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I am looking for some suggestions on a good calculus book I shall keep on hand all the time.

I am a graduate student who will be commencing research in the area of theoretical PDE (nonlinear). However I often get stuck on some basic calculus facts where most undergrad knows. My maths background is very applied(financial maths) hence I am lacking the actual preparation to work in theoretical PDE. However, it is too late for me to turn back.

Very often as I feel, research in theoretical discipline (especially the analysis of PDE) requires nothing advanced but rather some delicate calculus and real analysis (perhaps at high school level)

I found Stewart Calculus: concepts and context helpful helpful since we did not learn how to calculate stuff like surface integral (or any those engineering kind). But the book is too big and quite difficult to find a copy from the library (since first year students have the priority)

Spivak is also good. But too little multivariable stuff.

If I can find a book contains all that calculus facts allows one to study functional analytics aspects of nonlinear PDE, would be great!

Any suggestions appreciated.

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    $\begingroup$ I'm a fan of Folland's book Advanced Calculus, and the book Div Grad Curl and All That. I also wrote some notes that attempt to quickly explain the intuition behind multivariable calculus. $\endgroup$ – littleO May 10 '15 at 4:25
  • $\begingroup$ thanks. I can imagine how good folland's book is. But so hard to get a copy... $\endgroup$ – math101 May 10 '15 at 5:21
  • $\begingroup$ A Primer of Infinitesimal Analysis, John Bell. $\endgroup$ – user117644 May 23 '15 at 1:34
  • $\begingroup$ Advanced Calculus by Fitzpatrick. $\endgroup$ – icurays1 Jun 3 '15 at 20:45
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Thomas' Calculus: Early Transcendentals is solid. I consider it an alternative to Stewart's, similar in both style and accessibility.

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Calculus: The Classic Edition by Earl Swokoswki should be a good one, but it's big, so I would recommend a digital copy of it. It's a classic calculus book, serving as a basis for many other calculus books, including Stewart's Calculus: Early Transcendentals. Is that the kind of book you are looking for?

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Schaum's outlines are great reviews on the basics (which is what you need).

I also quite like Granville (free on the web or can buy old used copies). It was the defacto standard for about 1900 to 1960 in the US. Doesn't cover much multivariable calc, but then you said you wanted less of that anyhow.

I would avoid the theory emphasis texts that are usually recommended here (Spivak, Apastotol, Courant) because you need something pretty clean and simple to refer to when you have a basic question on a technique (e.g. integration by parts, partial fractions, etc.). [Doesn't mean those books are bad. Just that a simple, easy, terse, technique oriented book is what you are looking for, to look things up when needed.]

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