Class meets MWF 12:30 PM, and W 3:30 PM in Wean Hall 7316
Professor Mike Widom, Office 6424 Wean Hall
e-mail: widom@andrew.cmu.edu, Phone: 412-268-7645
Office Hours: Any time I'm not busy
This course covers mathematical physics at a first-year graduate level. Familiarity with topics in advanced undergraduate physics (E&M, Quantum Mechanics, Statistical Mechanics, Classical Mechanics) will be assumed. The theme of the course is to examine the mathematical methods that are used in these physics subject areas. Studying them as purely mathematical subjects should make you familiar with their use when you encounter them again in your physics courses. Facility with practical applications of mathematics will be emphasized. Proofs and derivations will be heuristic, not formal.
Books: Five books are on reserve in the E&S library.
1. S. Hassani, Mathematical Physics, call #530.15 H35M
2. J. Mathews and R.L. Walker, Mathematical methods of physics,
call #QA401.M42 1970
3. G.B. Arfken and H.J. Weber, Mathematical Methods for Physicists,
call #QA37.3 .A74 2005
4. P.M. Morse and H. Feshbach, Methods of Mathematical Physics,
call #QC20 .M6
5. R. Courant and D. Hilbert, Methods of Mathematical Physics,
call #QA29 .H5 R42 1986
The principal content of the course will be drawn from Hassani and from Mathews & Walker. The other books are alternate standard texts in Mathematical Physics.
Grading: Letter grades will be based on in-class exams and a final exam. The first in-class exam is scheduled for Friday, Sept. 26. Weekly homework assignments will be given out. Assignments are listed at http://euler.phys.cmu.edu/widom/teaching/33-759/hw.html. These will be discussed in class on Wednesday afternoons.
Course Outline:
Note this outline is only approximate. Actual class coverage can be found at http://euler.phys.cmu.edu/widom/teaching/33-759/coverage.html.
Weeks 1-3. Finite dimensional vector spaces.
Weeks 4-7. Infinite dimensional vectors spaces. Orthogonal functions and Fourier analysis.
Weeks 8-10. Complex analysis. Series expansions.
Weeks 11-15. Differential equations. Separation of variables in PDE's. Second order ODE's. Sturm-Liuville theory.