Physics 503
Methods of Mathematical Physics
Fall 2008
Tuesday & Thursday, 9:5011:10am.
Physics, P128
Final exam is scheduled on December 23, 810:30am, B128.
Review all homework problems (including ones with stars)
with solutions as a preparation for final.
Instructor: Dr. Alexander (Sasha) Abanov,
Associate Professor
Office: Physics B102
Phone: (631)6328174
Email:
alexandre.abanov@sunysb.edu
Web page:
http://felix.physics.sunysb.edu/~abanov/
Prerequisites
The main prerequisite for the course is the knowledge of
a standard (real variable) mathematical calculus. Also, you
have to know some theory of functions of complex variable
or to be a (very) quick learner to be able to follow the course.
The final grade for this course will be based on grades for
homeworks (30%), which will be given every
two weeks, the grade for midterm takehome exam (20%),
and on the grade for the final exam (50%).
Topics to be covered
 Functions of a complex variable
(6 lectures)
 Complex numbers
 Analytic functions
 Applications of functions of a complex variable
(9 lectures)
 Contour integration
 Conformal mapping
 Introduction to asymptotic methods (5 lectures)
 Asymptotic series
 Laplace method
 Method of steepest descent
 Method of stationary phase
 Poisson's formula
 Special functions (8 lectures)
 Gamma function
 Bessel functions
 Orthogonal polynomials
 Other special functions
Homeworks

Homework #1, due Tuesday, September 16, 2008
(PDF )

Homework #2, due Thursday, October 2, 2008
(PDF )

Homework #3, due Tuesday, October 28, 2008
(PDF )

Homework #4, due Tuesday, November 11, 2008
(PDF )

Homework #5, due Tuesday, November 25, 2008
(PDF )

Homework #6, due Tuesday, December 9, 2008
(PDF )

Homework #7, not for credit
(PDF )
Recommended Books
These books are all recommended but not required. They are
available from the University bookstore.

G. F. Carrier, M. Krook, and C. E. Pearson,
Functions of a complex variable: Theorie and Technique,
McGrawHill book company, New York, 1983.
This is a very good textbook which contains most of the
topics I am going to present.

C. M. Bender and S. A. Orszag,
Advanced Mathematical Methods for Scientists and Engineers I:
Asymptotic Methods and Perturbation Theory,
SpringerVerlag, New York, 1999.
This is a very good textbook on asymptotic methods.

G. M. J. Ablowitz and A. S. Fokas, Complex variables.
Introduction and Applications.,
Cambridge University Press, Second edition, 2003.
This book is a very good book on complex analysis. Close in topics to Carrier,
Krook and Pearson's book. Has an extensive chapter on RiemannHilbert problems.
Additional Books

F. W. Byron, Jr. and R. W. Fuller,
Mathematics of classical and quantum physics,
Dover, New York, 1992.
Good and affordable textbook on different mathematical methods.

G. B. Arfken, H. J. Weber, Mathematical methods
for physicists,
Academic press, London, 2001.
This book is probably the bestseller on the subject. It is
not a good textbook but contains all of the topics (except
for topology) and is nice to have as a reference.

B. A. Fuchs and B. V. Shabat,
Functions of a complex variable and
some of their applications,v. I,
Pergamon press, 1964.
This book contains a lot of examples, especially on conformal mappings
and residue calculus.
Stony Brook University Syllabus Statement
If you have a physical, psychological, medical, or learning
disability that may impact your course work, please contact
Disability Support Services at (631) 6326748 or
http://studentaffairs.stonybrook.edu/dss/
. They will determine with
you what accommodations are necessary and appropriate. All
information and documentation is confidential.
Students who require assistance during emergency evacuation are
encouraged to discuss their needs with their professors and
Disability Support Services. For procedures and information go to the
following website:
http://www.sunysb.edu/ehs/fire/disabilities.shtml
Last updated December 15, 2008