17Calculus - Books, Tools and Resources

SV Calculus

MV Calculus

Differential Equations

Advanced Calculus

Interesting Calculus Uses






Calculus 1 Practice

Calculus 2 Practice

Practice Exams


Calculus Tools

Additional Tools


SV Calculus

MV Calculus


Calculus 1 Practice

Calculus 2 Practice

Practice Exams


Calculus Tools

Additional Tools


This page discusses some specific tools and resources that we have found helpful and that we have used in our classes. For a complete list of books and resources, see the 17calculus bookstore page.

College Student Resources


Evernote - - For storing notes and organizing, one tool I've seen is EverNote. You can do a lot with the free version. Here are some ways you can use EverNote for school.
10 Evernote Tips For School – Education Series
How my students started using Evernote – Education Series

Other Resources
10 Mac Tools That Every Student Should Make Use Of

Online Tools

iHomework Keeps Track of School Assignments and Due-Dates
Remember The Milk is a great free task list manager.


Flashcards are a great way to learn new material, not only for math but also foreign language, history, geography, biology . . . almost anything you learn in school. Here are some suggestions.

The absolute best flashcards are the manual 3x5 cards that you buy at the bookstore and write yourself. I know it's a little old school but the actual writing on the cards gives you a learning boost that you cannot get anywhere else. That said, it's not always the most practical solution. So here are some other suggestions.

When I can't carry my 3x5 cards, I use Quizlet to set up my flashcards. Quizlet is free.
I have tried several different iPhone apps to go through my flashcards, include these.
- Flashcards++
- Quizlet Apps
Here are some other suggestions that might help you.
Smartr: Making Studying (Ever So Slightly) Fun


Here are some iPad related links.
10 Best iPad Apps for College Students
7 Ways To Use The iPad To Help Students Excel At School

Taking Notes

We have a 17calculus page dedicated to taking effective notes. Here are some links to apps that might also help you.
Most Popular Note Taking Application: Evernote
Five Best Note Taking Applications
The Top 12 Note Taking Apps for Getting Things Done in School

Study Techniques

We have a study techniques page with ideas to help you ace your courses. Here are some additional links.
How to Get Back Into Work or Study Mode After a Long Break


Here are some links to help you with your college expenses.
Why You (Probably) Shouldn't Take out Loans for College
5 Scholarship Search Sites To Help Students Get Financial Aid
How to Better Manage Your Student Loans and Graduate with Less Debt

Various Other Articles

Here are a few links to articles that will help you be a better college student.

4 Things That Totally Suck About Using Technology In School [Opinion]
Sometimes technology can actually make your school and learning experience MORE difficult, not easier.
Get a GPA Boost Just By Picking The Right Roommate
Did you know that your friends and roommates can help (or hurt) your education and learning?

You CAN Ace Calculus

Trig Formulas

The Unit Circle

The Unit Circle [wikipedia]

Basic Trig Identities

Set 1 - basic identities

\(\displaystyle{ \tan(t) = \frac{\sin(t)}{\cos(t)} }\)

\(\displaystyle{ \cot(t) = \frac{\cos(t)}{\sin(t)} }\)

\(\displaystyle{ \sec(t) = \frac{1}{\cos(t)} }\)

\(\displaystyle{ \csc(t) = \frac{1}{\sin(t)} }\)

Set 2 - squared identities

\( \sin^2t + \cos^2t = 1\)

\( 1 + \tan^2t = \sec^2t\)

\( 1 + \cot^2t = \csc^2t\)

Set 3 - double-angle formulas

\( \sin(2t) = 2\sin(t)\cos(t)\)

\(\displaystyle{ \cos(2t) = \cos^2(t) - \sin^2(t) }\)

Set 4 - half-angle formulas

\(\displaystyle{ \sin^2(t) = \frac{1-\cos(2t)}{2} }\)

\(\displaystyle{ \cos^2(t) = \frac{1+\cos(2t)}{2} }\)

Trig Derivatives

\(\displaystyle{ \frac{d[\sin(t)]}{dt} = \cos(t) }\)


\(\displaystyle{ \frac{d[\cos(t)]}{dt} = -\sin(t) }\)

\(\displaystyle{ \frac{d[\tan(t)]}{dt} = \sec^2(t) }\)


\(\displaystyle{ \frac{d[\cot(t)]}{dt} = -\csc^2(t) }\)

\(\displaystyle{ \frac{d[\sec(t)]}{dt} = \sec(t)\tan(t) }\)


\(\displaystyle{ \frac{d[\csc(t)]}{dt} = -\csc(t)\cot(t) }\)

Inverse Trig Derivatives

\(\displaystyle{ \frac{d[\arcsin(t)]}{dt} = \frac{1}{\sqrt{1-t^2}} }\)


\(\displaystyle{ \frac{d[\arccos(t)]}{dt} = -\frac{1}{\sqrt{1-t^2}} }\)

\(\displaystyle{ \frac{d[\arctan(t)]}{dt} = \frac{1}{1+t^2} }\)


\(\displaystyle{ \frac{d[\arccot(t)]}{dt} = -\frac{1}{1+t^2} }\)

\(\displaystyle{ \frac{d[\arcsec(t)]}{dt} = \frac{1}{\abs{t}\sqrt{t^2 -1}} }\)


\(\displaystyle{ \frac{d[\arccsc(t)]}{dt} = -\frac{1}{\abs{t}\sqrt{t^2 -1}} }\)

Trig Integrals

\(\int{\sin(x)~dx} = -\cos(x)+C\)


\(\int{\cos(x)~dx} = \sin(x)+C\)

\(\int{\tan(x)~dx} = -\ln\abs{\cos(x)}+C\)


\(\int{\cot(x)~dx} = \ln\abs{\sin(x)}+C\)

\(\int{\sec(x)~dx} = \) \( \ln\abs{\sec(x)+\tan(x)}+C\)


\(\int{\csc(x)~dx} = \) \( -\ln\abs{\csc(x)+\cot(x)}+C\)

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Topics Listed Alphabetically

Single Variable Calculus

Multi-Variable Calculus

Differential Equations





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math and science learning techniques

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.

College Student Resources

Math Links

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The Humongous Book of Calculus Problems

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