# Introduction to Differential Equations

This is a typical undergraduate course on ordinary differential equations. The following material is based on the classes I taught at the University of Michigan in Spring 2016, Fall 2017, and Spring 2018.

The Jupyter notebooks (see Jupyter) provided here are **just a proper subset** of what is covered in class and they are meant to be supplementary only.
The labs and the course used **MATLAB**, but in the notebooks I used the Julia language. You do not need to have Julia installed on your computer or to view the Jupyter notebooks. The interactive features work with web browsers Safari, Firefox, and Google Chrome as of now. Other browsers were not tested.

## Textbook

Differential Equations: An Introduction to Modern Methods and Applications, by *James Brannan and William Boyce*, 2015 (3rd edition), Wiley.

## Examples — Here’s How I’d Do It

While teaching the course, I regularly posted *handwritten examples* worked out in detail from somewhat more challenging subjects in the course. The series of these notes were called **Here’s How I’d Do It**. The files in PDF format are available here:

- Finding real-valued solutions when eigenvalues are complex
- Solving constant-coefficient second-order linear differential equations
- Deducing facts about eigenvalues from component plots
- A linear system with repeated eigenvalues and a one-dimensional eigenspace
- An application of the method of undetermined coefficients
- An initial-value problem with box-like forcing
- An application of variation of parameters
- Laplace transform method to solve a simple ODE
- Linearizing nonlinear systems, stability analysis