The Laplace transform of a function
How to write down the Laplace tranform of the solution of a forced oscillator
  diffeq
Solving forced oscillator diffeqs by inverting Laplace tran sforms
Fast Fourier point fit and Fourier integral fit
Combining Fourier fit and the Laplace transform to come up with good
  approximate formulas for periodically forced oscillators
Fourier analysis for detecting resonance

Euler's method of faking the plot of the solution of a differential equation
  and how it highlights the fundamental issue of diffeq
Reading a diffeq t hrough  flow plots
Solving diffeq's numerically with Mathematica
Systems of interacting differential equations: The predator-prey model
Sensitive dep endence on starter data
The drinking versus driving model
Population models and control; Logistic harvesting
Lanchester war model

Reading an autonomous diffeq through phase lines
Automomous diffeqs with parameters. Bifurcations and bifurcation points
Hand symbol manipulation: Separating the variables
Population models and control
Using bifurcation plots to study E. Coli growing in a chemostat
Automatically controlled air conditioning
Getting t here in infinite time versus getting there in finite time

Flows and their trajectories as pairs of solutions of a system of differential equations
Flow analysis of  the unforced linear oscillator differential equa tion by converting it to a system of two first order differential equations
Equilibrium points
Damped oscillators, undamped oscillators and van der Pol's nonlinea r oscillator
Linear systems and graphical meaning of eigenvectors of the coefficient matrix
Pursuit models
Boundary value problems: Shooting for a specified outcome

Eigenvectors of the coefficient matrix point in the directions of strongest inward and/or outward flow
Eigenvalues of the coefficient matrix indicate realtive streng hs of inward and/or outward flow
Eigenvalue-trajectory analysis to predict swirl in,swirl out or no swirl at all
Stability and instability
Reservoir Models for drug metabolization
Linear systems in life science, chemistry and electrical engineering
Higher dimensional linear systems

Using the Jacobian to approximate a nonlinear diffeq system by linearizing at equilibrium points
Attractors and repellers:Lyapunov's rules for detecting them via ana lysis of the eigenvalues of the Jacobian
The pendulum oscillator: Damped and undamped
When linearizations can be trusted and when they shouldn't be trusted & nbsp;
Linearization of pendulum oscillators: Using linearzation to estimate the amplitude and frequency of a pendulum oscillator
Energy and the undamped pendulum oscillator
The Van der Pol oscillator
Gradient and Hamiltonian systems
Lorenz's chaotic oscillator

Part 3:  Partial DiffEq: Heat and Wave Equations

Rigging on to get a pure sine fast Fourier fit of on
Fourier Sine fit for solving the heat equation.
Fourier Sine fit for solving the wave equation.
Solving the heat and the wave equations in the case that initial data are given by a data list.