What are the recommended textbooks for introductory calculus?

Question

I've already taken my calculus sequence and I'm interested in brushing up and staying sharp on the basics. So far, my calculus background is limited to single-variable calculus, which I applied in my physics sequence and engineering statistics. I learned a little bit of vector math in physics as well, but I'm not strong in it. My mathematical strengths lie in the discrete mathematics.

I'm particularly interested in studying for my IEEE Certified Software Development Associate exam - 10% of the exam is mathematics (calculus, differential equations, and statistics). Calculus is one of the mathematics knowledge areas that a software engineer should be competent in, so I'm looking for not only solidifying the courses that I've already taken, but moving forward with slightly more advanced topics, at an undergraduate mathematics level.

I'm currently using the textbook from my calculus sequence, but I'm interested to know what books other people used to learn calculus and if the book is potentially worth checking out.

What books are available to help me?

Answer 1

Thomas & Finney, Calculus and Analytic Geometry.

Spivak, Calculus.

Apostol, Calculus.

I recommend Apostol the most.

Answer 2

My university uses Calculus: Early Transcendentals by James Stewart in the standard calculus 3 quarter sequence, the prolonged 4 quarter calculus sequence, as well as in multivariable calculus. This book covers topics such as functions and models, limits and derivatives, differentiation and applications of differentiation, integrals, techniques of integration, vectors, vector functions, partial derivatives, multiple integrals, vector calculus, and second-order differential equations.

I also used a different James Stewart book in high school during pre-calculus and calculus. I don't remember the name of that book - it might have even been an earlier edition of this book.

Answer 3

Elementary Analysis : The theory of calculus by Kenneth Ross is a beautiful written book. Link is here : http://www.springer.com/mathematics/analysis/book/978-0-387-90459-7

Diferential and Integral Calculus by R.Courant is again a very good book which one can learn. http://books.google.co.in/books?id=eyC1nk9-YjkC&printsec=frontcover&dq=Calculus+R.Courant&source=bl&ots=v0rLcDvVW_&sig=VPB6ZBXfMm6yj0vLG4YalVkpV7I&hl=en&ei=_6ZlTLXAN47IvQOhtZHyDA&sa=X&oi=book_result&ct=result&resnum=2&ved=0CCEQ6AEwAQ#v=onepage&q=Calculus%20R.Courant&f=false

Advanced Calculus by J.M.H Ohmsted is also a very good book. Although title says advanced its not really advanced.

Answer 4

Even though I took a course out of it more than 10 years ago, I still refer back to Spivak's Calculus all the time.

Answer 5

Calculus from Graphical, Numerical, and Symbolic Points of View by Ostebee and Zorn is my favorite book from which to teach (er, actually, I have a slight preference for the 1st edition over the 2nd, but they're both good). It's aimed a little above average (i.e. harder than the Harvard Consortium book [Hughes-Hallett, Gleason, et al]), but it's much more of a modern reform-calculus than Spivak.

In particular, I think the conversational tone of the book makes it more readable and the variety of problems (especially the fact that it has challenging problems rather than just repetitive exercised) makes it a good book from which to study.

Answer 6

Calculus: Single Variable, Course Advantage Edition by Hughes-Hallett, Gleason, et al, aka the "Harvard Consortium" book, is perhaps the standard "reform calculus" book.

Answer 7

If you can get a copy (which is improbable, I'm afraid),

• Vladimir Smirnov, A Course of Higher Mathematics, VOLUME 1, Pergamon press 1964.

This is a translation of a beautiful treatise on mathematical analysis which served as a textbook for generations of engineering students in the USSR. The first volume, in particular, is one of the best introductions to calculus I've ever seen.