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Instructor:
Gil Refael
refael{at}caltech.edu |
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Grader: Shu-Ping Lee Hee-Joong Chung |
| To do the midterm first download the instructions. Instructions When you are ready to take the test, download the midterm: Mid-term Midterm Solution |
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Lecture Notes Sept 27th - Complex analysis review. Sept 29th - Scaling solutions. Oct 4th - Diffusion Green function+some review of FT. Oct 6th - FT applied to the diffusion and wave equations. Oct 11th - Wave equation solution with initial conditions, and the method of characteristics. Oct 13th - Initial condition requirements and the linear operator approach to Green functions. Oct 18th - Laplace equation and conformal mapping. Oct 20th - Nonlinear equations: shock waves and solitons. Traveling wave solution of the KdV equation. Oct 25th - Lax pairs: Shroedinger vs. KdV. For the commutator calculation: Mathematica notebook (.nb - run it yourself) Mathematica notebook (.pdf) Oct 27th - Inverse scattering quick and dirty: Evolution far from the scatterers. (Also see the chapters from Drazin's book added below) Nov 1st - Inverse scattering conclusion: Marchenko equation. (Also see the chapters from Drazin's book added below) Review for the first two weeks can be found in the PDE chapter of Stone and Goldbart's book ("Mathematics for Physics"). |
PS 1 HW1 Solution - Complex integration and scaling solutions. PS 2 HW2 Solution - Green Functions. PS 4 HW4 Solution - Conformal Mappings and the Laplace Equation
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Supplements The discussion of scaling solutions can be found in Nigel Goldenfelds book: "Lectures On Phase Transitions And The Renormalization Group" chapter 10.2 The inverse scattering method and its application to the KdV equation is described in this chapter of Drazin's book. For the Lax commutator method, here is the following chapter. |