Methods of Mathematical Physics I

PHY 615 (Section S), Fall Semester, August 26 - December 2, 2004

Dr. Thomas Curtright

In this class we will study some techniques from pure and applied mathematics which I have found to be useful in theoretical physics.

According to the course catalog, in PHY615 we should cover:  Special functions, PDEs, Green functions, Calculus of variations.
And in PHY616:  Different topics from Phy 615, including Vector spaces, Operators, Numerical analysis, Statistics.

Well ... we'll see about that.

Lectures:
3:30 - 4:45 pm, Tuesday and Thursday, 203 Knight Physics Bldg.

Discussions or Make-ups (as announced in class):
3:30 - 4:45 pm, Wednesday, 203 Knight Physics Bldg.

NB  Since Wednesday discussion and make-up sessions conflict with some of your other scheduled activities, instead, I will just "run long" on Tuesdays and Thursdays.  If this causes you any problems, please send me email, or talk to me about it.

Office and Hours:
325 Knight Physics Bldg.,  by appointment (phone: 284 - 2324 ext 4;  email:  curtright@physics.miami.edu).

Homework and Graded Problems:
These will be due as announced in lecture, about one week in advance.

Midterm Exam:
Thursday, 21 October, 3:30 - 4:45 pm, in the physics library.

Final Exam:
Monday, 13 December, 4:00 - 6:30 pm, in the physics library.

Grading Policy:
Your grade will be based with equal weight on each of
  1. the complete set of graded problems,
  2. the midterm exam,
  3. and the final exam.
Required Textbook:
None selected.  But see here.

Other Recommended Material:
(1) My lecture notes.
(2) Professor Nearing's on-line textbook for PHY515.
(3) Handbook of Mathematical Functions, M. Abramowitz and I. Stegun, National Bureau of Standards, AMS 55, 1964.
(4) Numerical Recipes in C / Fortran / Pascal. The Art of Scientific Computing, W. Press, S. Teukolsky, W. Vetterling, and B. Flannery, Second Edition, Cambridge University Press, 1992.
(5) A=B by Marko Petkovsek, Herbert Wilf and Doron Zeilberger, A K Peters Publishers, 1996.  A book about identities in general, and hypergeometric identities in particular, with emphasis on computer methods of discovery and proof.
(6) generatingfunctionology by Herbert Wilf, Second Edition, Academic Press, 1994.  Generating functions and their uses in discrete mathematics.
(7) Linear Mathematics in Infinite Dimensions, by U. H. Gerlach, Beta Edition, March 2004.  Signals, boundary value problems, and special functions.

Useful internet software sites:
(1)  Maple
(2)  Mathematica  (see especially the free information on the MathWorld and Functions pages)
(3)  Scientific WorkPlace  (free 30 day trial version!)

Fun links:
MAA (Mathematical Association of America):  See especially Ivars Peterson's MathTrek.