Books available to you to help you learn calculus can be one of your best resources when you are trying to learn new math. However, not all calculus books are very helpful. If you choose the wrong book, you might find that it makes things even more confusing than they already were. So I thought I would help you avoid that.
Of course, simply buying a book on this list alone won’t get you an A+ in calculus. You’ll need to put in the work of reading the explanations and doing the problems and exercises in the book. The most important part to learning calculus is practicing the concepts by completing problems. So an important part to any calculus book or textbook is the collection of practice problems included in the textbook.
Here are some of the best books to use as a resource to help you learn calculus and get an A+. I have also included some of the more popular calculus textbooks on this list to provide a bit more information as well as my input about the books.
The Calculus Lifesaver by Adrian Banner
I strongly recommend this book for anyone that is a non-math major taking calculus classes because they need to for their major. I would also recommend this book for any high school students taking AP Calculus AB or BC or taking IB Math SL or HL. It may be more applicable for an IB Math HL student than SL, but it would certainly be helpful for both. I think this book would also be immensely helpful for someone who is trying to learn calculus without having enrolled in a high school or college calculus class. The casual approach is perfect for anyone that is trying to get a grip on the basic concepts taught in calculus and how to apply them. Click here to go get yourself a copy of The Calculus Lifesaver.
However, if you are a math major or are interested in learning more about the ideas behind calculus or proving the concepts that make up calculus, this may not be the book for you. This is certainly not a proof-based resource and does not contain a ton of practice problems. So if you are looking to really dive deep into calculus, you may want to consider Calculus by Michael Spivak, which would be my personal recommendation for a proof-based approach to calculus and you can read more about that below.
Check out my full review of this book here.
Calculus by Michael Spivak
This is easily my favorite book I’ve read about calculus. Calculus by Michael Spivak is the best resource I’ve found to explain the “why” of calculus, rather than only focusing on the “how.” I would strongly recommend this book to anyone that wants to continue their academic math career beyond just the calculus or business calc class required by their school.
This calculus textbook spends a lot of time and energy discussing the proofs and analysis of the topics that are taught in most calculus courses. These explanations are in depth, thorough, and help to give context to many of the methods taught in calculus courses. However, this is likely not the best calculus textbook for you if you are taking the introductory calculus 1 course required at your school. The reason I say this is that many of the explanations and exercises in this text are based around proving concepts that an introductory calculus 1 course would only require you to know how to apply.
If you are studying calculus on your own, or looking to gain a deeper understanding of the concepts taught in your calculus class, this book is a MUST READ. One thing that always stands out in my mind about this book is its explanation of limits. I have never seen another source that explains what limits really mean and the mathematical proof behind any limit you run into as well as this book does.
Single Variable Calculus: Concepts and Contexts
By: James Stewart
This is a popular textbook required for calculus classes in high school and college. Single Variable Calculus: Concepts and Contexts is a solid resource for anyone trying to learn calculus 1, 2, or 3. It covers a wide range of calculus topics including limits, derivatives, integrals, sequences, series, and even some differential equations. This calculus textbook contains detailed explanations of necessary concepts and many examples to demonstrate the common topics covered in calculus courses. Although, I will admit that there are many types of problems included in the exercises at the end of each chapter that are not explained or covered earlier in the chapter, leaving you guessing or looking elsewhere for solutions to similar problems.
However, I think that James Stewart’s textbook does include a useful collection of problems throughout all of the chapters. He does provide plenty of opportunity for you to practice the concepts discussed in this text. As a result, I think that this book is an above average resource to gain an understanding of calculus concepts and a great resource if you are looking for extra problems to use as practice and hone your calculus skills. In fact, I use this book to get a lot of ideas for problems I solve on my website and YouTube channel!
* DISCLAIMER: Links on this page may be affiliate links meaning I would get a small commission from the sale at no extra cost to you. All opinions in this article are 100% my own and I just want to let you know what I think about the products listed here. *