# Differential Equations

A tour through some of the most beautiful methods for studying dynamic systems

Differential equations, studying the unsolvableWhat is a differential equation, the pendulum equation, and some basic numerical methodsChapter 1Mar 31, 2019

But what is a partial differential equation?The heat equation, as an introductory PDE.Chapter 2Apr 21, 2019

Solving the heat equationSolving the heat equation.Chapter 3Jun 16, 2019

But what is a Fourier series? From heat flow to circle drawingsHow Fourier series arose from studying heat flow, and how they can be thought of as decomposing any drawing in 2d into a sum of rotations.Chapter 4Jun 30, 2019

e^(iπ) in 3.14 minutes, using dynamicsA quick explanation of e^(pi i) in terms of motion and differential equationsChapter 5Jul 7, 2019

How (and why) to raise e to the power of a matrixExponentiating matrices, and the kinds of linear differential equations this solves.Chapter 6Apr 1, 2021