I'm interested in learning about **computational aspects of PDE and integro partial differential equations**.

In particular, I'd like to know some reference monographs that cover PDE and IPDE from  in **computational fluid dynamics**, **computational solid mechanics**, **computational biology** (including biomodeling, genomics, neuroscience), **computational chemistry and pharmacology**. 

I'd appreciate both *rigorous mathematical and numerical analysis*  and *extensive* use of *sample code written in MATLAB/Mathematica*.

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Here are two related questions that I have checked out:

- https://mathoverflow.net/questions/281979/reference-request-numerical-analysis-of-pdes-and-integro-partial-differential-e
- https://mathoverflow.net/questions/277002/books-and-resources-on-pdes-that-use-mathematica-and-matlab?noredirect=1&lq=1