In this tutorial, we will learn to approximate differentiable functions with polynomials. Beyond just being super cool, this can be useful for approximating functions so that they are easier to calculate, differentiate or integrate. So whether you will have to write simulations or become a bond trader (bond traders use polynomial approximation to estimate changes in bond prices given interest rate changes and vice versa), this tutorial could be fun. If that isn't motivation enough, we also come up with one of the most epic and powerful conclusions in all of mathematics in this tutorial: Euler's identity.

This is the second of two collections of lecture notes used to teach single-variable calculus at San Jacinto College (Houston TX). The notes are formatted as presentation slides and were typeset using Beamer (LaTeX). All the main topics of a second semester course in calculus are addressed. In this sense, the notes are self-contained. However, if one deems it necessary to supplement the notes with a full textbook, I recommend one or more of these open-source textbooks:Hoffman, Dale, Contemporary Calculus. 2013Strang, Gilbert and Edwin Herman, Calculus Volume 2. 2016Guichard, David, Community Calculus. 2022