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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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Before answering, please see our policy on resource recommendation questions. Please write substantial answers that detail the style, content, and prerequisites of the book, paper or other resource. Explain the nature of the resource so that readers can decide which one is best suited for them rather than relying on the opinions of others. Answers containing only a reference to a book or paper will be removed!

    
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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For the love of all that is good pedagogy, you should first make sure you understand the equivalent of a Green function in a finite vector space, i.e. with matrices. If you do this, everything else will be incredibly obvious. – DanielSank Feb 4 at 8:31

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You may want to refer to Jackson's 'Classical Electrodynamics' for several examples of solutions using Green functions. I also found chapter 7 of 'Mathematics for classical and quantum physics' by Byron and Fuller quite helpful. Its title itself is 'Green functions'.

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