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Ask HN: What's the best way of learning calculus, if you already know pure math

2 points by westoncb ↗ HN
I'm in an awkward position where I have good familiarity with pure math and don't have a problem doing proofs in e.g. abstract algebra, mathematical logic, theory of computation—but my applied math is pretty badly lacking.

The particular goal I have in mind at the moment is to be able to understand Maxwell's Equations clearly (partly because of their intrinsic and historical interest, partly because I think what I need for that will get me to what I need for other things). I also have a good amount of practice working with vectors and matrices already.

But, whenever I look for resources on calculus and differential equations, they are these massive text books, and I'm looking for something way more concise. I don't need a ton of practice doing calculations with these things (I don't think)—I would probably just use software if it came to it. I just want to be able to understand concepts expressed through them. (I'm also not a fan of videos, but would be open to using some as supplementary material.)

What resources/activities would you recommend to most efficiently re-learn basic calculus, and for the first time learn differential equations. (My top choice so far if I were forced to use a big textbook is Strang's "Calculus".)

4 comments

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psyklic
It sounds like you would most enjoy a Calculus book that introduces you to Real Analysis. So, take a look at Spivak's Calculus, which is rigorous and written for people passionate about math. Another rigorous alternative is Apostol's Calculus.

These books will prepare you for a more concise Real Analysis text such as Rudin's Principles of Mathematical Analysis.

impendia
I second psyklic's recommendation of Spivak and/or Apostol if you want to "learn calculus the hard way" -- e.g. if you want to learn calculus in a rigorous manner that prepares you well to keep going.

An informal, brief book on vector calculus is Schey's Div, Grad, Curl and all That. I have not read it personally, but I have heard good things about it. It is probably the quickest way of achieving your immediate goal of understanding Maxwell's equations.

Free online copy: ftp://collectivecomputers.org:21212/books/morebooks/Mathematics/Div,%20Grad,%20Curl%20and%20All%20That%20-%20Shey.pdf

For single variable calculus, if you want an entertaining and enlightening quick read, I recommend Thompson's Calculus Made Easy:

https://www.gutenberg.org/files/33283/33283-pdf.pdf

No proofs, but lots of helpful informal explanations.

westoncb
Heh, sounds like I made some decent choices then ;) I just saw your comment now, but in the interim picked up Calculus Made Easy and a short 'manual' on differential equations that John Baez recommended somewhere. I also recently acquired Div, Grad, Curl, but from the looks of it, I won't get much out of until after my little Maxwell's equations project. Thanks!