This page contains a list of all books and resources that we recommend.
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This section contains lists of recommended books. Most book links are affiliate links. Click the topic name to open the books list for a particular topic.
Free Textbooks - - - Recently, some free calculus textbooks have shown up online. Now, these are not the usual watered down versions. 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 editions 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 non-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. Here are the ETF editions.
Here are the corresponding non-ETF editions.
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 How To Save On and Use College Books 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.
There are many books 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 page How To Save On and Use College Books.
Ordinary Differential Equations
Elementary Differential Equations by Boyce and DiPrima has been the standard textbook at many universities for years. New versions are still being produced but it can often be difficult to read because it can be quite terse. So you need to take a lot of notes and fill in a lot of blanks. That said, it is still a good book and will give you a good grounding in first semester differential equations, if you are willing to put in the work.
This link is to a more current edition of the textbook. If you don't require a specific edition, an earlier edition will work nicely.
If you are required to have this book for your class, we recommend you get a supplementary text as well.
Ordinary Differential Equations (Dover Books on Mathematics) is a great supplementary text for beginning differential equations. It has great reviews on Amazon. We recommend most Dover books because they are well written and have great content, while at the same time discussing topics with depth and insight. This book will not disappoint the serious student.
We recently discovered this book and, from what we have seen, it is a good book. We looked primarily at the chapter on series solution. This book goes into more detail about the radius of convergence of power series about singular points than we have seen in most books.
Partial Differential Equations
These next two books discuss partial differential equations, usually taken the semester after ordinary differential equations. Dover books are some of the best supplementary math books out there, including these.
On the How To Study Math Proofs 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.
These two books explain real analysis in fairly good detail.
This next book, Rudin's Principles of Mathematical Analysis (sometimes called baby Rudin) is the classical text used at many universities. It is concise and I suspect used to weed out the students that are not committed to learning advanced math. You will really need to use the study suggestions on the page on How To Read and Learn From Math Books. You will also need one of the above supplementary texts or a supplementary text that you have found. Additionally, it will help you to read the Learning Techniques page.
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.
Here are some good books on how to learn many things, not just math. As you can see, there are a lot of books on this topic. The best place to start is to read the first book, Deep Work.
For recommendations on what to look for before buying a calculator, check out the supplies page on 17Calculus.
Really UNDERSTAND Calculus
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