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

17Calculus - What This Site Is About

SV Calculus

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Differential Equations

Advanced Calculus

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Practice Exams

Calculus Tools

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This site is intended to supplement your calculus learning by explaining concepts, giving examples and providing practice problems to help you better understand calculus concepts. Calculus is not easy. But you CAN ace calculus with the right tools and persistence.

There are two main types of calculus taught at the college level based on a student's major or emphasis. Business calculus is usually geared toward business, life sciences and other majors that do not use calculus a lot but need some exposure to the subject. Math and engineering calculus is for students in mathematics, engineering, physics, chemistry and other majors where calculus is a critical part of their subject. This site is geared toward students in this category who need to know, understand and use calculus. Business calculus students can get a lot out of this site too but we emphasize understanding concepts and how the math works at a deep level, not just how to use the equations.


There are a lot and I mean a LOT of calculus videos out there, both on individual sites and on YouTube. However, many of them show bad or downright incorrect techniques. Some teach you how to work problems by getting around what you need to learn rather than helping you understand and learn the concepts correctly. We have chosen the best videos to post on this site that follow these standards:
1. show good accurate techniques
2. use mostly correct notation
3. help you understand and use calculus (the most important criterion)
4. the presenter must speak clearly without a heavy accent
5. the presenter writes out his work rather than using all prepared slides (like PowerPoint)
Of course, there are exceptions to these rules (except for #3) but they are rare.

We want to make it clear that we don't necessarily agree with everything in all the videos on this site. But for now the ones we've chosen are the best we've seen.

Featured Instructors

Here at 17calculus.com, we have combed through lots of videos on youtube and found the best instructors who use the best notation, are easy to listen to and who communicate calculus clearly and correctly. These are the ones that we think will help you the most. [At this time, we do not record our own videos, since we don't think we could do any better than these instructors.]
Note - - These rankings and comments are our opinions only. It is okay to disagree with us as long as you learn calculus.

1. Dr. Chris Tisdell

Dr Chris Tisdell [ link to website ]

Rank 1 - Always watch these videos on every topic

Notation: Excellent

Accuracy: Excellent

Theory: Some but only enough to make the topic clear without distracting from how to use the information

Examples: Very good, ranging from moderate to challenging with a few easy ones here and there

Level: All levels including upper level topics like differential equations

This guy is fun to listen to and I wish I had taken calculus and differential equations from him. He has a good sense of humor and a neat accent but it is still very easy to understand him. He is an instructor at a school in Australia. He communicates very well and his theory supports his calculus without being too heavy. He communicates well and is an excellent teacher. He has some materials on his website, as well as links to his materials on other sites that you can download and use as you watch his videos.

2. Black Pen Red Pen

Black Pen Red Pen [ link to his youtube channel ]

Rank 2 - Watch these videos on every topic, if you have time

Notation: Very Good

Accuracy: Very Good

Theory: Some

Examples: Very good, all types from easy to extremely difficult

Level: All calculus levels

We really like this guy. His English is very good and he is easy to understand. He is fun to watch and his examples are very good. We especially like his videos where he spends hours doing problems. Watch for more of his videos showing up on our pages.

2. Professor Leonard

Professor Leonard [ link to his youtube channel ]

Rank 2 - Watch these videos on every topic, if you have time

Notation: Very Good

Accuracy: Very Good

Theory: Some

Examples: Very good, ranging from easy to moderate

Level: All calculus levels

We were recently alerted to this guy on youtube and we think his videos will help you. His videos are full-length class videos from his teaching at Merced College. He explains concepts well and it seems like you are in his class when you watch his videos. He seems to be a fun teacher and makes it easy to watch his videos.

3. PatrickJMT

PatrickJMT [ link to website ]

Rank 3 - Watch as many of these as you have time for

Notation: Very Good

Accuracy: Very Good

Theory: Little to none; mostly before working practice problems

Examples: Very good ranging from easy to moderate

Level: Most single variable and multi-variable calculus topics with some differential equations

This guy is very good at explaining topics and he is thorough and meticulous. He doesn't give as much theory as Dr Tisdell but he shows good examples and is easy to listen to. He teaches (or has taught) at several schools, so he has experience in the classroom which is important in anticipating problems you might have with certain techniques. He has some neat ways of looking at problems and has lots of suggestions on how to work problems. He has some materials to download on various sites that you can use.

4. Krista King Math

Krista King Math [ link to website ]

Rank 4 - Watch these if you need more examples

Notation: Fair

Accuracy: Good

Theory: Little to none; mostly within the context of practice problems

Examples: Good, mostly easy ones with a few moderate ones

Level: Mostly single variable with some multi-variable calculus and differential equations

This gal is easy to listen to and she explains things well. She also has some good examples, mostly easy ones to get you started. She seems to have a good grasp on what problems students have with certain topics. We think she has most of her experience from being a student and tutoring, which is good, since she knows what you are going through right now. In general, she is very good and we highly recommend that you watch her videos. She has some tables and materials on her website that you can use.

Honorable Mentions

You will find videos from other instructors as well. However, we usually include them only if they will help you understand something better or if they give a different perspective other than is given by the instructors listed above.

MIT - - One of other favorite video sources is MIT OpenCourseWare. They are great videos and you will find some pages with those videos. They are longer videos with LOTS of theory. They are very good but it is better to get most of your learning from your classes and your textbook. We have included them so that you have a way to learn more theory. Watch them when you have time.

MIP4U - - This stands for Math Is Power For You. We kind of like that name. He has some good videos that we include if we don't have enough from our featured instructors. He has some good examples and he explains things well and has some good insight. So we have included some of his videos to supplement discussion and practice problems.

Organic Chemistry Tutor - - This guy has some great videos and examples. We have incorporated a lot of his examples in precalculus and may be adding some to calculus and differential equations as well.

Additional Comments
Make sure you watch all videos with a critical eye. As with any instructor, there are errors and notation mistakes. We try to include comments with the videos when we catch a mistake but we do not mention all of them. You need to be able to see when they make mistakes. Do this in class too. Your instructor is not perfect, no one is. If you can pick up mistakes, that is an indication that you are starting to understand calculus.

Other Videos
We pick out some videos from other instructors here and there but most other videos are not very good. They show you how to get around learning calculus, have poor notation or bad suggestions, the presenter has a heavy accent and, therefore, is difficult to understand or they work the problems incorrectly. (No one is perfect, so you need to watch all videos, including ones we recommend, for mistakes.)

Who We Are

We are just me, right now. I taught math, including all three calculus courses, for over 15 years at several schools in the US. 17Calculus started around 2010 as a way to help my students. I stopped teaching to move to Europe and have focused on building this site ever since.
After returning to the US, I built iOS and Android apps with the material hoping that I could at sustain enough income to cover my costs, and maybe a little more. However, I found that the apps stifled my attempts at helping you with calculus and it cost more to build and maintain them than I wanted to spend. Besides, I consider myself a mathematician first and software developer second and I was spending way too much time maintaining the structure of the apps without the time to give you more great content. After more than a year and half of frustration, I removed them from the stores. At this time, I believe a free website is a better way to help you with calculus.
My goal is to keep everything on this site free for as long as I can. I think students already spend a lot of money for an education, so this is my way of helping.
Not only do I love math, I have a passion for engineering and science. I have degrees in math, computer science and engineering, including a masters degree in engineering. I started my PhD in math at Iowa State University but got distracted by teaching. I have a passion to see students really understand math, science and engineering because I know how wonderful it feels when it happens. I also want to ignite a passion for learning that never goes out.
I hope you enjoy my site and find it helpful. Contact me and let me know how it has helped you or where it can be improved/corrected.

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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effective study techniques

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How to Ace the Rest of Calculus: The Streetwise Guide, Including MultiVariable Calculus

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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 what kind of person you are in public. Choose now to be a person of integrity and discipline.

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.

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