Mathematical Physics 212B
Spring 2009
Instructor: Dr. Sasha Chernyshev, Assistant
Professor
Office: RH 310F
Phone: (949)-824-6440
E-mail: sasha@uci.edu
Web page: http://www.physics.uci.edu/faculty/chernyshev.html
Office Hours:
open door policy
Introduction
This course will be about some of mathematical methods
used in physics.
Topics to be covered
Here is a list of topics I am planning to cover in this course.
- Integral Transforms
- Fourier, Laplace, and others
- Applications
- Applications of complex variables
- Conformal mapping
- Dispersion relations
- Green's Functions
- Integral equations
- Classification
- Applications
- Calculus of variations
- Euler-Lagrange
- Problems with constraints
- Connections with eigenvalue problems
Recommended Books
- J. Mathews and R. L. Walker, Mathematical methods of
physics, Addison-Wesley Publishing Cimpany, Inc., 1970.
I will mostly follow this book (Chapters 4, 5, 9, 10, 11, 14, 16)
- G. Mahan, Applied Mathematics, Kluwer
Academic/Plenum Publishers, New York, 2002.
... with some examples from this one ...
- F. W. Byron and R. W. Fuller, Mathematics of
classical and quantum physics, Dover Publications, Inc.,
New York, 1992.
... and this one ...
- G. F. Carrier, M. Krook, and C. E. Pearson, Functions
of a complex variable: Theorie and Technique, McGraw-Hill book
company, New York, 1983.
... and, perhaps, this one too.
Homeworks
Homeworks will be assigned weekly. They will be collected three
times during the course on the "target" dates (approximately
once
every three week) and graded.
The target dates will be announced separately.
The course will be concluded by a comprehensive take-home Final
exam. The grade is 50% Final, 50% homework.
- Homework, week #1: (all from
M&W) 4-5, 4-6, 4-7, 4-8, 4-9
- Homework, week #2:
4-12, 4-13, 4-14, verify the Table 4-1
(p. 119) by explicitly evaluating the direct and inverse Laplace
Transforms.
- Homework, week #3:
5-1, 5-5 part (a) only, 5-7(a), (b)
- Homework, week #4:
Find the dispersion relations of the kind (5-13), (5-14), M&W
p. 131, for the "odd symmetry case f(-z)=-f*(z*). Also problems
5-9 and 5-10.
- Homework, week
#5: Is the Sturm-Liouville differential
operator (p. 264, bottom) Hermitian? Problems 9-1, 9-2, 9-3.
- Homework, week
#6: Problems 11-1, 11-2.
- Homework, week
#7: Problems 11-4, 11-6, 11-7, 11-3, 11-9.
- Homework #8
Final exam
Final exam is here. It is due Tuesday,
June
15 at 10:00 am.
Solution for the final is here
(most of the problems). Problem 5-6a is here.