Differential Equations Practice Tests

Practice Tests

Topics

• Introduction to Differential Equations

  • Definitions & Terminology

  • Initial-Value Problems

  • Mathematical Models

• First-Order Differential Equations

  • Separable Variables

  • Linear & Exact Equations

• Higher-Order Differential Equations

  • Modeling Higher-Order Differential Equations

  • Linear Equations

  • Undetermined Coefficients

  • Variation of Parameters

• The Laplace Transform

  • Definition of Laplace Transform

  • Transforms of Periodic Functions

• System of Linear First-Order Differential Equations

  • Homogeneous Linear Systems

  • Nonhomogeneous Linear Systems

  • Matrix Exponentials

• Numerical Solutions of Ordinary Differential Equations

  • Euler Method

  • Multi-step Methods

  • Second-Order Boundary-Value Problems

• Introductions to PDEs

  • Initial & Boundary Value Problems

  • Existence & Uniqueness

  • Derivatives from Conservation Laws

• First Order PDEs

  • Linear & Quasi-Linear PDEs

• Second Order Linear PDEs

  • Wave Equations

  • Heat Equations

  • Separation of Variables