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Can anyone give some advice about books where I could find introductory information about Green's function. What are the methods of constructing Green's function. Actually, Green's function for 3D diffusion equation in unbounded domain is of interest. I am novice in this topic (Green's function for ODE and PDE) and any help is appreciated. Thank you in advance!

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I think that "Boundary Value Problems and Green's Functions" by Stakgold and Holst is a good text.

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By the way, for the classical linear pde's Evans has a very good derivation of the Green functions. – guacho May 21 '13 at 20:30

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