Recommendations for Learning Ordinary Differential Equations

Can anyone recommend some good resources for learning ordinary differential equations? I’m not looking to become an expert or to write my own solvers - I’m just looking for something that will provide me with a good solid understanding of the basics so that I can understand (at a high level) how some of the packages in the Julia ecosystem work…For now, my end goal would be to just know enough to be able to formulate and solve basic ODE problems with Julia and be able to explain (again, at a high level) how the problems are solved.

I bought a copy of the Tenenbaum & Pollard book which seemed to be highly recommended on various sites/forums across the web but, honestly, I’m finding reading through it to be quite brutal. A resource that leverages Julia would be really fantastic, if one exists.

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Gil Strang has a series on differential equations, with examples in MATLAB on youtube MIT Learn Differential Equations - YouTube I haven’t watched it but given his amazing teaching ability I’d expect it’s very clear and engaging.


N. Trefethen: Exploring ODEs, SIAM 2018, is available for download together with Matlab codes on the authors’s web page. It is a beautiful textbook (well any book from this guy is a marvel). It does exactly what the (unusual) title says: it helps explore. It does not just provide definitions and proofs but rather uses numerical computation to help develop insight into many really fundamental issues.

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I would recommend two sources:

The content is very good, but the camera is from the Stone Age for some reason.

I would also recommend another classic on the topic:

“Differential Equations with Applications and Historical Notes” G. F. Simmons

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