# Differential Equations

This is an overview of differential equations.

### Format

- You should visit the sections below in order starting with Section 1.
- Each section below has several videos explaining the listed concepts, and then exercises with videos.
- If you have watched the videos below and want to see more videos to better understand the material, you can see Chapter 2, Section 3.6, and Chapter 7 of our course MATH 308: Differential Equations. Note these MATH 308 videos are outside the scope of this mini-course and not required viewing.

## Differential Equations

View Section 1: Integrating Factor- Definitions and terminology for ordinary differential equations
- Using an integrating factor to solve a first-order linear differential equation

- Definition of separable differential equations
- How to solve separable differential equations

- Using differential equations to solve problems for compound interest
- Solving compound interest problems when deposits are made at regular intervals

- Solving first-order linear equations using the method of variation of parameters

- Systems of normal, first-order differential equations
- Writing systems of first-order linear differential equations in matrix form

- Matrix operations
- Gaussian elimination
- The inverse of a matrix

- Systems of linear equations
- Linear independence
- Eigenvalues and eigenvectors

- Solving a homogeneous first-degree, linear system of differential equations with constant coefficients

- Solving systems of linear, first-order differential equations with real and complex roots
- Finding complex eigenvalues and the corresponding eigenvectors

- Definition of a fundamental matrix for a system of equations
- Properties of a fundamental matrix

- Solutions to a system of equations where the coefficient matrix has a repeated eigenvalue
- Finding a generalized eigenvector

- Solving a nonhomogeneous system of equations
- Using the method of Variation of Parameters (Lagrange Method) to find the particular solution