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Comment by fussypart | Hacker News Reader

I have a CS degree but haven't done math in a few years. Last course I completed was an MITx - intro to probability. While I enjoyed its rigor and detail, I am looking for something practical without proofs.

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Oh well you might really like this, which I think is amazing. Steve Brunton from U Washington has an incredible course on DEs and dynamical systems. It’s a playlist on youtube where he talks through everything on a lightboard in a really incredibly clear way, there are tons of great examples, and he illustrates all the models using python and matlab code. And then a bunch of notes, problem sets etc are available online at the link.

https://faculty.washington.edu/sbrunton/me564/

I second that.

Also recommend this course by Gilbert Strang @ MIT:

https://ocw.mit.edu/courses/res-18-009-learn-differential-eq...

https://www.youtube.com/playlist?list=PLUl4u3cNGP63oTpyxCMLK...

Brunton is one of the greatest unsung YouTube stars for sure.

There is a course [0] from MITx that should be right for you. I had started it once, and it was very well-designed. But it was a bit slow-paced for my taste and I did not finish it.

For textbooks, I can recommend you the fantastic book- Non-Linear Dynamics and Chaos by Steven Strogatz. It is fully concerned with chaos theory and applications of DEs.[1]

I recommended these to you since you are looking for "practical" stuff.

A lot of DE courses deal with DEs mechanically, i.e. "here's this method, here are some examples, and this is how you use the method to solve it". I don't really like this approach, and I have never needed them outside college. If you like this, then look no further than Paul's Online Notes [4].

Here is also something you could consider: "Differential Equations: From Calculus to Dynamical Systems: Second Edition by Virginia W. Noonburg" [2] I haven't read it in full, but AMS generally has good taste when it comes to authoring good textbooks.

I also second the suggestion to check out stuff from Steve Brunton. [3]

If you want something practical, you might have a field in mind. So, you could also choose to read a basic course, and then dive into the field itself by looking up "Differential Equations in X books" where X is Physics, Biology, Finance, etc. For the absolute basics, Khan Academy is also good. I also mentioned two in the original post. Riley, Hobson, Bence is better for your needs.

I have recently come across Differential Equations with Applications and Historical Notes By George F. Simmons [5]. It might also float your boat.

I am aware that I have given you too many choices. But learning DEs is a months-long endeavor and I want you to spend at least some hours choosing your textbook/course/hybreed before you start your journey. This is how I chose my books in college. Multiple teachers, seniors would suggest ~10 books on each topic, and I would go to the library and spend two full days skimming through all of them, and choose 1-2 books.

[0]: https://mitxonline.mit.edu/courses/course-v1:MITxT+18.03.1x

[1]: https://www.stevenstrogatz.com/books/nonlinear-dynamics-and-...

[2]: https://bookstore.ams.org/text-43

[3]: https://databookuw.com/

[4]: https://tutorial.math.lamar.edu/classes/de/de.aspx

[5]: https://www.routledge.com/Differential-Equations-with-Applic...

Thanks, just bought them. What about calculus refreshers any recommendation?

Since you are eyeing DEs, I would suggest not to spend too much time on Calculus.

I have two resources in mind: Calculus Made Easy (available freely on Project Gutenberg) by Thompson, and simply Khan Academy.

Paul Lamar has detailed notes on Calculus, too [0].

[0]: https://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx

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