\( \newcommand{\abs}[1]{\left| \, {#1} \, \right| } \) \( \newcommand{\cm}{\mathrm{cm} } \) \( \newcommand{\sec}{ \, \mathrm{sec} \, } \) \( \newcommand{\units}[1]{\,\text{#1}} \) \( \newcommand{\vhat}[1]{\,\hat{#1}} \) \( \newcommand{\vhati}{\,\hat{i}} \) \( \newcommand{\vhatj}{\,\hat{j}} \) \( \newcommand{\vhatk}{\,\hat{k}} \) \( \newcommand{\vect}[1]{\boldsymbol{\vec{#1}}} \) \( \newcommand{\norm}[1]{\|{#1}\|} \) \( \newcommand{\arccot}{ \, \mathrm{arccot} \, } \) \( \newcommand{\arcsec}{ \, \mathrm{arcsec} \, } \) \( \newcommand{\arccsc}{ \, \mathrm{arccsc} \, } \) \( \newcommand{\sech}{ \, \mathrm{sech} \, } \) \( \newcommand{\csch}{ \, \mathrm{csch} \, } \) \( \newcommand{\arcsinh}{ \, \mathrm{arcsinh} \, } \) \( \newcommand{\arccosh}{ \, \mathrm{arccosh} \, } \) \( \newcommand{\arctanh}{ \, \mathrm{arctanh} \, } \) \( \newcommand{\arccoth}{ \, \mathrm{arccoth} \, } \) \( \newcommand{\arcsech}{ \, \mathrm{arcsech} \, } \) \( \newcommand{\arccsch}{ \, \mathrm{arccsch} \, } \)

17Calculus - How To Save On and Use College Books

SV Calculus

MV Calculus

Differential Equations

Advanced Calculus

Interesting Calculus Uses






Calculus 1 Practice

Calculus 2 Practice

Practice Exams

Calculus Tools

Learning Tools


Here are some great ideas for how to save money on college textbooks and supplementary books. Before you dismiss any of these ideas, keep reading. We include three ideas on how to save money and still keep all the material handy for future classes by renting, buying online or purchasing ebooks and sharing in a study group. Then we give you suggestions on how to buy and use supplementary books. But first, let's address a question that you may have about what type of book, in general, you should buy, a paper book or an ebook.

Paper or Ebook?

There are several important factors that will affect your decision.
1. What does your instructor require? As an instructor, I have always allowed textbooks to be used during exams but, with classes that have students who want to buy an electronic version of the textbook, I have had to move to allowing a formula sheet instead. Before buying a book, paper or ebook, try to find out what your instructor requires.

2. Is your book even available in ebook form?

3. Which do you prefer? If there are no outside factors that require your textbook to be in a certain format, then you get to decide. Do you need to carry your book with you to class, library or study area? If so, think about how heavy the book is. Do you like to write in the margins?

4. Something To Think About - - Science shows that reading paper books helps with comprehension and is good for your brain. [source: Science Has Great News for People Who Read Actual Books].

All things equal, paper books are better for learning than ebooks.

Save Money By Renting Your Textbooks

By renting your textbooks instead of purchasing them, you can save a LOT of money. But what if you need the material in the book for later classes but you don't want to copy everything into your notes? Here is the key: buy a previous edition of the book also. Sometimes, you can get the previous edition for as little as $10. Then, while you have the rented book, go through the previous edition at the same time and take notes on any differences. Usually, there will be very few changes, maybe chapter numbering or order, minor corrections and some different exercises. But the point is, you will have all the subject material that you need without the expense. Let's look at an example.

Example - - Calculus: Early Transcendental Functions
As of January 2016, the current edition is the 6th edition. It retails for about $310.95, which is probably what you would pay at your campus bookstore. On Amazon, you can rent this textbook for about $38.57 per semester. Since this textbook covers 3 courses/semesters, you would need to rent this for 3 semesters for a total rental cost of $115.71.
In addition, buying a previous version would be about $10.43 (for the 5th edition) or $2.16 (for the 4th edition). I would probably go with the 5th edition since it is still very cheap and it is only one edition removed from the current edition. Therefore the differences are probably fewer between editions compared to the 4th/6th editions. However, for this textbook (since we have used it in our classrooms for several years), the 4th edition is also a good choice. So, let's compare the two options, side-by-side.




$115.71 + $10.43 = $126.14

Savings: $184.81 (over 3 semesters)

The savings are substantial and I hope you see that this option is worth looking into.

Save Money By Buying Online or eBooks

Buying your textbooks online is a great way to save money over buying them from your campus bookstore. I, personally, purchased about $400 worth of books one semester in graduate school for about $75. So I know this works. The thing you have to keep in mind is to decide on your classes and buy early. One of those textbooks that I bought came from China but it was so cheap and I knew for sure that I was going to take the class that I purchased it about 3 weeks before classes started. However, not all shipping takes that long. So even if the semester has already started, you can still order them online.

Another idea is that, if you don't need a paper copy of the book, you can sometimes get an electronic copy, like for a Kindle, for much less. Check with your instructor first to see if that is okay with them.

Buying used will also save you a lot.

Here is another idea. Try to buy only the chapters you need. In addition to these links, check the website of your textbook publisher to see if they offer the purchase of individual chapters.

Save Money By Sharing In A Study Group

Okay, so the ideas so far seem pretty obvious. You may have already thought of those. But here is one that you may not have thought of. Form a study group and buy one copy of the textbook, the current edition required by the instructor. Then, share the book by deciding on a length of time for each person in the group to use the book, so that each person gets the book for at least one day a week. Then, each person individually purchase a previous edition of the same book. You can sometimes get a previous edition for as little as $10.

Then, while you have the current edition, go through and compare the pages for that week with your previous edition and note any changes either in the previous edition itself or in your notes.

Things To Remember - - Make sure to get the current edition to the next person after you like you agreed to, so they can use it. Think about what it would feel like if the person before you didn't get the book to you in time and how that would set you back. Make sure to select people for your study group that you know and can trust to keep their word and won't lose the book you are sharing. Check with your instructor to make sure this is okay. I have known instructors that require you to bring your textbook to use in exams and having a previous edition may not work.

Here are the best places I've found to get previous editions of books.

The bottom line is that you are not tied in to buy your book at the school bookstore. Other options include buying a used book from a friend who took the class a previous semester. Find out what the bookstore is buying books for and offer your friend a little more. Both of you will save money this way. Be creative.

Buying and Using Supplementary Books

Looking for math books to help with precalculus, calculus or differential equations?

When looking for supplemental books, here are a few things to consider.
1. Do not purchase any book that has the word dummy or idiot or a similar derogatory word in the title. You are none of those and reading a book with that kind of title is not what you want to be telling yourself. Little by little, whether you mean to or not, you will start believing that you are those things and that will make learning math even more difficult.

2. Look for books with lots of worked out practice problems, not with just answers.

3. Before buying a book, take a few minutes and look through the pages. Make sure the notation is similar to what you have in your current textbook. Unfortunately, there are usually several ways to write math and you need a reference book that is similar so that you don't have to learn two types of notation. Not always, but sometimes, other countries will use different notation. So watch out for that.

4. When using a reference book, make sure you follow the notation in your textbook and what your instructor uses, not what is in the supplemental books, if it is different. This is because anyone can write a supplemental textbook but there are reasons that schools choose textbooks and teachers expect higher standards. The supplemental book may not even use correct notation which could trip you up and cause you to lose points if you follow their example.

Before buying any math books, check out this article on how to read math books
(yes, there are specific techniques that help you read and learn from math books).

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

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


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

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


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

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


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

To bookmark this page and practice problems, log in to your account or set up a free account.

Search Practice Problems

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.

learning and study 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.

Under Armour Clothing - Just Launched at eBags.com!

Shop Amazon - Textbook Trade-In - Get Up to 80% Back

As an Amazon Associate I earn from qualifying purchases.

How to Develop a Brilliant Memory Week by Week: 50 Proven Ways to Enhance Your Memory Skills

Under Armour Clothing - Just Launched at eBags.com!

Shop Amazon - Used Textbooks - Save up to 90%

As an Amazon Associate I earn from qualifying purchases.

Do NOT follow this link or you will be banned from the site!

When using the material on this site, 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 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 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 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.

We use cookies on this site to enhance your learning experience.


Copyright © 2010-2020 17Calculus, All Rights Reserved     [Privacy Policy]     [Support]     [About]

Real Time Web Analytics
We use cookies to ensure that we give you the best experience on our website. By using this site, you agree to our Website Privacy Policy.
Real Time Web Analytics
We use cookies to ensure that we give you the best experience on our website. By using this site, you agree to our Website Privacy Policy.