Ordinary differential equations

Educational level: this is a tertiary (university) resource.

Resource type: this resource is a course.

Subject classification: this is a mathematics resource .

Completion status: this resource is just getting off the ground. Please feel welcome to help!

School:Mathematics > Topic:Differential_Equations > Ordinary Differential Equations

This course is intended to be an introduction to ordinary differential equations and their solutions. A differential equation (DE) is an equation relating a function to its derivatives. If the function is of only one variable, we call the equation an ordinary differential equation (ODE). Equations relating the partial derivatives (See: Vector calculus) of a function of several variables are called partial differential equations (PDEs). Ordinary differential equations are much easier to solve than partial differential equations, so these will be our main focus.

Syllabus

• First Order Equations
  • Separable Equations 50%
  • Exact Equations 25%
  • Homogeneous equations 25%
  • Integrating Factors 25%
  • Change of Variables 25%
• Higher Order Linear Equations
  • Linear Homogeneous Equations 25%
  • Inhomogeneous Equations 25%
  • Laplace Transforms 25%
  • Power Series 25%
• Introduction to Nonlinear equations
  • Stability problems in 1D
  • Stability problems in 2D
  • Approximate Solutions