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
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...
December 4 28. Field theory, group theory
Reading: Chapter 6,
Section 6.4 Heat equation.
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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