

Ask HN: A good book on Calculus? - mannicken

Hi,<p>After a year-long break I'll continue studying math this fall.<p>What I want is some refreshment on calculus. Does anyone know something similar to Feynman's Lectures on Physics, just on calculus? Feynman's books were really fucking awesome and I would like a similar fun read for calculus: derivation/integration, series, and multivar (and beyond, if possible but for now this will suffice).<p>I'm not really looking for "here's a bunch of formulas for derivation: And here's what Taylor serie looks like:". I already know that. I want to know what goes on under the hood, proofs, dissections, analogies.<p>Similar question goes for chemistry/biology but I think HN is much more math-oriented.<p>Suggestions?
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jeffcoat
You may be having trouble finding things because calculus done with full rigor
is called "analysis". The classic introductory-but-extremely-dense text is
Rudin's _Principles of Mathematical Analysis_. If you're reading on your own,
though, I expect you'll get a lot more out of a friendlier book; my first
analysis course was taught out of Strichartz's _The Way of Analysis_.

N.B.: Most everything in either book will be completely new to you. 1st-year
calculus courses have absolutely no interest in teaching you what goes on
under the hood; there's just no time. But I think the analogy to Feynman's
lectures holds up pretty well.

~~~
mannicken
Looks like The Way of Analysis is what I need, thank you :)

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billswift
Apostol's Calculus texts (2 volumes) are the best with the supporting theory.
I'm more from an engineering perspective, for readers looking for a book from
that direction is Kline's "Calculus: An Intuitive and Physical Approach".

Introductory general biology texts have a lot more variation in how the
material is presented, but have to cover such an incredible amount of facts
that there is actually less effective difference. Some biology texts tend to
be more ecologically oriented (Campbell), where others are more cellular and
chemically oriented (Curtis), but the difference tends to get lost somewhat
with the need to cover everything, and the sheer mass of material each HAS to
cover.

You might try Pauling's "General Chemistry" text for a more theoretical
treatment in chemistry.

Both Kline's calculus and Pauling's chemistry texts were from the 1960s and
reprinted by Dover in the 1990s; you might try checking the Dover catalog to
see if there are any more similar reprints out.

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enum
Michael Spivak's Calculus text:

<http://www.amazon.com/gp/product/0914098918>

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jpwagner
volume 1 of the best series out there...

[http://www.amazon.com/Calculus-Vol-One-Variable-
Introduction...](http://www.amazon.com/Calculus-Vol-One-Variable-Introduction-
Algebra/dp/0471000051)

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splat
If you'd like to read a refresher on the calculus of multiple variables, I
think you'd enjoy Div, Grad, Curl and All That. It's in the same sort of
informal style of Feynman's Lectures. It's not rigorous like Rudin, but it
gives you a good intuitive understanding of the subject.

