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While the linked course seems a lot more thorough, I took the Udacity "Differential Equations in Action" [1] course, which I found very well done. For the homework you write Python programs to compute things like gravitational slingshots, modeling epidemics, wildfires, and the n-body problem. [1] https://www.udacity.com/course/differential-equations-in-act...
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With calculus, you are already well into ordinary differential equations -- partial differential equations are different, but with calculus you have a good start on the basics of those, too. A simple ordinary differential equation is below where of course just from calculus y'(t) = d/dt y(t) and the equation is y'(t) = k y(t) ( b - y(t)) So, for the context: t is time, say, in seconds. y is some real valued function…
> I looked through it, saw lots of intricate stuff, but wondered just why I should dig into that. Since then I read a story about Rota about how, apparently, he felt much the same about the material Ah yes, the classic rant by Rota. Entertaining read, and good perspective (10 pages). Apparently written in 1997. https://web.williams.edu/Mathematics/lg5/Rota.pdf
On a related note, how do you take notes for math subjects with their multiline integrals and sumation and subscripts, division etc? I'm very much attached to recording every thing in simple text editors. Is there a "Notepad" or "TextEdit" for mathematical notation?
Look at Arnold's book on Diff, it is harder then others, but has absolutely different outlook.
That book is totally mindblowing, and obliterates artificial boundaries between physics and mathematics. It also (in the older Dover editions) had a cover where the phase portrait on the front looked like two angry eyes glaring at you that you hadn't learned enough math yet.
Lately I have been looking for a practical (not too much theory) book on how to model problems with differential equations, with lots of examples. I imagine I'd plug them into Wolfram Alpha to get a solution. Does anyone have recommendations?
I personally have used Stella by isee systems, which will output an equation from your model if you are so inclined, but I think there is cheaper/free software out there that will do similar types of modeling.
Speaking of differential equations, an oldie (1997) but goodie, "Ten Lessons I Wish I Had Learned Before I Started Teaching Differential Equations" by Gian-Carlo Rota: https://web.williams.edu/Mathematics/lg5/Rota.pdf
As someone who has basically no formal training in mathematics outside what's required for undergraduate computer science this is a big one. The first time I saw it I was blown away. Everyone who knows of it seems to treat it as natural as breathing, and not worth the exposition
While the linked course seems a lot more thorough, I took the Udacity "Differential Equations in Action" [1] course, which I found very well done. For the homework you write Python programs to compute things like gravitational slingshots, modeling epidemics, wildfires, and the n-body problem. [1] https://www.udacity.com/course/differential-equations-in-act...
https://github.com/madengr/nbody
While it was a good course, I wish it covered the analytic portion, rather than dive straight into numerical solutions.
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Those useless transforms (are you referring to Laplace and friends?) are pretty useful in EE.
Yep, the transforms and series solutions are actually the most important part of ODEs, not just in EE but also in PDEs.
I was left with feeling that I had only learned yet another trick until I read Churchill & Brown's Complex Variables and Applications.