# Mount Holyoke College

# Math 333: Differential Equations

# Syllabus

### Introduction (Chapter 1)

- Equations and their solutions.
- Differential equations.
- ODE and PDE and their solutions.
- Order of a differential equation.

### First order ODEs (Chapter 2)

- Separable ODEs. Homogeneous Equations.
- Exact equations. Integrating factors.
- Linear equations. Reduction of order.

### Second order ODEs (Chapter 3)

- General solution. Use of a known solution to find another.
- Homogeneous equations with constant coefficients.
- The method of undetermined coefficients.
- The method of variation of parameters.

### Systems of first order ODEs (Chapter 10)

- Linear systems.
- Homogeneous linear systems with constant coefficients.
- Nonlinear systems. Volterra's prey-predator eauation.

### Nonlinear ODEs (Chapter 11)

- Autonomus systems. The phase plane.
- Types of critical points. Stability.
- Critical points and stability.
- Simple critical points of nonlinear systems

### Qualitative properties of solutions (Chapter 4)

- Oscilations and the Sturm separation theorem.
- The Sturm comparison theorem.

### Power series solutions (Chapter 5)

- Series solutions of first order ODEs.
- Second order linear ODEs.
- Regular singular points.
- Gauss's hypergemetric equation.