I am working on solving stokes flows to derive the fundamental 'Stokeslet' solutions using the Green functions. I would be very grateful if someone could point me to a book which could provide a detailed introduction to Green's functions and their applications to some physical problems.
@ Roshan
You can find some really nice videos on introduction aspect of GF in youtube lecture videos. Try NPTEL lectures of Prof. Balakrishnan. Either in classical mechanics or quantum mechanics lecture videos, he has taught GF in two lecture videos (an hour each). An easy intro.
Some mathematical physics books where you can find a chapter or at least few problems devoted to GF are by Arfken and Weber, Kreyszig, and Riley-Hobson, and also Chattopadhyay.
But if you want A-to-Z of Green's function, with its applications and also without the need of going through abstract mathematics, then there is only one book you need. The book is,
Green's functions with applications - by Dean G. Duffy. The book has 7 chapters.
1 Historical Development
2 Background Material (mathematical transforms and development of GF)
3 Green’s Functions for Ordinary Differential Equations
4 Green’s Functions for the Wave Equation
5 Green’s Functions for the Heat Equation
6 Green’s Functions for the Helmholtz Equation
7 Numerical Methods
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