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17Calculus Math Books
On this page, we give you suggestions for the best math books we've seen or heard of, some of them for free, all others reasonably priced.
Before buying any math books, make sure you know how to read them (yes, there are specific techniques that will help you read and study math books). We give you some helpful suggestions here.
Precalculus and college algebra books are quite plentiful but not all of them are helpful. Here are the ones that we think will help you the most. For suggestions on how to select and use supplementary books, read the discussion on the main books page.
Free Textbooks - - - Recently, some free calculus textbooks have shown up online. Now, these are not the usual watered down versions that are everywhere. These are full textbooks that instructors are using in classrooms at reputable colleges and universities.
The best free book we've seen so far is Active Calculus by Matt Boelkins. It is over 500 pages of good material and there is a free workbook available as well. A second book we recommend is simply entitled Calculus I, II, III by Jerrold E. Marsden and Alan Weinstein. This book is actually three books and there are student guides as well. For a list of other free textbooks, check out the American Institute of Math - Approved Textbooks.
Purchased Textbooks - - - As far as purchased textbooks go, the best we've found is Larson Calculus. If you have a choice, go with Larson. If you are looking for a textbook for reference, go with an early edition of Larson. The third and fourth edition are both good.
There are a couple of things you need to know when navigating through the list of Larson Calculus textbooks.
1. There are two main types of books, Early Transcendental Functions (ETF) and not ETF. The difference is in the structure of the material. The ETF version has the calculus of exponentials, logarithms and trig mixed in with calculus of polynomials. The non-EFT version has all the calculus of those functions separated out in later chapters. We recommend the ETF version since the flow of the material is better in our opinion and easier to learn from. However, you need to go with whatever your instructor suggests.
2. There is also the option of purchasing a copy that says just Single Variable Calculus. This is basically the first half of the full book (which contains both single and multi-variable calculus). We recommend the full version, since you never know when you might need an extra chapter or two. But, again, go with what your instructor recommends.
Here are some links to Larson textbooks, several editions. We include only the full ETF version. However, you can use these links to look for other versions, if these don't fit you needs.
Reference Books - - - For a reference book to help you learn calculus or give you extra practice, we recommend these books. The absolute best books to supplement your calculus knowledge are How To Ace Calculus and How To Ace The Rest Of Calculus. For suggestions on how to select and use supplementary books, read the discussion on the main bookstore page.
Books for differential equations need to be more indepth and comprehensive than for calculus or precalculus, since differential equations might be considered advanced math and is usually required for students who are actually going to use it and therefore really need to know it.
Boyce and DiPrima seems to be the standard textbook many colleges use but it can be quite terse. So a supplementary book may be in order. I have always found that the Dover Books are helpful. There are many out there but these suggestions should get you started for ordinary and partial differential equations. For suggestions on how to select and use supplementary books, read the discussion on the main bookstore page.
On the Math Tools page, we give concrete techniques on how to read and understand math proofs, as well as some links for additional help. Here are some book suggestions if you are interested in learning more.