
Ask HN: What's the best way of learning calculus, if you already know pure math - westoncb
I&#x27;m in an awkward position where I have good familiarity with pure math and don&#x27;t have a problem doing proofs in e.g. abstract algebra, mathematical logic, theory of computation—but my applied math is pretty badly lacking.<p>The particular goal I have in mind at the moment is to be able to understand Maxwell&#x27;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.<p>But, whenever I look for resources on calculus and differential equations, they are these massive text books, and I&#x27;m looking for something <i>way</i> more concise. I don&#x27;t need a ton of practice doing calculations with these things (I don&#x27;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&#x27;m also not a fan of videos, but would be open to using some as supplementary material.)<p>What resources&#x2F;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&#x27;s &quot;Calculus&quot;.)
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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](https://www.gutenberg.org/files/33283/33283-pdf.pdf)

No proofs, but lots of helpful informal explanations.

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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!

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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.

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kazishariar
[https://www.maa.org/press/maa-reviews/divine-proportions-
rat...](https://www.maa.org/press/maa-reviews/divine-proportions-rational-
trigonometry-to-universal-geometry) \-- o0o, but that's trig rie?

