Methods of Mathematical Physics
Tuesday & Thursday, 9:50-11:10am.
Final exam is scheduled on December 23, 8-10:30am, B-128.
Instructor: Dr. Alexander (Sasha) Abanov,
Review all homework problems (including ones with stars)
with solutions as a preparation for final.
Office: Physics B102
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 take-home exam (20%),
and on the grade for the final exam (50%).
Topics to be covered
- Functions of a complex variable
- Complex numbers
- Analytic functions
- Applications of functions of a complex variable
- 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
Homework #1, due Tuesday, September 16, 2008
Homework #2, due Thursday, October 2, 2008
Homework #3, due Tuesday, October 28, 2008
Homework #4, due Tuesday, November 11, 2008
Homework #5, due Tuesday, November 25, 2008
Homework #6, due Tuesday, December 9, 2008
Homework #7, not for credit
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,
McGraw-Hill 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,
Springer-Verlag, 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 Riemann-Hilbert problems.
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
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
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disability that may impact your course work, please contact
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. They will determine with
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Last updated December 15, 2008