Mount Holyoke College
Math 333: Differential Equations
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.