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Applied Ordinary Differential Equations

Chapter 0 - Differentiation and Integration Formulas

Chapter 1 - The Basic Terminology of Differential Equations

  • What is a Differential Equation?
  • Ordinary Differential Equation (ODE) vs Partial Derivative Equation (PDE).
  • The Order of a Differential Equation.
  • Different Forms of a Differential Equation.
  • Linear vs Non-Linear Differential Equation.
  • Explicit Solution vs Implicit Solution.
  • Family of Solutions.
  • Initial-Value Problems.
  • Existence of a Unique Solution.
  • A 10-Minute Lecture on the Basic Terminology of Differential Equations. 
  • Problems.

Chapter 2 - First-Order Differential Equation

  • Autonomous Differential Equations
  • Separable Differential Equations
  • Linear Differential Equations
  • Exact Equations
  • Solution by Substitution
  • Linear Models
  • Problems

Chapter 3 - High-Order Differential Equation

  • Theory of Linear Equations
  • Reduction of Order
  • Homogeneous Linear Differential Equations with Constant Coefficients
  • Non-Homogeneous Linear Differential Equations
  • Cauchy-Euler Differential Equations
  • High-Order Linear Differential Equations with Variable Coefficients
  • Problems

Chapter 4 - Functions of Complex Variable

  • Complex Numbers
  • Powers and Roots
  • Problems
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