Competing Species. (pdf file) A model of an ecosystem consisting of two species that compete for a common food supply.

Derivation of the Wave Equation. (pdf file) These notes show that the equation of motion for small amplitude transverse oscillations of an elastic string is the wave equation.

Flow from a Tank. (pdf file) Derives a differential equation modelling the flow of water out of a tank.

Logistic Growth. (pdf file) A simple model for population size.

The Pendulum. (pdf file) Derives the differential equation of the simple pendulum.

The RLC Circuit. (pdf file) Derives and solves the differential equation of the RLC circuit.

Planetary Motion (with corrections from general relativity) (pdf file) Simplifies Newton's equations for planetary motion to a second order constant coefficient ODE. The most important corrections from general relativity add a small nonlinear perturbation to the equation.

Predator Prey. (pdf file) A model of an ecosystem consisting of two populations. One is a predator and the other its prey.

The Telegraph Equation. (pdf file) A model for signal transmission along wires.

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