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