Methods of Mathematical Physics I

PHY 615 (Section P), Fall Semester, August 25 - December 2, 2011

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:  Vector spaces, Operators, Numerical analysis, Probability and Statistics.  I plan to pick and choose various topics from all of these areas as the semester progresses, but not necessarily in the order given.

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


Discussions or Make-ups:
To be scheduled, as announced in class
.

Office and Hours:

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


Reading Assignments and Homework Problems:
Graded homework will be due as announced in lecture.  Usually you will have about a week to work on the problems.

Midterm Exam:
To be scheduled.

Final Exam:
Thursday, 8 December, 11:00 - 1:30 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:
You may have already purchased this text for use in PHY515 last year.
Mathematical Methods for Physics and Engineering: A Comprehensive Guide, 3rd Edition [Paperback]
K. F. Riley, M. P. Hobson, S. J. Bence


Other Recommended Material:
(1) My old lecture notes.
(2) Professor Nearing's online textbook for PHY315, also available in hardcopy, Mathematical Tools for Physics, Dover, 2010.
(3) Mathematics for the Physical Sciences and generatingfunctionology by Herbert Wilf.
(4) 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.
(5) Linear Mathematics in Infinite Dimensions, by U. H. Gerlach, Beta Edition, May 2010.  Signals, boundary value problems, and special functions.
(6) Mathematical Methods in Biology, Leah Edelstein-Keshet, SIAM, 2005.
(7) Handbook of Mathematical Functions, M. Abramowitz and I. Stegun, National Bureau of Standards, AMS 55, 1964.
(8) 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.


Useful software internet sites:
(1)  Maple
(2)  Mathematica  (free 15 day trial version!  also see the free information on the MathWorld and Functions pages)
(3)  Scientific WorkPlace  (free 30 day trial version!)