# Which book among these would you recommend for first year calculus?

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.

• Ideally, you would use a combination of books. Try also adding to the list a book that has lots of exercises. I would search for this among Russian books.
– OR.
Mar 19, 2014 at 15:14
• Hardy's book is probably in the public domain by now. You can likely find it online. Mar 19, 2014 at 15:15
• hey! I'm doing limits too ( at final stage of it , solving problems etc.). I found this book Elemantary Real analysis by Thomas Bruckner,you can find it for free online by a google search. for intuition , I watched Harvey mudd lectures. Mar 20, 2014 at 9:50

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.

• On 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... Mar 19, 2014 at 15:49
• well everybody is free to give his/her opinion...as far as i am concerned...i liked it. Mar 19, 2014 at 16:07
• @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. Mar 19, 2014 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. Mar 19, 2014 at 16:40

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.

• Is Apostol good for a beginner in calculus? I have background in high school algebra, trigonometry. I also did functions, derivatives, etc in high school. Mar 19, 2014 at 15:18
• Yes, it definitely is. Mar 19, 2014 at 15:20

Maybe Sasane's "The How and Why of One Variable Calculus"?

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

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).