17Calculus and 17Precalculus Apps Support
Recommended Books on Amazon (affiliate links)  

Join Amazon Student  FREE TwoDay Shipping for College Students 
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.
17Calculus and 17Precalculus Apps 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.
You can also access the same (and more) information outside the app on 17calculus.com.
2. What do I get in the inapp purchases?
InApp 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 Problems^{1,2} 

basic conceptual understanding of the derivative 

notation 

limit definition of the derivative  13 
constant and constant multiple rules  
addition and subtraction rules  
power rule  17 
product rule  18 
quotient rule  17 
chain rule  29 
trig and inverse trig derivatives  25 
implicit differentiation  42 
exponentials  10 
logarithms  17 
logarithmic differentiation  21 
inverse functions  6 
hyperbolic and inverse hyperbolic functions  26 
higher order derivatives 

Graphing  
slope, tangent and normal lines and linearization  22 
graphing  5 
increasing and decreasing intervals and critical points  9 
first derivative test  7 
concavity and inflection points  5 
second derivative test  3 
Applications  
related rates (4 pages)  44 
linear motion  8 
mean value theorem  10 
optimization  29 
differentials 

newton's method^{3} 

Totals (as of 2019.October)  
more than 35 pages  more than 350 practice problems 
Notes
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 indepth but we may provide you some videos and how to get started.
The integrals module is quite extensive and covers indepth some of the more difficult topics like integration by parts and partial fractions.
Topic Description  Practice Problems^{1,2} 

notation and basic formulas  14 
sigma notation  8 
definite integrals 

both fundamental theorems  5 
integration by substitution  31 
definite integration substitution  3 
integration by parts  26 
partial fractions  24 
improper integrals  41 
Trig Integrals  
trig integration  22 
sine/cosine integration  27 
sine/cosine reduction  7 
secant/tangent integration  10 
secant/tangent reduction  5 
trig substitution  27 
Integrals Practice^{3}  
calculus 1 integrals practice  11 
calculus 2 integrals practice  10 
Area and Volume  
area under a curve  9 
area betwen curves  28 
surface area  7 
volume with known crosssection  9 
describing plane regions^{4} and volumes of rotation 

washer/disc method  27 
cylinder/shell method  28 
volume practice  8 
Applications  
linear motion  4 
arc length  17 
work  4 
Hooke's law  8 
work changing weight  12 
work moving fluid  16 
moments, center of mass 

Totals (as of 2019.October)  
more than 35 pages  more than 425 practice problems 
Notes
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, sidebyside so that you can determine the best technique to use in your work.
Topic Description  Practice Problems^{1,2} 

notation 

sequences  16 
divergence test  7 
pseries  3 
geometric series  18 
alternating series  27 
telescoping series  12 
ratio test  23 
limit comparison test  24 
direct comparison test  22 
integral test  16 
root test  10 
convergence value 

infinite series summary list 

choosing a test 

Applications  
absolute/conditional convergence  2 
power series  41 
taylor/maclaurin series  21 
radius/interval of convergence  25 
remainder and error bounds  8 
fourier series  3 
Tools  
study techniques 

practice problems^{3}  5 
exam preparation 

2 full practice exams^{4}  22 
Totals (as of 2019.October)  
more than 25 pages  more than 300 practice and exam problems 
Notes
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 multivariable 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 
curvature 
vector functions exam 

Partial Derivatives with more than 55 practice problems 
partial derivatives 
chain rule 
first derivative test 
second order partial derivatives 
gradient 
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 nonrectangular 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 
curl 
divergence 
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 
Note
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. 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 nonETF. 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 nonEFT 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 multivariable 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 nonETF 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.
You CAN Ace Calculus
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  doubleangle formulas  

\( \sin(2t) = 2\sin(t)\cos(t)\) 
\(\displaystyle{ \cos(2t) = \cos^2(t)  \sin^2(t) }\) 
Set 4  halfangle 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
\(\displaystyle{ \frac{d[\arcsin(t)]}{dt} = \frac{1}{\sqrt{1t^2}} }\) 
\(\displaystyle{ \frac{d[\arccos(t)]}{dt} = \frac{1}{\sqrt{1t^2}} }\)  
\(\displaystyle{ \frac{d[\arctan(t)]}{dt} = \frac{1}{1+t^2} }\) 
\(\displaystyle{ \frac{d[\arccot(t)]}{dt} = \frac{1}{1+t^2} }\)  
\(\displaystyle{ \frac{d[\arcsec(t)]}{dt} = \frac{1}{\abs{t}\sqrt{t^2 1}} }\) 
\(\displaystyle{ \frac{d[\arccsc(t)]}{dt} = \frac{1}{\abs{t}\sqrt{t^2 1}} }\) 
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, log in to your account or set up a free account.
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. 