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.
Lectures:
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:
curtright@physics.miami.edu).
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
- the complete set of graded
problems, or
- 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.