you do not have access to the bCourses page.

Grading: 100% Homework.

Homework: 6-7 assignments, due roughly every two weeks.

Comments: The lowest homework score will be dropped.