Calculus Books - Best Textbooks for Calculus

by cazort

Reviews and recommendations of textbooks in Calc I, II, and III/Multivariable, as well as supplemental books for self-study or enrichment.

This page provides recommendations of calculus textbooks and other books on calculus at three levels: basic intro level (Calc I and II, and Calc III/Multivariable), two calculus-related books for people who already know calculus, that provide a novel approach and new perspectives, and the Advanced Calculus or introductory Mathematical Analysis course most grad students or advanced undergraduates take.

I have a B.A. in Mathematics from Oberlin College (2002), an M.S. in Applied Mathematics from the University of Delaware (2007) and an M.A. in Statistics from Yale University (2008). I have taught calculus I and II at the undergraduate level, and have tutored all levels of math from 2nd grade through Ph.D. students.

In the course of my studies, I read (and at times, taught from) many different math books. This page shares my experiences with the books I found most useful, starting from high school, so that you can make an informed decision, whether you're choosing a book for a class, or buying your own book for self-study.

Mainstream Intro Calculus Textbooks

Books for Calculus I and II, Intro Calculus (Includes AB/BC AP Test)

These are standard intro calculus books for college students or advanced high-school students. They are suitable for the classes most people know as "Calc I" and"Calc II", and they cover the material for the AP Calculus AB and BC exams as well.

I have used all these books (although not the current editions) and would recommend all of them. The Larson/Edwards or Larson/Edwards/Hostetler book was the book I used in high school. The Stewart text is the one I taught from at University of Delaware, and is perhaps very slightly more technical and rigorous. The Larson/Edwards and Stewart texts are very similar to each other.  I find the Larson/Edwards book more accessible and prefer it for this reason.

The Apostol book is radically different. It teaches integration (calculation of area) first, and then teaches differentiation (calculation of slope / rates of change). This book follows the natural order in which Calculus was historically developed. But it is not the order in which the subject is taught in most modern classes. I also find that the Apostol book teaches deeper mathematical concepts. It will better prepare students who are planning to do graduate coursework in math, or more advanced undergraduate work.

Calc 3 / Multivariable: Separate or Together?

"Calc 3" or Multivariable Calculus are sometimes separated into extra books. I recommend picking up a copy of the Larson & Hostetler or Stewart books that includes Calc 3, rather than buying the separate additional volume, if you need to learn this material, because it can save you money and you will have everything in one place in the same book.  One possible downside is that this leaves you with a single, very heavy volume.

Calculus (Larson/Edwards/Hostetler)

The text I learned from in High School, and kept for later reference. Includes Multivariable / Calc 3 too. Earlier editions are fine (and cheaper).

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Calculus (Stewart), 7th Edition

The book I have used to teach college-level Calc 1 and 2. Another good choice. Earlier editions are fine (and cheaper).

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(Apostol) Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra

My favorite book, with an unorthodox approach that I actually find is better for learning the subject deeply. 1 of 2 Volumes.

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Calculus Books to Broaden Your Perspective

Supplemental books offering genuinely new or different perspectives

Do you want to have fun with math, and also understand it on a deeper level? Do you want to appreciate the strangeness in the field of Calculus? Here I highlight two books are not textbooks, but which I think offer something really unique and refreshing for the math lover.

Robert Young's Excursions in Calculus is a book of bizarre tricks that will wow any math lover who has a solid understanding of Calculus. The book is accessible but generally requires a fairly thorough understanding of calculus to get the most out of. This book can be great if you are a math teacher or professor, looking to come up with interesting results, problems, or topics that can stir up passion, enthusiasm, or a sense of awe and wonder at mathematical truth.

Eric Schechter's Handbook of Analysis and its Foundations is a completely different book. It is oriented towards the beginning graduate student, and is ideal for self-study before beginning grad school in mathematics. However, more advanced students and professors may also find it incredibly useful. It has a focus on mathematical logic, and it draws connections between abstract structures in diverse branches of mathematics, leading towards an understanding of math that is both broad and deep. This book is also very modern, pulling in results from the 1980's and later, which are often left out of most books written at this level.

Excursions in Calculus: An Interplay of the Continuous and the Discrete (Dolciani Mathematical Ex...

A fun and sometimes deep diversion, not essential, but useful for both students and teachers to liven up the subject.

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Handbook of Analysis and Its Foundations

A heavy hardback volume, this is the sort that a serious mathematician will keep for life and utilize heavily.

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Advanced Calculus Books

Books for Advanced Calculus or Mathematical Analysis

These are advanced calculus books, NOT introductory calculus books. These books are intended for advanced undergraduates or intro graduate students. They require a thorough understanding of calculus as well as some experience with proof and abstract mathematics. These books focus on proof and deep understanding of the principles in calculus. For intro textbooks for first-year calculus, see the other section above.

Of these books, the easiest to read and understand is the Taylor and Mann: it has very clear explanatory prose, and covers less material, but gives more explanation. Apostol is more advanced, but provides ample explanation. Rudin is the hardest to understand, and I would not recommend it if it is the only book on this topic that you purchase. It is extremely concise and makes a useful reference for people who are already well-versed in mathematical analysis.

Mathematical Analysis, Second Edition

This text is written at a relatively high level, but is in-depth and comprehensive, covering a great deal of material. If you only buy one book in this subject, I recommend this one.

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Advanced Calculus

The most elementary of these three books, this is the slowest-paced, most accessible, and covers the least material. Recommended if you want the easiest time learning the subject.

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Principles of Mathematical Analysis (International Series in Pure and Applied Mathematics)

A very concise text, not suitable for a first-time learner but more useful as a reference or for people wishing to develop mastery of the material.

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Buying Used Books and Old Editions

Older editions can save lots, especially for intro calc texts with many editions.

Math books can be very expensive...often as high as $200 for some of the larger textbooks in their newest editions.  This sounds like bad news, but the good news is that you don't need to spend this much!  Here are a few tips:

Buy old editions: For advanced calculus and mathematical analysis, I recommend the newest edition of each book, because in these cases, new editions often correct logical errors that can be confusing and take a lot of time to figure out. However, for mainstream introductory texts that go through 7-10 or more editions, the differences between each edition are small, and you'll save a lot of money, and won't lose much, by buying an old edition--not the first or second but maybe 1-3 editions before the last.

Be careful though if you're taking a class. Old editions are fine for self-study or reference, but the problems often change, so you will need access to an up-to-date book to do the assignments or homework.

Try is my favorite place to buy textbooks; I bought more textbooks there than anywhere else. Even if you limit yourself to books in new or like new condition, you can save considerable money, especially if buying old editions. A lot of bookstores dump old editions on and sites like it, so you can pick up good deals.

You can also buy used calculus books of recent editions in college bookstores. Check the book to make sure it's not missing pages, the spine is intact, and it's not marked up or highlighted. If it is, try to talk them down further on the price...heavily used textbooks do not have much resale value and you don't ever need to pay more than a book is worth because of the internet, and you can use this as a bargaining chip to get a fair price.

More of my Math Book Reviews

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Reviews of introductory textbooks in statistics, from more general-audience books to mathy books for advanced or graduate students.
Recommendations and reviews of textbooks for linear algebra at both undergraduate (college) and graduate levels.
Reviews of textbooks in complex analysis, the subfield of calculus dealing with imaginary and complex numbers.
Updated: 04/01/2015, cazort
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