Physics
605
Methods
of Mathematical Physics
(Fall
2005)
Location: LederleTower 1033
Time: 9:30AM 10:45AM
Days: Tuesday and Thursday
Instructor: Boris Svistunov
E-mail: svistunov@physics.umass.edu
Office:
HAS 408
Phone:
5-4428
Course Outline:
Functions of a Complex Variable
Hilbert Spaces
Generalized Functions
Fourier Analysis
Second Order Linear Differential
Equations
Separation of PDE's
Integral Transforms
Sturm-Liouville Theory
Green's Functions
Complex Variables in Classical
Hamiltonian Mechanics. Bogoliubov Transformation
Course Requirements: There will be problem
sets every week.
There will be one midterm exam and a final
exam.
Grading: grades will be based on the
following percentages:
Problems:
50%
Midterm Exam: 25%
Final Exam: 25%
However,
I reserve the right to modify them
in the case when the exam credits are
much lower than the home work ones.
Recommended
textbook: G.B. Arfken and H.J. Weber,
Mathematical Methods
for Physicists, Academic Press, 2000.
Another
interesting text: F.W. Byron, Jr. and R.W.
Fuller, Mathematics
of Classical and Quantum Physics, Dover
Publ.
Link to a History of
Complex Numbers
LECTURE NOTES:
Functions of a Complex Variable
(+ Problems )
Linear Response
Hilbert Spaces (+
Problems)
Separation of Variables in 1D
Linear PDE (+ Problems)
Separation of Variables in 3D/2D Linear
PDE (+ Problems)
Green's Functions (+ Problems)
Fourier Series and Integral. Generalized
Functions ( + Problems)
Green's Function
of the Wave Equation (No problems)
Laplace
Transform ( + Problems)
Fundamental Solution
(+ Problem)
Complex Variables in
Classical Hamiltonian Mechanics. Bogoliubov transformation