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I am a Computational Biology master's student and I would like to study differential equations (both ODEs and PDEs).

I tried to have a look at the available textbooks but what I found is either too theory-oriented or too applications-oriented. I do not want to waste time proving theorems but I do not want to simply solve basic equations using finite differences.

The only text I found is Ordinary and Partial Differential Equations by Henner. Unfortunately, I was not able to find any review of it and it's quite huge. I also toke into consideration doing the ODE part by watching Gilbert Strang's short videos online and the PDE part watching some lectures on YouTube (commutant's channel), but I was wondering whether this is too basic (MOOC style). Any suggestion?

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    $\begingroup$ Unless you're looking for something with a numerical bent, this question should probably be moved to math.SE. $\endgroup$ – David Ketcheson Oct 15 '17 at 1:09
  • $\begingroup$ @DavidKetcheson Well, probably. I was more interested in the opinion of a computational scientist rather than a mathematician. Is it possible to delete it now? $\endgroup$ – wrong_path Oct 15 '17 at 5:10
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Check out this new book about ODEs by Trefethen et al. It focuses on interpretation of solutions' behavior and on nonlinear problems.

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For ODEs I'd learn them as dynamical systems through Strogatz's book. Getting analytical solutions is far less important than analysis of nonlinear ODEs in most contexts since having an analytical solution is a special case.

For PDEs I wouldn't treat it as a subject to learn unless you are a mathematician and really want to dive into function spaces and regularity theory. I would treat the types of PDEs your interested in as the subject. Pick a PDE from your subject you'll find books which cover that subject in detail. I would say you have to learn the numerical methods to really explore the pde as well.

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  • $\begingroup$ Thanks a lot. Well, I have a basic knowledge of functional analysis and numerical methods (FD and FEM). The problem now is that, for doing modern physics, I sometimes need to know something about the "origin" of a PDE and some analytical solutions. So I wanted to study them once for all! $\endgroup$ – wrong_path Oct 15 '17 at 9:36
  • $\begingroup$ I don't think there's such a thing as a book or even methods that are once and for all. Hyperbolic PDEs are so different from elliptic (which are closer to parabolic) PDEs that they require their own heuristics. Then nonlinear pdes are all pretty unique but build off of their linear counterparts. If you know the numerical methods and function space theory then you already know what's transferable. $\endgroup$ – Chris Rackauckas Oct 15 '17 at 9:40
  • $\begingroup$ *Study the basics of ODEs and PDEs once and for all. $\endgroup$ – wrong_path Oct 15 '17 at 9:41

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