3 ms·

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

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.

seanhunter 2y ago
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/ https://faculty.washington.edu/sbrunton/me564/
- lagrange77 2y ago
  I second that. Also recommend this course by Gilbert Strang @ MIT: https://ocw.mit.edu/courses/res-18-009-learn-differential-equations-up-close-with-gilbert-strang-and-cleve-moler-fall-2015/ https://ocw.mit.edu/courses/res-18-009-learn-differential-eq... https://www.youtube.com/playlist?list=PLUl4u3cNGP63oTpyxCMLKt_JmB0WtSZfG https://www.youtube.com/playlist?list=PLUl4u3cNGP63oTpyxCMLK...
- deleted 2y ago
  [deleted]
- CamperBob2 2y ago
  Brunton is one of the greatest unsung YouTube stars for sure.
__rito__ 2y ago
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 https://mitxonline.mit.edu/courses/course-v1:MITxT+18.03.1x [1]: https://www.stevenstrogatz.com/books/nonlinear-dynamics-and-chaos-with-applications-to-physics-biology-chemistry-and-engineering https://www.stevenstrogatz.com/books/nonlinear-dynamics-and-... [2]: https://bookstore.ams.org/text-43 https://bookstore.ams.org/text-43 [3]: https://databookuw.com/ https://databookuw.com/ [4]: https://tutorial.math.lamar.edu/classes/de/de.aspx https://tutorial.math.lamar.edu/classes/de/de.aspx [5]: https://www.routledge.com/Differential-Equations-with-Applications-and-Historical-Notes/Simmons/p/book/9781032477145 https://www.routledge.com/Differential-Equations-with-Applic...
- fussypart 2y ago
  Thanks, just bought them. What about calculus refreshers any recommendation?
  - __rito__ 2y ago
    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 https://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx

seanhunter 2y ago

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

lagrange77 2y ago
I second that. Also recommend this course by Gilbert Strang @ MIT: https://ocw.mit.edu/courses/res-18-009-learn-differential-equations-up-close-with-gilbert-strang-and-cleve-moler-fall-2015/ https://ocw.mit.edu/courses/res-18-009-learn-differential-eq... https://www.youtube.com/playlist?list=PLUl4u3cNGP63oTpyxCMLKt_JmB0WtSZfG https://www.youtube.com/playlist?list=PLUl4u3cNGP63oTpyxCMLK...
deleted 2y ago
[deleted]
CamperBob2 2y ago
Brunton is one of the greatest unsung YouTube stars for sure.

__rito__ 2y ago

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 https://mitxonline.mit.edu/courses/course-v1:MITxT+18.03.1x [1]: https://www.stevenstrogatz.com/books/nonlinear-dynamics-and-chaos-with-applications-to-physics-biology-chemistry-and-engineering https://www.stevenstrogatz.com/books/nonlinear-dynamics-and-... [2]: https://bookstore.ams.org/text-43 https://bookstore.ams.org/text-43 [3]: https://databookuw.com/ https://databookuw.com/ [4]: https://tutorial.math.lamar.edu/classes/de/de.aspx https://tutorial.math.lamar.edu/classes/de/de.aspx [5]: https://www.routledge.com/Differential-Equations-with-Applications-and-Historical-Notes/Simmons/p/book/9781032477145 https://www.routledge.com/Differential-Equations-with-Applic...

fussypart 2y ago
Thanks, just bought them. What about calculus refreshers any recommendation?
- __rito__ 2y ago
  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 https://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx