Expository

This is a collection some of the expository notes that I have written, they range in topic, some closer to my research and some farther away. As opposed to posts in "Mathematical Diversions", posts here are intended to be read by other people. I welcome comments and corrections.

Embedding theorems for Weighted Sobolev Spaces
Last updated on 8 min read Expository

This post concerns the second mean value theorem for definite integrals. Theorem    [Second MVT for Integrals] Let $w$ be a …
Last updated on 4 min read expository

Since I am preparing to teach intro real analysis this fall, it is a good time for me to get reacquainted with Riemann integration and …
Last updated on 8 min read expository

This short post aims at proving a general version of the Moore-Osgood Theorem on interchanging of limits. Theorem   …
Last updated on 2 min read expository

How to compute the volume of a simplex using the Cayley-Menger determinant, and a higher dimensional Pythagorean theorem
Last updated on 11 min read expository

When does a polynomial with real coefficients have only real roots? Here's one way to determine it.
Last updated on 4 min read expository

Driving down the highway in upstate Michigan yesterday, I saw a State Police billboard that states (I paraphrase) Drivers who text are …
Last updated on 7 min read expository

A follow up to my previous post on Young's inequality.
Last updated on 10 min read expository

Some introductory notes about the definition and geometry of Lie groups, and their analysis.
Last updated on 19 min read expository

This post is about the formulation of the dynamics of a rigid body, under rotations, as dynamics on a Lie group. I'm writing this to …
Last updated on 9 min read expository