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this post was submitted on 07 Nov 2023
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So aside from Evans which seems like the gold standard, I also found "Partial Differential Equations Modeling Analysis, Computation" by Mattheij, Rienstra and ten Thije Boonkkamp as a prominent recommendation.
It seems like it has a soft introduction so good for getting back into math, as well as a side-focus on numerical methods and modeling, so playing around with some made-up real-life problems in SageMath or Matlab (and lets be honest drawing pictures is the fun part of this endeavour) should be achievable.
I personally haven't used it so can't vouch for it but these two books are what my library has as the standard textbooks on PDE.
Oh this is wonderful comrade, this'll be helpful i hope in my studies. i've been meaning to model biological systems (populations of bacteria and microbes) since there were a few interesting ideas i wanted to explore.
Best of luck