17calculus
Limits Derivatives Integrals Infinite Series Parametrics Polar Coordinates Conics
Limits
Epsilon-Delta Definition
Finite Limits
One-Sided Limits
Infinite Limits
Trig Limits
Pinching Theorem
Indeterminate Forms
L'Hopitals Rule
Limits That Do Not Exist
Continuity & Discontinuities
Intermediate Value Theorem
Derivatives
Power Rule
Product Rule
Quotient Rule
Chain Rule
Trig and Inverse Trig
Implicit Differentiation
Exponentials & Logarithms
Logarithmic Differentiation
Hyperbolic Functions
Higher Order Derivatives
Differentials
Slope, Tangent, Normal...
Linear Motion
Mean Value Theorem
Graphing
1st Deriv, Critical Points
2nd Deriv, Inflection Points
Related Rates Basics
Related Rates Areas
Related Rates Distances
Related Rates Volumes
Optimization
Integrals
Definite Integrals
Integration by Substitution
Integration By Parts
Partial Fractions
Improper Integrals
Basic Trig Integration
Sine/Cosine Integration
Secant/Tangent Integration
Trig Integration Practice
Trig Substitution
Linear Motion
Area Under/Between Curves
Volume of Revolution
Arc Length
Surface Area
Work
Moments, Center of Mass
Exponential Growth/Decay
Laplace Transforms
Describing Plane Regions
Infinite Series
Divergence (nth-Term) Test
p-Series
Geometric Series
Alternating Series
Telescoping Series
Ratio Test
Limit Comparison Test
Direct Comparison Test
Integral Test
Root Test
Absolute Convergence
Conditional Convergence
Power Series
Taylor/Maclaurin Series
Radius of Convergence
Interval of Convergence
Remainder & Error Bounds
Fourier Series
Study Techniques
Choosing A Test
Sequences
Infinite Series Table
Practice Problems
Exam Preparation
Exam List
Parametrics
Parametric Curves
Parametric Surfaces
Slope & Tangent Lines
Area
Arc Length
Surface Area
Volume
Polar Coordinates
Converting
Slope & Tangent Lines
Area
Arc Length
Surface Area
Conics
Parabolas
Ellipses
Hyperbolas
Conics in Polar Form
Vectors Vector Functions Partial Derivatives/Integrals Vector Fields Laplace Transforms Tools
Vectors
Unit Vectors
Dot Product
Cross Product
Lines In 3-Space
Planes In 3-Space
Lines & Planes Applications
Angle Between Vectors
Direction Cosines/Angles
Vector Projections
Work
Triple Scalar Product
Triple Vector Product
Vector Functions
Projectile Motion
Unit Tangent Vector
Principal Unit Normal Vector
Acceleration Vector
Arc Length
Arc Length Parameter
Curvature
Vector Functions Equations
MVC Practice Exam A1
Partial Derivatives
Gradients
Directional Derivatives
Lagrange Multipliers
Tangent Plane
MVC Practice Exam A2
Partial Integrals
Describing Plane Regions
Double Integrals-Rectangular
Double Integrals-Applications
Double Integrals-Polar
Triple Integrals-Rectangular
Triple Integrals-Cylindrical
Triple Integrals-Spherical
MVC Practice Exam A3
Vector Fields
Curl
Divergence
Conservative Vector Fields
Potential Functions
Parametric Curves
Line Integrals
Green's Theorem
Parametric Surfaces
Surface Integrals
Stokes' Theorem
Divergence Theorem
MVC Practice Exam A4
Laplace Transforms
Unit Step Function
Unit Impulse Function
Square Wave
Shifting Theorems
Solve Initial Value Problems
Prepare For Calculus 1
Ready For Calculus 2?
Trig Formulas
Describing Plane Regions
Parametric Curves
Linear Algebra Review
Word Problems
Mathematical Logic
Calculus Notation
Simplifying
Practice Exams
17calculus on YouTube
More Math Help
Tutoring
Tools and Resources
Academic Integrity
Learning/Study Techniques
Math/Science Learning
Memorize To Learn
Music and Learning
Note-Taking
Motivation
Instructor or Coach?
Books
Math Books
How To Read Math Books

Academic Integrity

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

17Calculus - What This Site Is About

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.

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.

Videos
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. Here are the instructors in the videos that we especially recommend, called our featured instructors.

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. There are three that we think will help you the most. [ We do not record many of 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.

Dr Chris Tisdell

PatrickJMT

Krista King Math

Dr Chris Tisdell Website

PatrickJMT Website

Krista King Math Website

Rank 1 - Always watch these videos on every topic

Rank 2 - Watch as many of these as you have time for

Rank 3 - Watch these if you need more examples

Notation: Excellent

Notation: Very Good

Notation: Fair

Accuracy: Excellent

Accuracy: Very Good

Accuracy: Good

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

Theory: Little to none; mostly before working practice problems

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

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

Examples: Very good ranging from easy to moderate

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

Level: Upper level topics including differential equations

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

Level: Mostly single variable with some multi-variable calculus and 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.

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.

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.


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.

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.

Professor Leonard - - We were recently alerted to this guy on youtube and we are currently going through some of his videos to see if there anything that we think will help you. His videos are full-length class videos from his teaching at Merced College. He seems to be a fun teacher and makes it easy to watch his videos. [ Prof. Leonard youtube link ]

Other Videos
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. )

How This Site Was Built

Although I had some programming experience before choosing to become a teacher, I had a lot of help learning to build websites. The first site that helped a lot (and that I keep going back to) is called 2 Create A Website. There are some great videos, blog entries and information to get started building a website. If you are thinking of building your own website, then I highly suggest you start there.

Once I read through 2 Create A Website, I decided to start with a system called Site Build It! from SiteSell (you can find information on SiteSell here). This system jump-started me without having to learn a lot of html, javascript and php. However, later I developed a hunger to learn more. So that's when I switched to HostGator, which gives me more freedom and flexibility than I had with SiteSell. I highly recommend both systems. If you have ever wanted to have your own website, click the banner below to get more information or to get started. [ Note: By clicking on the HostGator banner below (or the link above) and signing up, 17calculus will be compensated. This will allow you to support 17calculus at no additional cost to you. ]

How To Get The Most Out Of This Site

To get the most benefit from this site, it will help for you to have an idea of the structure and where to find what you are looking for. I have designed this site so that you decide how much information you want to see using scrolling and tabbed panels. This avoids information overload, focuses your attention and saves you time. Additionally, to get equations to show up correctly, you may need to tweak your system; details below.

Loading Equations (Slow Load?)

This site uses a system called MathJax to load fonts and display mathematical equations. If your computer is taking a long time (more than a few seconds) to correctly display math, there is something you can do to speed it up. It is very easy and quick. Basically, you just need to download a math font called STIX. Here is the page that contains the instructions and download link: MathJax STIX Font.

If you don't do this, you can still use this site and see equations (although some may be difficult to read). However, it will take longer (more than a few seconds) to display math equations and your experience here may not be completely satisfying. Downloading these fonts is quick and painless and, as the use of MathJax spreads (which I think it will), your computer will already be set up. I believe this is the future standard for displaying math on webpages. So you will be ahead of the game by doing this now.

Main Navigation

To the left is the main navigation menu. To open the menu, click the 3-bars button at the top. Then scroll down to the topic you are looking for. You can click the title to open a list of links that will take you to the page you are interested in.

Structure Of The Core Pages

The main pages containing the core calculus information are in two parts. First, the top part contains core discussion with additional topics in drop-down panels. Some pages contain several topics which may be separated into panels. To open a topic, click on the topic name anywhere in the panel tab. The panel will then drop down showing the information. To close the panel, click the panel tab again.

The bottom half of each page contains additional resources like tables, practice problems and additional links. To more easily navigate the core pages, you will find a set of buttons in the tools menu.

We hope this format helps you find your topic more quickly and efficiently. Your time is valuable and you should not have to spend a lot of time searching through pages to find the information you need.

Having Trouble Finding Your Topic?

Near the bottom of most pages, a search box exists to search 17calculus. To scroll to the search box, click the magnifying glass icon in the left column.

Search 17Calculus

Real Time Web Analytics
menu top search
17
menu top search 17