Differential Equations

1.  Differential Equations

2.  First Order Systems

3.  Linear Systems

4.  Forcing and Resonance

5.  Nonlinear Systems

6.  Laplace Transforms


A.  The Derivative and Integral

B.  Complex Numbers, Polynomials, and the Quadratic Formula

C.  Linear Algebra

D.  Partial Fractions and Completing the Square


1.  Algebra, Calculus, Trigonometry, etc.

2.  Laplace Transforms


1.  Free Falling Bodies

2.  Population Growth

3.  Diffusion of a Solute and a Cooling Body

4.  Water in a Draining Tank

5.  A Mixing Problem

6.  Oscillating Spring Mass System

7.  Forced Spring Mass System

8.  A Simple Pendulum

9.  An Electrical Circuit

10.  Deflection of a Beam

11.  Reacting Chemicals

12.  The Predator-Prey System


1.  Quadratics

2.  Graphing

3.  Eigenvalues and Eigenvectors (2×2 matrices)

4.  Solutions of Differential Equations

5.  Separation of Variables

6.  First Order Linear Equations