Methods of Mathematical Physics II

PHY 616 (Section P), Spring Semester,
January 16 - May 3, 2007

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.

Office and Hours:

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

Thursday, 3 May, either 11:00 - 1:30 pm, in the physics library, or else as a take-home exam (to be decided).

Grading Policy:

Your grade will be based on either

- the complete set of graded
problems, or

- your in-class presentation.

Other Recommended Material:

(1) My lecture notes.

(2) Professor Nearing's textbook for PHY515. (Freely available online!)

(3) Mathematics for the Physical Sciences, Herbert Wilf, Dover, 2006. (Freely available online!)

(4)

(ongoing NIST project to update this handbook in an electronic format)

(5)

(6) 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.

(7) generatingfunctionology by Herbert Wilf, Second Edition, Academic Press, 1994. Generating functions and their uses in discrete mathematics.

(8) Linear Mathematics in Infinite Dimensions, by U. H. Gerlach, Beta Edition, October 2006. Signals, boundary value problems, and special functions.

(9) Chaos - classical and quantum, P Cvitanović, et al. (Freely available online!)

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.