Mathematical Methods of Physics I

Instructor

Roman Grigoriev
Office: Howey W304 (office hours: Tuesday 2-3pm)
Phone: (404) 385-1130
E-mail:

Yamato Matsuoka
Office: Howey W503 (office hours: Wednesday 1-3pm)
Phone: (404) 894-9407
E-mail: yamaton@gmail.com

Tuesdays and Thursdays, 12-1:30pm
S204, Howey Physics Building

The course provides an overview of complex variables, matrix theory, perturbation theory, integral transformations, ordinary and partial differential equations with applications to various physics problems.

G. B. Arfken and H. J. Weber, Essential Mathematical Methods for Physicists (Academic Press, San Diego, August 2003), ISBN: 0120598779. Click here to find online retailers who sell the book. New books can be purchased at the Engineer's bookstore on Marietta street.

Homework assignments will be posted on the web every Thursday and will be due next Thursday in class. You can discuss problems with each other, but the solutions have to be executed and submitted individually. All students are expected to comply with the academic honor code. There will be no exams, your performance will be assessed based on the homeworks, so day-to-day participation is very important.

August 21
1. Introduction
Reading: lecture notes

August 23
2. Complex variables
Reading: Chapter 6, lecture notes

August 28
3. Conformal maps
Reading: lecture notes

August 30
4. Applications of conformal maps
Reading: lecture notes
Problem set #1: assignment, solutions

September 4
5. Integration in complex plane
Reading: Chapter 6, lecture notes

September 6
6. Calculus of residues
Reading: Chapter 7, lecture notes
Problem set #2: assignment, solutions

September 11
7. Asymptotic evaluation of integrals
Reading: Chapter 7, lecture notes

September 13
8. Fourier Series
Reading: Chapter 7, lecture notes
Problem set #3: assignment, solution

September 18
9. Fourier transform
Reading: Chapter 7, lecture notes

September 20
10. Applications of Fourier transform
Reading: Chapter 14, lecture notes
Problem set #4: assignment, solutions

September 25
11. Linear operators and matrices
Reading: Chapter 15, lecture notes

September 27
12. Eigenvalue problem
Reading: Chapter 3, lecture notes
Problem set #5: assignment, solutions

October 2
13. Eigenvalue problem
Reading: Chapter 3, lecture notes

October 4
14. Properties of eigenvectors and eigenvalues
Reading: Chapter 3, lecture notes
Problem set #6: assignment, solutions

October 8-9
Mid-term recess

October 11
15. Normal modes
Reading: lecture notes

October 16
16. Matrices and linear ODEs
Reading: lecture notes

October 18
17. Perturbation theory for algebraic equations
Reading: lecture notes
Problem set #7: assignment, solutions

October 23
18. Perturbation theory for eigenvalue problem
Reading: lecture notes

October 25
19. Perturbation theory for differential equations
Reading: lecture notes
Problem set #8: assignment, solutions

October 30
20. WKB theory
Reading: lecture notes

November 1
21. WKB theory
Reading: lecture notes
Problem set #9: assignment, solutions

November 6
No class (Physics Fall Picnic)

November 8
23. Separation of variables in PDEs
Reading: Chapter 16, lecture notes
Problem set #10: assignment, solutions

November 13
24. Boundary value problem
Reading: Chapter 9, lecture notes

November 15
25. Sturm-Liouville problem
Reading: Chapter 9, lecture notes
Problem set #11: assignment, solutions

November 20
No class

November 22
School holiday

November 27
26. Rayleigh-Ritz method
Reading: Chapter 18, lecture notes

November 29
27. Green's function for ODEs
Reading: Chapter 16, lecture notes
Problem set #12: assignment, solutions

December 4
28. Green's function for PDEs
Reading: lecture notes

December 6
29. Ill-posed boundary value problems
Reading: lecture notes

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