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For a physics major, what are the best books/references on Greens functions for self-studying?

My mathematical background is on the level of Mathematical Methods in the physical sciences by Mary Boas.

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You should be more specific. There are Green's functions which are general linear kernels, and more specific uses in quantum mechanics, where the Greens' function is the energy representation of the propagator. –  Ron Maimon Jan 24 '12 at 23:36
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I recommend Sommerfeld. The sixth volume of his physics series is pure maths, PDE's of Physics and is a wonderful physicists' view of the maths.

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