1. Calculus of variations
Reading: Goldbart notes
Reading: Chapter 1
Problem set #0 (optional)
August 23 - lecture by Paul Goldbart
2. Lagrange-Euler equations
Reading: Chapter 1
Problem set #1
August 28
3. Lagrange multipliers
Reading: Section 1.5
Problem set #2
August 30
4. Lagrange multipliers 2.0
Optional reading, only if things nonlinear interest you:
A variational principle for periodic orbit searches
(read "Turbulent fields and their recurrences" first)
September 4 - lecture by Cristel Chandre
5. From Lagrange to Hamilton
Reading: Chandre lecture notes
Problem set #2 due 3pm, Academic Office Howey W111, c/o Kevin Carter
Problem set #2a
September 6 - lecture by Cristel Chandre
6. Constrained Hamiltonian systems
Dirac theory
Reading: Chandre lecture notes
September 11
7. Fun(ction) spaces
Norms, operators and delta functions
Reading: Chapter 2 ; what is a 'kernel'? a 'smooth operator'?
Problem set #3
September 13
8. Hilbert spaces
Optional reading: Does learning via smart phone make you smarter?
September 14
For something completely different
3pm graduate seminar in L5, P. Cvitanović:
"Got turbulence? tachycardia? and what to do about it"
September 18
9. Orthogonal polynomials
Problem set #4
September 20
9. Partial differential equations
Reading: Goldbart notes, up to p. 20 (skip "Characteristic surfaces" and the rest)
Reading: Chapter 6, up to Section 6.3.1, can skip the rest.
September 25
10. Cauchy data, wave equation
Reading: Chapter 6 (Sects. 6.2 and 6.3 covered in the lecture, please do study 6.3.1 as well).
Problem set #5
September 27
11. Separation of variables; Series solutions of ODEs
Reading: Goldbart notes, skip Sect. 5 "Wronskians", pp 2/20-2/22
Reading: Goldbart notes
October 2
12. Adjoint operators
Reading: Goldbart notes pp. 2/36-46
Optional: Chapter 4; Appendix A, sects. A.1-A.3; Grigoriev notes
Problem set #6
[Jim: There is an error in the T-square posted solution for problem 2.b. The function a_1 should be -3x instead of -3]
October 4
13. Sturm-Liouville eigenproblems
October 9
14. Vectors and tensors
Scalar quantity: Having only magnitude, not direction
Chapter 10 sects. 10.1-10.2.
Problem set #6a, due October 25
October 11
15. Calculus on smooth manifolds
Chapter 11 sects. 11.1-11.2, 11.5
October 13-16
Mid-term recess
October 18
16. Inhomogenous PDEs
Goldbart notes (note: updated Oct 18), skip sect. 6.2.1.
Chapter 5 sects. 5.1-5.4, optional 5.5.
Optional: Appendix A, sect. A.5.2 Fredholm alternative;
Our competition: MIT 18.085 Computational Science and Engineering I
October 23
17. Green's functions
Optional: Grigoriev notes
Problem set #7
October 25
18. Green's functions
as the prelude to Quantum Chaos
Fun reading, link from Ravi: All about the Dirac delta function
October 26
Physics Homecoming
be there or be square, and do let Lori know that you are coming.
October 29
Spring registration starts
[Critics Choices: graduate PHYS 8803 or Bellissard PHYS 6102]
October 30
19. Complex numbers
Goldbart notes, pages 1/10 - 1/180
Problem set #9 (there is no Problem set #8)
November 1
20. Complex differentiation
Goldbart notes, pages 1/200 - 1/300
Chapter 17 sect. 17.1.
November 6
21. Complex functions
Goldbart notes, pages 1/310 - 1/580
Compulsory reading:
- (translation)Problem set #10
November 8
22. Contour integration
Goldbart notes, pages 2/10 - 2/120
November 13
23. Contour integration
Goldbart notes, pages 2/130 - 2/330
Alex: What is Quantum Hall Effect?
Problem set #11 (aka "Assignment 2")
November 15
24. Cauchy integral formula
Grigoriev notes, up to p. 3.3
Optional reading: Goldbart notes
November 16
Spring registration ends
[Critics Choices: graduate PHYS 8803 or Bellissard PHYS 6102]
November 20
25. Dispersion relations; Causality
Grigoriev notes, pp. 3.3-3.6
Reading: Sections 5.5.1, 5.5.2, 18.2
Optional reading: Goldbart notes
Green or Green's?
Problem set #12, due November 29
November 22
Thanksgiving
November 27
26. Riemann surfaces
R. Penrose: a Riemann surface
Goldbart notes
Choices: so much mathemqatical physics, so little time...
November 29
27. Probability, field theory
(what really happened?)
Our competition: MIT again! (spool to 3 min 20 sec)
Problem set #13, exercises 5.A.1 and 5.A.2, rest bonus, due December 6
December 4
28. Field theory, group theory
Reading: Chapter 6, Section 6.4
Notes (Version 3.6, rewritten for this course): read Chapter 1 "Lattice field theory."
December 6
29. Knowing when to stop: How noise frees us from determinism
Stochastic (Wiener) path integral; Orstein-Uhlenbeck; but there was no time for the optimal partition hypothesis...
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December 7
last day of classes
December 17
grades due