Methods of Mathematical Physics II

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

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.

11:00 - 12:15 pm, Tuesday and Thursday, 203 Knight Physics Bldg.

Office and Hours:

325 Knight Physics Bldg.,  by appointment (phone: 284 - 2324 ext 4;  email:

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

Midterm Exam:  (see grading policy below)
Thursday, 8 March,
either 11:00 - 1:30 pm, in the physics library, or else as a take-home exam (to be decided).

Final Exam:  (see grading policy below)
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
  1. the complete set of graded problems, or
  2. your in-class presentation.
Required Textbook:
None selected.  But see here.

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) Handbook of Mathematical Functions, M. Abramowitz and I. Stegun, National Bureau of Standards, AMS 55, 1964.     
        (ongoing NIST project to update this handbook in an electronic format)
(5) 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.
(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.