E 442final-2022-v1.pdf 2 / 4 136% + 2 (1) This problem will teach you about Green's functions, which are useful for adva

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E 442final 2022 V1 Pdf 2 4 136 2 1 This Problem Will Teach You About Green S Functions Which Are Useful For Adva 1 (186.94 KiB) Viewed 70 times

E 442final-2022-v1.pdf 2 / 4 136% + 2 (1) This problem will teach you about Green's functions, which are useful for advanced physics, in a context we studied. You can consult the textbook (e.g., p. 67) as well as other allowed sources. (a) (5 pts) Write the 1D heat equation in the form Lu 0, and identify the partial differential operator L. (Feel free to take the diffusion constant D to be 1 for simplicity if you want.) (b) (5 pts) The Green's function for the 1D heat equation can be defined as the function g g(x, t) solving (Lg)(x, t) = 8(x,t), with g(x,0) = 0, where 8(x, t) = S(x)8(t) is a Dirac delta function. What is the solution g of this PDE for t > 0, using e.g., formula (2) in the book? For full credit, please simplify g. =