5 ms·

Could you tell me a bit about your background, your level in mathematics, and the type of book you prefer? Do you enjoy highly rigorous, proof-heavy texts, or d

Could you tell me a bit about your background, your level in mathematics, and the type of book you prefer? Do you enjoy highly rigorous, proof-heavy texts, or do you prefer books where the author explains concepts in a more conversational and detailed way—still rigorous, of course, but more wordy?

fussypart 2y ago
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...
  - 2y ago
seanhunter 2y ago
I wish more people did this (get the required context) before steaming in with recommendations tbh. That said, I will steam in with some starting points that may be helpful. 1) An “anti-recommendation”: Probably don’t get Edwards and Penney unless you are forced to for some course. It’s _fine_ I guess - like you will learn from it, but it is staggeringly overpriced for what it is and there are enough typesetting errors and other little niggles that grate when a book is as expensive as that. The one good part about it is there are tons of problems but for many/most of them it just gives the answer not a full solution, so it’s not very helpful if you are stuck or your solution looks very different from theirs and you don’t know where to go from there. 2) If you want a free pdf or online resource, mathematics libretexts has “Differential equations for engineers” by Jiri Lebl, which is at least as good as Edwards and Penney and is free and you get the pdf if you want to download it https://math.libretexts.org/Bookshelves/Differential_Equations/Differential_Equations_for_Engineers_(Lebl) https://math.libretexts.org/Bookshelves/Differential_Equatio... 3) Dover Books publish “Ordinary Differential Equations” by Tennenbaum, Morris and Pollard, which I don’t have personally but a lot of people recommend. It’s a Dover book which means it is cheap and some of the terminology and notation is probably a little bit old-fashioned but it’s going to be a lot cheaper than Edwards and Penney if you want a physical book and as I say a lot of people recommend it. So to complement what the parent said, one approach if you’re not sure what type of book you prefer, is check out Lebl (because it’s online and free so easy to dip into) and then you can explore from there. But don’t get Edwards and Penney. I got a cheap second-hand copy and I still think I probably overpaid. I would add get a CAS. You could use wxmaxima (which is OSS) or get Mathematica or something if you can get a cheap student license. It’s going to help a lot to develop intuition by allowing you to plot direction fields etc much more easily as well as doing some of the heavy lifting of verifying solutions etc (although you really need to do that a bunch yourself so you get good at it).

fussypart 2y ago

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...
- 2y ago

seanhunter 2y ago

I wish more people did this (get the required context) before steaming in with recommendations tbh. That said, I will steam in with some starting points that may be helpful. 1) An “anti-recommendation”: Probably don’t get Edwards and Penney unless you are forced to for some course. It’s _fine_ I guess - like you will learn from it, but it is staggeringly overpriced for what it is and there are enough typesetting errors and other little niggles that grate when a book is as expensive as that. The one good part about it is there are tons of problems but for many/most of them it just gives the answer not a full solution, so it’s not very helpful if you are stuck or your solution looks very different from theirs and you don’t know where to go from there. 2) If you want a free pdf or online resource, mathematics libretexts has “Differential equations for engineers” by Jiri Lebl, which is at least as good as Edwards and Penney and is free and you get the pdf if you want to download it https://math.libretexts.org/Bookshelves/Differential_Equations/Differential_Equations_for_Engineers_(Lebl) https://math.libretexts.org/Bookshelves/Differential_Equatio... 3) Dover Books publish “Ordinary Differential Equations” by Tennenbaum, Morris and Pollard, which I don’t have personally but a lot of people recommend. It’s a Dover book which means it is cheap and some of the terminology and notation is probably a little bit old-fashioned but it’s going to be a lot cheaper than Edwards and Penney if you want a physical book and as I say a lot of people recommend it. So to complement what the parent said, one approach if you’re not sure what type of book you prefer, is check out Lebl (because it’s online and free so easy to dip into) and then you can explore from there. But don’t get Edwards and Penney. I got a cheap second-hand copy and I still think I probably overpaid. I would add get a CAS. You could use wxmaxima (which is OSS) or get Mathematica or something if you can get a cheap student license. It’s going to help a lot to develop intuition by allowing you to plot direction fields etc much more easily as well as doing some of the heavy lifting of verifying solutions etc (although you really need to do that a bunch yourself so you get good at it).