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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 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.

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.

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.

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:

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.

It's Sage Week!

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.