This page contains a collection of PDF documents I have written in LaTeX on a variety of topics in math and physics. Most of them are me working through problems I've been assigned or loose ends that were not tied up in class.
At the bottom of each section I list a few problems I am currently working on.
From Maxwell's equations that govern classical electromagnetism, Einstein concluded that light must travel at the same speed in all reference frames. This assumption destroys much of the physics we have learned up to this point. So, how do we reconcile special relativity with Newtonian Mechanics? How does Special Relativity adjust our understanding of electromagnetism to remove the contradictions created by changing reference frames?
Given two points, what is the shortest time path between them, assuming only gravity is acting? This is a famous problem known as the Brachistochrone problem, and I have a method to solve it, but it requires taking the derivative of a function with respect to another function.