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 EquationsSeparable Differential EquationsLinear Differential EquationsExact EquationsSolution by SubstitutionLinear ModelsProblems Chapter 3 - High-Order Differential Equation Theory of Linear EquationsReduction of OrderHomogeneous Linear Differential Equations with Constant CoefficientsNon-Homogeneous Linear Differential EquationsCauchy-Euler Differential EquationsHigh-Order Linear Differential Equations with Variable CoefficientsProblems Chapter 4 - Functions of Complex Variable Complex NumbersPowers and RootsProblems