Our latest video is Refactoring Introductory Calculus, Part 1.

In computer programming, the word “refactoring” refers to taking a process apart and putting it back together with the components slightly shifted in order to make the result both easier to understand and use while simultaneously being more powerful. This is the first episode in a series about rethinking the way that calculus is taught and communicated in order to do the same thing – simplify the foundations while increasing the power of those foundations.

In this part, we will talk about how focusing on differentials instead of derivatives makes the process of calculus easier, giving a unified set of rules for single-variable, implicit, and multivariable derivatives. Additionally, the process given here removes the need for the chain rule, which simply follows naturally from the process rather than having to be some special rule.

Unfortunately, YouTube doesn’t allow arbitrary links, so we are linking all of the YouTube cards in the video to this post. Here are the links to the items discussed in the YouTube cards:

- Simplifying and Refactoring Introductory Calculus. This is the paper that serves as the basis for the video series.
- To see how this works with higher-order differentials, see the paper Extending the Algebraic Manipulation of Differentials.