PHYS 6124 Mathematical Methods of Physics - schedule
Mathematical Methods of Physics I
PHYS 6124
Fall semester 2011
August 23
1. Calculus of variations
Reading: Chapter 1
Problem set #0
August 25
2. Lagrange-Euler equations
Reading: Chapter 1
Problem set #1
August 30
3. Lagrange multipliers
Reading: Section 1.5
Compulsory reading:
Problem set #2
September 1
4. Cost of straying from the correct path
Optional reading, only if things nonlinear interest you:
A variational principle for periodic orbit searches
(read "Turbulent fields and their recurrences" first)
September 2
For something completely different
3pm graduate seminar in L5, P. Cvitanović:
"Got turbulence? tachycardia? and what to do about it"
September 6
5. Fun(ction) spaces ,
no distributions
Reading: Chapter 2
Problem set #3, with solutions
September 8
6. Norms, operators and delta functions
Reading: Chapter 2
September 13
7. Partial differential equations
Reading: Goldbart PDE notes ,
up to p. 20 (skip "Characteristic surfaces" and the rest)
Problem set #4
September 15
8. Partial differential equations
Reading: Chapter 6 , up to Section 6.3.1, can skip the rest.
September 20
9. Separation of variables
Reading: Goldbart notes ,
skip Sect. 5 "Wronskians", pp 2/20-2/22
Problem set #5 (updated Sep 22)
September 22
10. Series solutions of ODEs
Reading: Goldbart notes
September 27
11. Adjoint operators
Reading: Goldbart notes
pp. 2/36-46;
Chapter 4
Optional: Appendix A , sects. A.1-A.3;
Grigoriev notes
Problem set #6
September 29
12. Sturm-Liouville eigenproblems
Reading: Goldbart notes
pp. 2/47-55
October 4
13. Inhomogenous PDEs
Goldbart notes ,
skip sect. 6.2.1.
Chapter 5
sects. 5.1-5.4, optional 5.5.
Optional: Appendix A , sect. A.5.2 Fredholm alternative;
Optional: Grigoriev notes
Problem set #7
October 6
14. Green's functions
Our competition: MIT 18.085 Computational Science and Engineering I
October 11
15. Green's functions
Fun reading, link from Ravi: All about the Dirac delta function
October 13
16. Complex numbers
Goldbart notes ,
pages 1/10 - 1/180
October 15-18
Mid-term recess
October 20
17. Complex differentiation
Goldbart notes ,
pages 1/200 - 1/300
Chapter 17
sect. 17.1.
Problem set #8
October 25
18. Complex functions
Goldbart notes ,
pages 1/310 - 1/580
Problem set #9
October 27
19. Contour integration
Goldbart notes ,
pages 2/10 - 2/120
October 28
Physics Homecoming
October 31
Spring registration starts
November 1
20. Contour integration
Goldbart notes ,
pages 2/130 - 2/330
Problem set #10 (aka "Assignment 2")
November 3 - lecture by Roman Grigoriev
21. Cauchy integral formula
Grigoriev notes , up to p. 3.3
Optional reading:
Goldbart notes
November 8
22. Causality
Grigoriev notes , pp. 3.3-3.6
Optional reading:
Goldbart notes
Problem set #11
November 10
23. Dispersion relations; Multifunctions
Reading: Sections 5.5.1, 5.5.2, 18.2
Goldbart notes 4/80-4/90
Goldbart notes
6/10-6/60
November 15
24. Asymptotic expansions
Goldbart notes
6/10-6/60
Problem set #12
November 17
25. Asymptotic expansions
Goldbart notes 8/150-8/180, 8/250-8/370
November 18
Spring registration ends
[Critics Choice]
November 22
26. Feynman diagrams
Reading: Chapter 2 , pp 9-17, from
Field Theory webbook
Let's draw Feynman diagrams!
Can we learn more Quantum Field Theory ?
Problem set #13: exercises 2.B.1, 2.E.2; optional 2.E.3, 2.I.1.
November 24
Thanksgiving
November 29 - lecture by Roman Grigoriev
27. Perturbation theory
R. Grigoriev notes
Problem set #14 (solution , ready next tuesday)
December 1 - lecture by Roman Grigoriev
28. Perturbation theory for eigenvalue problems
R. Grigoriev notes
We were promised Group Theory ?
December 6 - lecture by Roman Grigoriev
29. Singular perturbation theory
R. Grigoriev notes - Singular perturbation theory for ODEs
R. Grigoriev notes - Rescaling in perturbation theory
Problem set #14 solution
December 8 - lecture by Shina Tan
30. WKB
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