The Top 10 Calculus Websites

As a new semester begins it is important to start collecting the Calculus resources you will need. In this blog post I want to give you the top 10 Calculus websites. They are not ranked in any particular order. Instead I have categorized them by videos, calculators, textbooks and solutions. This categorization is more art than science as many of these sites have content in more than one category. And what criteria did I judge these sites on? Free, big, useful, and authoritative. Let's get started.

Videos

1) MIT OpenCourseWare

MIT OpenCourseWare is a great site with videos and PDFs on a wide range of subjects. The Mathematics Department has several courses on Calculus. As a first time Calculus student you will be looking for the courses entitled Single Variable Calculus. There are three of them for 2005, 2006, and 2010. The format of each course is dictated by each course's professor so no strict organization is enforced on the site. A good starting point is the 2010 Single Variable Calculus course. It is broken into sessions with each session containing several videos, a PDF of the lecture notes, and at the bottom of the page you will find PDFs of homework problems and their solutions.

2) Khan Academy

Salman Khan began making math videos for his cousin in 2004. He posted them on YouTube and they have become a mainstay for anyone looking for math videos. When you log into the site for the first time you can browse and navigate to a subject via the "Subjects" drop-down at the top left corner next to the Khan Academy logo. If you go to math section you will not find a specific entry for Calculus. Instead you will find Calculus broken down by Differential Calculus, Integral Calculus, Multivariable Calculus, and Differential Equations. As a first time Calculus student you will only want to look at the Differential Calculus and Integral Calculus sections. When you first go to the section on Differential Calculus it may start you off with solving a problem. This is probably not what you want if you are looking for videos. Click on the "View full list of Differential calculus content" at the top right of the page to begin navigating to the videos. Here are the direct links for the Differential Calculus and Integral Calculus videos. Finally, if you are not familiar with Khan Academy, then there is a good overview video here by Salman Khan himself.

3) The Worldwide Center of Mathematics

The Worldwide Center of Mathematics is a for-profit site dedicated to Calculus education and research. The site's videos are free so you can check them out here. The lectures are well designed and the writing done on the blackboard is clearly visible. Their collection also includes pre-calculus videos in case you need a refresher.

Calculators

4) Wofram|Alpha

Wolfram Research was started by Stephan Wolfram in 1987 and they are best known for Mathematica which specializes in solving math problems symbolically. They provide the power of Mathematica for free via the Wolfram|Alpha website. You can type things like "derivative of x^4+exp(x)" into the text box and it will provide the result, a graph, and other information that may (or may not) be helpful to you. You can also type more general questions like "what is calculus" and be directed to Wolfram MathWorld which is their online mathematics documenation. You can get step-by-step solutions in their "Pro" version which can cost around $3.75 per month with an annual billing.

5) SageMathCloud

Sage is a FREE software package that combines a lot of other FREE software packages together to solve math problems quickly and easily. Think of it as equivalent to Wolfram Research's Mathematica but for free. More importantly, you don't have to worry about installing it! Sage is available online through SageMathCloud which is supported by the University of Washington, the National Science Foundation and Google. This means you have the smartest people on the planet supporting a platform that you can use for FREE 24/7 to solve almost any math problem. This alone should convince you to check it out. Sage has a steeper learning curve than Wolfram|Alpha, but we have a five part blog series here that will get you logged in and solving Calculus problems very quickly.

Textbooks

6) AIM Open Textbook Initiative

Open textbooks are books that are written for the purpose of being freely distributed. Many universities and other organizations promote open textbooks so look to see if your university has a website promoting them. If not then you can head over to the American Institute of Mathematics Open Textbook Initiative to get their listing of books that they have "approved" as being open textbooks. They have both beginning and advanced texts on Calculus as well as Precalculus textbooks. I recommend downloading them for easy reference throughout the semester.

7) Paul's Online Class Notes

Paul Dawkins is a Lamar University professor who has published his class notes online. Sadly, the site looks like it was created in the '90s and has never been updated. Fortunately, the class notes do a great job of explaining things and working out problems in detail. Make sure you grab his 704 page PDF "E-Book Practice Problems Solutions" located on the right side drop-down here.

8) Wikipedia

Wikipedia is another well known site so little introduction is needed. If you are interested in seeing a lot of different Calculus topics without purchasing a ton of books then this is the place to go for both beginner and advanced topics. If you are a first time Calculus student, then you may want to go to some of the other sites on this page before you head down to Wikipedia. There is a lot here, but the presentation is more of a brain dump than a structured approach to teaching Calculus.

Solutions

9) Google Search

Got a problem to solve? That's right, Google it! The real advantage of using Google as a problem solver is that it will look for answers across multiple sites (Khan Academy, Stack Exchange, Yahoo! Answers, etc.) and across multiple media types (video, blog, PDF, image, etc.) Just make sure that you try different versions of your problem. For example, if you need a solution to a problem with the exponential function in it, then try both "e^x" and "exp(x)" in your Google search.

10) Stack Exchange

Stack Exchange is a network of question and answer communities organized around very specific subjects. For Calculus you want the Mathematics community. Stack Exchange is simple in that it can be used by anyone to answer any question. However, this site can delve into very complex questions and equally complex answers. Don't be surprised to see posts that look like Egyptian hieroglyphs mixed with Star Trek terminology. If you have a hard problem to solve, then this is a good place to post to after you have exhausted your other resources. Just be sure to tag your problem "calculus" so those wanting to answer Calculus problems will know you posted a question for them.