 # 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
View Section 2: Separable Equations
• Definition of separable differential equations
• How to solve separable differential equations
View Section 3: Compound Interest
• Using differential equations to solve problems for compound interest
• Solving compound interest problems when deposits are made at regular intervals
View Section 4: Variations of Parameters
• Solving first-order linear equations using the method of variation of parameters
View Section 5: Systems of Ordinary Differential Equations
• Systems of normal, first-order differential equations
• Writing systems of first-order linear differential equations in matrix form
Section 6: Matrices
• Matrix operations
• Gaussian elimination
• The inverse of a matrix
Section 7: Systems of Equations, Linear Independence, and Eigenvalues & Eigenvectors
• Systems of linear equations
• Linear independence
• Eigenvalues and eigenvectors
Section 8: Homogeneous Linear Systems with Constant Coefficients
• Solving a homogeneous first-degree, linear system of differential equations with constant coefficients
Section 9: Complex Eigenvalues
• Solving systems of linear, first-order differential equations with real and complex roots
• Finding complex eigenvalues and the corresponding eigenvectors
Section 10: Fundamental Matrices
• Definition of a fundamental matrix for a system of equations
• Properties of a fundamental matrix
Section 11: Repeated Eigenvalues
• Solutions to a system of equations where the coefficient matrix has a repeated eigenvalue
• Finding a generalized eigenvector
Section 12: Nonhomogeneous Linear Systems
• Solving a nonhomogeneous system of equations
• Using the method of Variation of Parameters (Lagrange Method) to find the particular solution