Textbooks on Poisson equation, Green's function and Green's theorem

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APoorStudent
Please recommend two textbooks about Poisson equation, Green's function and Green's theorem for a theoretical physics student. One is easy to read so that I can have an overall understanding of the topics, another is mathematically rigorous and has a deep and modern exploration of these topics. Thanks a lot!
 

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You find a very nice (non-rigorous) introduction to vector calculus in

A. Sommerfeld, Lectures on theoretical physics vol. 2
 

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