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Topics Involve Linear & Nonlinear, Homogeneous & Nonhomogeneous Differential Equations

Introduction to Differential Equations

First Order Linear Differential Equations, Integrating Factor

Existence and Uniqueness of Solutions / Exact
Differential Eqs

Phase Diagrams for Autonomous Differential Equations

Slope Fields, Solution Curves, and Semi-stable Equilibrium Solutions 

Separable Differential Equations/ Growth and Decay Applications

Approximate Methods for First Order Differential Equations

First Order Nonlinear Differential Equations

Related Rate Applications

Existence and Uniqueness of Solutions of Linear Second Order Differential Equations

Basics of 2nd Order, Ordinary Differential Equations/
Method of Reduction

Particular Solutions of Non-homogeneous Differential Equations

Mechanical Vibrations

Method of Variation of Parameters

Initial Value, Boundary Value, and Eigenvalue Problems

Fourier Series

Heat Conduction in a Thin Rod

1-D Wave Equation/String Vibrations

Dirichlet Applications - Heat Conduction in a Plate

Overview of
Boundary Value
Applications

Steady Periodic Vibrations

Sturm-Liouville Applications

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