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I'm struggling a bit with functions(limits, squeeze theorem, etc).

I have done some research and found a list of books on calculus but I'm not sure which one would be better suited for me, so I would appreciate if some experienced people here could advise me which books would be better to master the basics so I can move on with derivatives, etc. Limits is my main problem, so I need a book which explain this in depth so I can master it. Then I'll keep going on with the same book for other chapters.

Below is the list which I found here:

  • Apostol T.M. Calculus Vol. 1
  • Burn R.P. Numbers and Functions: Steps into Analysis
  • Courant R. and John F. Introduction to Calculus and Analysis I - One of the better calculus text in print.
  • Crowell B. Calculus
  • Dawkins, P Calculus I and Calculus II
  • Garrett P. Calculus
  • Ghorpade S.R. and Limaye B.V. A Course in Calculus and Real Analysis
  • Gill G.S. Calculus Bible
  • Guichard D. Whitman Calculu.
  • Hardy G.H. A Course of Pure Mathematics
  • Hwang A.D. Calculus for Mathematicians, Computer Scientists, and Physicists: An Introduction to Abstract Mathematics
  • Santos D. Differential Calculus
  • Shapiro B.E. Calculus and Analysis
  • Spivak M. Calculus
  • Strang G. Calculus
  • Thomas G.B. and Finney R.L. Calculus and Analytic Geometry
  • Tranter C.J. Advanced Level Pure Mathematics
  • Tranter C.J. Techniques of Mathematical Analysis
  • Veeh J.A. Lectures Notes on Calculus

So far I narrowed my list down to Hardy, Spivak and Apostol based on further research, but I haven't got my hands on these books yet to compare them and I'm not sure if these books will be good for me.

Thanks.

Matthew Cassell
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Sab ಠ_ಠ
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4 Answers4

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Spivak is very good for learning calculus as it has very thorough explanations (though sometimes become too chatty). Be sure to do all the exercises. Have Apostol by your side too.

wanderer
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    On http://matheducators.stackexchange.com (currently in closed beta) someone mentioned that after studying math, and then tutoring several years, there still were problems in Spivak he would stay well away from... – vonbrand Mar 19 '14 at 15:49
  • well everybody is free to give his/her opinion...as far as i am concerned...i liked it. – wanderer Mar 19 '14 at 16:07
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    @vonbrand: That's probably true. But it's no reason why an amateur should not read it. Spivak was pretty much the only text I used to grasp the $\epsilon$-$\delta$ arguments. Didn't need anything else. – Ishfaaq Mar 19 '14 at 16:34
  • +1 for Spivak. @vonbrand: the "star" questions in Spivak are not for the faint of heart; but the book is very good at building understanding. – Martin Argerami Mar 19 '14 at 16:40
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Maybe Sasane's "The How and Why of One Variable Calculus"?

http://eu.wiley.com/WileyCDA/WileyTitle/productCd-1119043387.html

https://www.amazon.com/How-Why-One-Variable-Calculus/dp/1119043387/ref=sr_1_3?ie=UTF8&qid=1475415606&sr=8-3&keywords=sasane

M. Esanto
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Apostol is a classical textbook that we often use also in Italy. Hardy's course is really old-fashioned, while Spivak is probably my favorite although somebody thinks it is a bit harder that Apostol's.

Siminore
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You might want to look around for lecture notes on the web. E.g. the ones by William Chen cover much of the (beginning) undergaduate curriculum quite well. Going into analysis more deeply is Clark's "Honor Calculus". I'm sure you'll find plenty of good material at OCW or other places. Many courses publish homework and exams (often with complete solutions).

Community
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vonbrand
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