Pages similar to: The Forward Euler algorithm for solving an autonomous differential equation
- Spruce budworm outbreak model
A graphical analysis of a differential equation model reveals how the spruce budworm could devastate forests every 40 years. - Introduction to bifurcations of a differential equation
Representing the influence of a parameter on the behavior of a differential equation in terms of a bifurcation diagram of equilibria. - An introduction to ordinary differential equations
An introduction using simple examples explaining what an ordinary differential equation is and how one might solve them. - Exponential growth and decay: a differential equation
Solving a differential equation to find an unknown exponential function. - A simple spiking neuron model
An introduction to the Fitzhugh Nagumo model of a spiking neuron, including basic phase plane analysis. - Ordinary differential equation examples
Simple examples of solving ordinary differential equation. - Solving linear ordinary differential equations using an integrating factor
Illustration of the procedure to find an integrating factor that allows integration of a first order linear ordinary differential equation. - Examples of solving linear ordinary differential equations using an integrating factor
Examples of finding an integrating factor and integrating first order linear ordinary differential equations. - Another differential equation: projectile motion
Calculating an equation for the position of an object acted upon by only gravity. - Solving single autonomous differential equations using graphical methods
Using graphical methods, one can observe where the rate of change is positive or negative and determine the behavior of a solution to a differential equation. - Single autonomous differential equation problems
Sample problems involving analysis of a single autonomous differential equation. - Introduction to visualizing differential equation solutions in the phase plane
- Two dimensional autonomous differential equation problems
Sample problems involving analysis of a two coupled autonomous differential equations. - Solutions to two dimensional autonomous differential equation problems
Solutions to sample problems involving analysis of a two coupled autonomous differential equations. - Numerical integration
Methods to approximate the value of definite integrals and estimate the error in the approximations. - Equilibria in discrete dynamical systems
An introduction to the concept of equilibria in discrete dynamical systems and how to calculate them. - The idea of stability of equilibria for discrete dynamical systems
An introduction to the concept of stable and unstable equilibria and how to use cobwebbing to identify stability. - Initial dynamical systems exploration
Exploring models of anteater population growth and lead decay in the bloodstream using interactive applets. - Discrete dynamical systems as function iteration
The simplest versions of discrete dynamical systems can be viewed as evolving due to iterating a function repeatedly. - Solving linear discrete dynamical systems
One can solve a linear discrete dynamical system analytically. The result is an exponential function of the time step.