# 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.

### Some Notes on Weighted Sobolev Spaces

Embedding theorems for Weighted Sobolev Spaces

### The Second Mean Value Theorem for Integrals

This post concerns the second mean value theorem for definite integrals. Theorem    [Second MVT for Integrals] Let $w$ be a …

### Integration Theories

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 …

### Moore-Osgood Theorem

This short post aims at proving a general version of the Moore-Osgood Theorem on interchanging of limits. Theorem   …

### Volume of Simplices

How to compute the volume of a simplex using the Cayley-Menger determinant, and a higher dimensional Pythagorean theorem

### A Criterion for Real Roots

When does a polynomial with real coefficients have only real roots? Here's one way to determine it.

### You are 23 times more likely to crash

Driving down the highway in upstate Michigan yesterday, I saw a State Police billboard that states (I paraphrase) Drivers who text are …

### A Weighted/Interpolated Young's Inequality

A follow up to my previous post on Young's inequality.

### Lie Groups

Some introductory notes about the definition and geometry of Lie groups, and their analysis.

### Dynamics of a Rigid Body

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 …