Mathematical Methods of Physics I
PHYS 6124
Fall Semester 2014
August 19
1. Linear algebra: vectors, matrices, eigenvalues
Lecture notes and problem set #1 (due Tuesday, August 26)
Optional reading: Grigoriev Lecture notes; Stone & Goldbart Appendix A; Arfken & Weber Chapter 3
Feel free to add your topics suggestions at any time: suggestions by students and faculty
August 21
2. Linear operators, matrices and ODEs
Lecture notes (revised August 26)
you got a new idea?
August 26
3. Eigenvalue problems: Moment of inertia tensor
Lecture notes and problem set #2 (due Tuesday, September 2)
August 28
4. Eigenvalue problems: Normal modes
Optional reading: Grigoriev lecture notes; Arfken & Weber Example 3.6.1
September 2 - Kimberly Y. Short
5. Stability of a 2-dimenional flow
Lecture notes and problem set #3 (due Tuesday, September 9)
Our competition: MIT 18.085 Computational Science and Engineering I
September 4
6. Complex variables
Reading: Chapter 6 - analytic functions, Cauchy-Riemann conditions, mappings, Riemann surfaces, conformal mappings.
suggestions by students and faculty (feel free to add your comments at any time).
September 9
7. Lagrangian constraints and rank-nullity theorem
Lecture notes and problem set #4 (due Tuesday, September 16)
and thanks!
September 11
8. Calculus of residues
September 16
9. Calculus of residues
Reading: Arfken & Weber Chapter 6 - Laurent expansion; chapter 7 - residues
Lecture notes and problem set #5 (due Thursday, September 25)
September 18
10. Integration in complex plane
Reading: Arfken & Weber Chapter 7, section 7.1
Grigoriev lecture notes
September 23
11. Asymptotic evaluation of integrals
Jensen's theorem, saddle point method.
Lecture notes and problem set #6 (due Tuesday, October 7)
September 25
12. The Gamma, Airy function estimates
Reading: Grigoriev lecture notes.
September 30
13. Lattice propagator
Lecture notes and problem set #7 (due Thursday, October 9)
October 2
14. Discrete Fourier Transform
October 7
15. Fourier Transform; Gibbs phenomenon
Lecture notes and problem set #8 (due Thursday, October 16)
October 9 - Mohammad Farazmand
16. Fourier Transform; Gibbs phenomenon
October 11-14
Mid-term recess
October 16
17. Finite groups
Lecture notes and problem set #9 (due Thursday, October 30)
October 21
18. Finite groups
Lecture notes and problem set #10 (will never be ready)
October 23
19. Finite groups
Unitary representations, Schur's lemma, orthogonality theorem, characters
Lecture notes: ChaosBook.org - "World in a mirror". Skip sections 9.3 and 9.4 except for example 9.12 3-disk game of pinball.
Optional fun reading: Penrose and no need to learn all these "Greek" words
October 28
20. Group theory
Reading: Lecture notes and problem set #11 (due Tuesday, November 11)
October 30
21. Characters
November 4
22. Normal modes from characters
Reading: Lecture notes and problem set #12 (due Thursday, November 13)
November 6
23. Continuous groups: unitary and orthogonal
November 11- Mohammad Farazmand
24. Continuous groups: SO(3) and SU(3)
Reading: Lecture notes and problem set #13 (not ready) (no problem set for Tuesday, November 18, courtesy of NSF)
November 13
25. Symmetries in QM
November 18
26. Probability and statistics
Reading: Lecture notes and problem set #14 (due Tuesday, November 25)
So much mathematical physics, so little time...
What an experimentalist must know: I. Taboada's Probability theory notes
November 20
27. Probability and statistics
November 25 - Sara A. Solla
28. Bayesian statistics
Reading: Lecture notes and problem set #15
(amemded version December 2; due Thursday, December 4)
November 27
Thanksgiving
December 2
29. Random walks, Langevin, Fokker-Planck
Reading: Lecture notes #16; no problem set
December 4
30. Ornstein-Uhlenbeck 'harmonic oscillator' of stochastics
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