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"17Calculus might appear intimidating, but it’s an exhaustive, complete guide to college-level calculus."
wikiHow - How to Relearn Math
"17Calculus is an excellent site for college level calculus."
MakeUseOf.com - The 20 Websites You Need to Learn Math Step by Step
This site is dedicated to upper-level college mathematics (including calculus, precalculus and differential equations), science and engineering.
We search the internet for comprehensive, in-depth material on upper-level mathematics, science and engineering. Then, we integrate the best videos, material and links into our discussion to help you learn, understand and use what you are currently studying. Our pages are not meant to replace your book or class materials but to supplement and enhance them or to refresh your skills.
Who is this site for?
- students in traditional classrooms
Here is what you will find on more than 395 pages.
more than 3425 videos
more than 3850 practice and exam problems all with complete, worked out, step-by-step solutions
FREE personal account with the ability to save practice and page bookmarks as well as the ability to rate practice problems.
How much will this cost you?
Zero, nothing, nic . . . Everything on this site is free.
We are dedicated to helping you learn, understand and use calculus, precalculus and differential equations (and perhaps other science, engineering and mathematics topics in the future).
But wait, what's the catch?
There is no catch. I am a former calculus instructor who thinks students pay enough already. I don't want you to just survive calculus.
I want to help you learn calculus so that you understand it and are able use it.
This section contains lists of recommended books. Most book links are affiliate links. Click the topic above 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 How To Save On and Use College Books page.
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.
These links are to more current editions of the textbook. If you don't require a specific edition, an earlier edition will work nicely.
If you are required to have it for a 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.
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.
This next book, Rudin's Principles of Mathematical Analysis 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.
Two Excellent, Highly Recommended Books
This book could catapult your learning, if you apply the techniques and insights carefully and radically.
Indistractable - Control Your Attention and Choose Your Life - We recently discovered this book and found that it contains very practice advice on how to focus. Combined with Deep Work, you get techniques on how to control your focus and perform deep work.
You CAN Ace Calculus
17calculus is intended to help you learn calculus so that you can work problems on your own, do well in your course on your own and, later on, use calculus in your discipline on your own. Please do not use this site to cheat or to avoid doing your own work. What you do in private eventually comes to light and shapes the kind of person you are in public.
Choose now to be a person of integrity and discipline.
Here are several ways to get started.
1. Select a topic from the menu or from the alphabetical listing.
2. Search for a specific topic using the search option on the menu.
3. Start learning calculus: first topic is limits.
5. Go to the About page for a short explanation on how to get the most out of this site.
Single Variable Calculus
Do you have a practice problem number but do not know on which page it is found? If so, enter the number below and click 'page' to go to the page on which it is found or click 'practice' to be taken to the practice problem.
The 17Calculus and 17Precalculus iOS and Android apps are no longer available for download. If you are still using a previously downloaded app, your app will be available until the end of 2020, after which the information may no longer be available. However, do not despair. All the information (and more) is now available on 17calculus.com for free.
This site contains lots of information without flashy ads and graphs that distract your attention. You will find this site either boring or refreshing. While you are here, you can focus your attention and really learn what we are teaching you. For more information see our About page.
"Of the ten websites it is likely that most students will find Khan Academy and 17Calculus to be the best overall sites for working through all the calculus topics step by step."
Top-Site-List.com - Top Ten Calculus Sites
Who We Are
I have a passion to see students really understand math, science and engineering. I know how wonderful it feels when it happens.
Before you learn from this site, you need to know who is teaching you, their background, experience and motivation. Read about me on the About page.
The Coursera online course Learning How to Learn: Powerful mental tools to help you master tough subjects is a free, on-demand course that starts right way. We have personally been through this course and highly recommend it. You can find more information about the free course in section 1 of the 17calculus learning and study techniques page.
Are you willing to do whatever it takes to learn better? If so, watch this video by the author of Deep Work: Rules for Focused Success in a Distracted World. Keep your mind open and be honest with yourself.
Whoever is responsible for this website is absolutely brilliant. I don’t even have words to tell you how fantastic your website is and how much it has helped me. The person(s) who did this website is a perfectionist, because it is extremely thoughtful and, well, perfect. It challenges you so that you truly understand the material, it is thorough, and it leaves no questions unanswered.
Can I donate a little something? Sure, I am a poor student right now, but I feel a DUTY to give something for the immense gratitude I have for people who can put together an educational tool like this and so generously offer it for nothing. I am a much older student trying to get a master’s in statistics, so I can appreciate this website much more than the younger folks who take a lot of this type of online material for granted. I should not even compare it to other online math help sites. It truly is in a class of its own, and you should be very proud of this site.
Thank you, thank you, thank you!!!!
Just a quick thank you. I did indeed ace calc2 last semester, thanks in no small part to your website. I took the class online, and it was very much a "you’re on your own, good luck" type of affair. Your website was absolutely invaluable to me, and I recommend it to everyone I encounter who is struggling with calculus. Thanks again!