# Calculus Center's blog

## Calculus Rhapsody - The Math Behind This Creative Video You're Guaranteed to Be Tested On

If you haven't seen it, the Calculus Rhapsody music video on Youtube is worth watching. It's creative, funny, and educational all at the same time. So what does this video teach us? Did they get anything wrong? What did they get right? Let's go through the video to see what parts of Calculus they're singing about.

First, here's the video:

## 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.

## The Calculus Chain Rule

The Chain Rule is one of those Calculus rules that you have to always have in the back of your mind when you are doing differentiation. When we have two functions there are several ways that we can combine those two functions to create another function. We can add them, subtract them, multiply them, or divide them. Another way you can combine two functions is by Function composition. Function composition is used to describe and summarize complex dependencies in nature. For example, when sea temperatures rise there are less krill.

## Finding Critical Points and Limits with Sage!

This is the fifth lesson in five where we are discussing Sage and how it can be used to make your Calculus life easier. In the first lesson you learned how to create your own account and how to create a worksheet. In the second lesson you learned how to plot functions with Sage. In the third lesson you learned how to differentiate using Sage.

## Integrating Functions with Sage!

This is the fourth lesson in five where we are discussing Sage and how it can be used to make your Calculus life easier. In the first lesson you learned how to create your own account and how to create a worksheet. In the second lesson you learned how to plot functions with Sage. In the third lesson you learned how to differentiate using Sage. In this lesson we are going to learn how to calculate integrals.

## Differentiating Functions with Sage!

This is the third lesson in five where we are discussing Sage and how it can be used to make your Calculus life easier. In the first lesson you learned how to create your own account and how to create a worksheet. In the second lesson you learned how to plot functions with Sage. In this lesson we are going to learn how to calculate derivatives.

## Plotting with Sage!

Yesterday we talked briefly about Sage, had you create an account and a project called 'Calculus Center'.  Today we are going to use that project to plot functions.  Let's get started:

## A Calculus Specific Alternative to Khan Academy Videos

We make it pretty clear up front that we don't do videos.  It's not that we don't like them, it's that there are so many high quality videos out there that we don't feel the need to recreate our own.  While everyone knows about Khan Academy, very few know about the Worldwide Center of Mathematics.

## The Easy Way To Find $(x+y)^n$

In many courses in Mathematics we oftentimes have to expand out things like $(x+y)^n$ where $n$ is an integer and $x$ and $y$ are real numbers. So many of us will happily expand it out and collect like terms. But this is kind of hard. Isn't it? Well we want to show you an easier and shockingly fast way to just do it.