Computing Improper Integrals using the Residue Theorem | Cauchy Principal Value

Welcome back to a new school year! In this video, I begin by defining the Cauchy Principal Value and proving a couple of theorems about it. Then, I use those theorems to establish a technique which may be used to evaluate improper integrals of certain rational functions, after which I conclude by applying this technique to a simple example. If you would like me to do more complicated examples (since some of you may like them), let me know in the comments! For now though, I'm going to temporarily move away from Complex Variables and focus on my other playlists (though I do plan on returning for videos on topics like conformal mapping *wink*). Questions/requests? Let me know in the comments below! How to find Residues:    • How to find the Residues of a Complex Func...   Prereqs: The videos before this one on the playlist:    • Complex Variables and Functions   Lecture Notes: https://drive.google.com/file/d/0BzC4... Patreon: https://www.patreon.com/user?u=4354534 Twitter:   / facultyofkhan