17Calculus and 17Precalculus

You CAN Ace Calculus

1. Download the free app from the App Store on your iPhone and iPad.

2. Refresh your precalculus knowledge, if needed, using the 17Precalculus app.

3. Start learning calculus: first topic is Limits.

4. Check out the tools menu for more options including study suggestions and motivation to learn calculus.

5. As you continue on in your calculus course, pay for only the sections you need. The small fee for each section allows us to continue to offer and improve 17Calculus.

17Calculus and 17Precalculus Support Questions Answered

1. I get a blank tutorial screen or practice problem screen. What do I need to do?
Make sure you have the latest version of the app and that you have a good internet connection.

2. What do I get in the inapp purchases?

In-App Purchases Topics

In order to continue to provide and improve the 17Calculus material to everyone, we are asking for a small purchase for these modules in the app. Before purchasing, you may want to know if the modules contain the information you need. Here are lists of what each topic covers.

The derivatives section is the least expensive since derivatives is the easiest topic and you will probably need the least amount of help. However, there are sections that are difficult to understand without some help and lots of diverse practice problems. Here are the topics included in the derivatives module.

Topic Description

Practice Problems1,2

basic conceptual understanding of the derivative


limit definition of the derivative


constant and constant multiple rules

addition and subtraction rules

power rule


product rule


quotient rule


chain rule


trig and inverse trig derivatives


implicit differentiation






logarithmic differentiation


inverse functions


hyperbolic and inverse hyperbolic functions


higher order derivatives


slope, tangent and normal lines and linearization




increasing and decreasing intervals and critical points


first derivative test


concavity and inflection points


second derivative test



related rates (4 pages)


linear motion


mean value theorem





newton's method3

Totals (as of 2019.October)

more than 35 pages

more than 350 practice problems

1. The number of practice problems will change frequently as we continue to add more. This is a (very close) approximation to the actual number you will find in each section.
2. Some of the pages do not show the number of practice problems. Some of the practice problems appear on other pages or the practice problems have combined techniques. For example, most practice problems use the constant and constant multiple rules and they are such simple rules that we do not have practice problems that involve only these rules. There are examples in those sections but you learn to use these rules within the context of other more involved rules. We believe this is the best way to learn these simple rules.
3. We do not cover these topics in-depth but we may provide you some videos and how to get started.

The integrals module is quite extensive and covers in-depth some of the more difficult topics like integration by parts and partial fractions.

Topic Description

Practice Problems1,2

notation and basic formulas


sigma notation


definite integrals

both fundamental theorems


integration by substitution


definite integration substitution


integration by parts


partial fractions


improper integrals


Trig Integrals

trig integration


sine/cosine integration


sine/cosine reduction


secant/tangent integration


secant/tangent reduction


trig substitution


Integrals Practice3

calculus 1 integrals practice


calculus 2 integrals practice


Area and Volume

area under a curve


area betwen curves


surface area


volume with known cross-section


describing plane regions4 and volumes of rotation

washer/disc method


cylinder/shell method


volume practice



linear motion


arc length




Hooke's law


work changing weight


work moving fluid


moments, center of mass

Totals (as of 2019.October)

more than 35 pages

more than 425 practice problems

1. The number of practice problems will change frequently as we continue to add more. This is a (very close) approximation to the actual number you will find in each section.
2. Some of the pages do not show the number of practice problems. Some of the practice problems appear on other pages or the practice problems have combined techniques. For example, there are many practice problems involving definite integrals. However, they are scattered around on various pages involving other rules.
3. These practice pages are to help you prepare for your exams. They contain practice problems in no specific order much like you will see your exam. We do not tell you which technique to use and they are perfect for honing your exam skills.
4. This topic is not usually covered separately in a calculus course. Instructors may expect you to pick this up as you go. However, we believe that a thorough coverage of this topic will help you significantly when learning how to calculate volumes of revolution.

Infinite Series is one of the most difficult topics in single variable calculus. It is strange in that it is one of the first topics you will run across that does not involve direct calculations. Also, there are usually multiple ways to solve a given problem, so it confusing to determine what technique to use. We show you what to look for when solving these problems and we show multiple ways to work them, side-by-side so that you can determine the best technique to use in your work.

Topic Description

Practice Problems1,2




divergence test




geometric series


alternating series


telescoping series


ratio test


limit comparison test


direct comparison test


integral test


root test


convergence value

infinite series summary list

choosing a test


absolute/conditional convergence


power series


taylor/maclaurin series


radius/interval of convergence


remainder and error bounds


fourier series



study techniques

practice problems3


exam preparation

2 full practice exams4


Totals (as of 2019.October)

more than 25 pages

more than 300 practice and exam problems

1. The number of practice problems will change frequently as we continue to add more. This is a (very close) approximation to the actual number you will find in each section.
2. Some of the pages do not show the number of practice problems. Some of the practice problems appear on other pages or the practice problems have combined techniques.
3. These practice problems show several ways to determine convergence/divergence. They discuss which techniques to choose and why.
4. The practice exams are actual exams given in calculus 2 courses and include complete written out solutions.

The multi-variable calculus sections cover the entire third semester of calculus. There are four sections, vector functions, partial derivatives, partial (iterated) integrals and vector fields. Here is a breakdown of the material in each section.

Vector Functions with more than 60 practice problems

basics of vector functions

smooth vector functions

limits of vector functions

derivatives of vector functions

integrals of vector functions

projectile motion

unit tangent vector

principal unit normal vector

acceleration vector

arc length

arc length function

arc length parameter


vector functions exam

Partial Derivatives with more than 55 practice problems

partial derivatives

chain rule

first derivative test

second order partial derivatives


directional derivative

gradient applications

lagrange multipliers

partial derivatives exam

Partial (Iterated) Integrals with more than 100 practice problems

basics of partial integrals

double integrals

double integrals in rectangular coordinates

double integrals over rectangular regions

double integrals over non-rectangular regions

switching order of integration

calculating area

calculating volume

polar coordinates

triple integrals

triple integrals in rectangular coordinates

cylindrical coordinates

spherical coordinates

partial integrals exam

Vector Fields with more than 100 practice problems

basics of vector fields



conservative vector fields

potential functions

path integrals

line integrals

line integrals with unit tangent vector

line integrals in differential form

fundamental theorem of line integrals

Green's Theorem

surface integrals

Stokes' Theorem

Divergence Theorem

vector fields exam

Totals (as of 2019.November)

more than 50 pages with more than 300 practice problems

The number of practice problems will change frequently as we continue to add more. These are (very close) approximations to the actual number you will find in each section.

3. Do you recommend any books or have resources that will help me learn calculus and precalculus?

This section contains lists of recommended books discussed in the app. 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.

Larson ETF 3th Edition
Larson ETF 4th Edition
Larson ETF 6th Edition

Here are the corresponding non-ETF editions.

Larson non-ETF 7th Edition
Larson non-ETF 8th Edition
Larson non-ETF 11th Edition

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.

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.

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.

In 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.

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.

Deep Work: Rules for Focused Success in a Distracted World
On Course: Strategies for Creating Success in College and in Life
Moonwalking with Einstein: The Art and Science of Remembering Everything
The Practicing Mind: Developing Focus and Discipline in Your Life - Master Any Skill or Challenge by Learning to Love the Process
A Mind for Numbers: How to Excel at Math and Science (Even If You Flunked Algebra)
Becoming a Master Student
How to Become a Straight-A Student: The Unconventional Strategies Real College Students Use to Score High While Studying Less
Study Smarter, Not Harder
What Smart Students Know: Maximum Grades. Optimum Learning. Minimum Time.
Concentration: Strategies for Attaining Focus
How to Develop a Brilliant Memory Week by Week: 50 Proven Ways to Enhance Your Memory Skills
Learn to Remember : Practical Techniques and Exercises to Improve Your Memory
College Study Skills: Becoming a Strategic Learner
How to Think Like a Mathematician: A Companion to Undergraduate Mathematics
You Can Have an Amazing Memory: Learn Life-Changing Techniques and Tips from the Memory Maestro
How to Read a Book: The Classic Guide to Intelligent Reading

The Art of Electronics
Schaum's Outline of Electric Circuits
Control Systems Engineering

Excellent, highly recommended book. This book could catapult your learning, if you apply the techniques and insights carefully and radically.
Deep work is necessary as a student to succeed but few students do it. This leaves a huge chasm of possibility for you to stand out and achieve the seemingly extraordinary feat of acing calculus. This book not only explains deep work but also how to implement it in your life.
Why You Need To Work Deeply (from chapter 1)
- Deep Work Helps You Quickly Learn Hard Things
- Deep Work Helps You Produce at an Elite Level
Order this book now [ Deep Work: Rules for Focused Success in a Distracted World ] and read it during your next semester break. It will be time well spent.

When using the material on this site and in the app, check with your instructor to see what they require. Their requirements come first, so make sure your notation and work follow their specifications.

DISCLAIMER - 17Calculus owners and contributors are not responsible for how the material, videos, practice problems, exams, links or anything on this site or in the app are used or how they affect the grades or projects of any individual or organization. We have worked, to the best of our ability, to ensure accurate and correct information on each page and solutions to practice problems and exams. However, we do not guarantee 100% accuracy. It is each individual's responsibility to verify correctness and to determine what different instructors and organizations expect. How each person chooses to use the material on this site or in the app is up to that person as well as the responsibility for how it impacts grades, projects and understanding of calculus, math or any other subject. In short, use this site and app wisely by questioning and verifying everything. If you see something that is incorrect, contact us right away so that we can correct it.

Links and banners on this page are affiliate links. We carefully choose only the affiliates that we think will help you learn. Clicking on them and making purchases help you support 17Calculus at no extra charge to you. However, only you can decide what will actually help you learn. So think carefully about what you need and purchase only what you think will help you.


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