Differential equations

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

Subject classification: this is a mathematics resource.

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

Differential equations serve as mathematical models of physical processes. 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

• Introduction to ordinary differential equations.
  • Ordinary Differential Equations
  • Slope Fields
• First-order equations
  • Introduction to First Order Linear Differential Equations
  • Separable differential equations 50%
  • Exact differential equations 25%
  • Homogeneous differential equations 25%
  • Integrating factors 25%
  • Change of variables 25%
• Higher-order linear equations
  • Linear homogeneous differential equations 25%
  • Linear inhomogeneous differential equations 25%
  • Laplace transforms 25%
  • Power series solutions 25%
• Introduction to nonlinear equations
  • Stability problems in 1D/
  • Stability problems in 2D/
  • Approximate solutions to differential equations

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