Pages similar to: Solutions to two dimensional autonomous differential equation problems
- 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. - Spruce budworm outbreak model
A graphical analysis of a differential equation model reveals how the spruce budworm could devastate forests every 40 years. - Single autonomous differential equation problems
Sample problems involving analysis of a single autonomous differential equation. - Two dimensional autonomous differential equation problems
Sample problems involving analysis of a two coupled autonomous differential equations. - An introduction to ordinary differential equations
An introduction using simple examples explaining what an ordinary differential equation is and how one might solve them. - 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. - Exponential growth and decay: a differential equation
Solving a differential equation to find an unknown exponential function. - Another differential equation: projectile motion
Calculating an equation for the position of an object acted upon by only gravity. - Introduction to visualizing differential equation solutions in the phase plane
- The Forward Euler algorithm for solving an autonomous differential equation
Using the linear approximation, or tangent line, to the solution of a differential equation to estimate the solution over small intervals. - 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. - A simple spiking neuron model
An introduction to the Fitzhugh Nagumo model of a spiking neuron, including basic phase plane analysis. - The idea of a dynamical system
The basic concept of a dynamical system as the evolution of something over time. The fundamental ideas of the state space and temporal evolution rules are illustrated with examples featuring interactive graphics. - An introduction to discrete dynamical systems
Overview of discrete dynamical systems, focusing on the simplest one-dimensional case, where the dynamics are given by iterating a function. - Developing an initial model to describe bacteria growth
By analyzing some data and hypothesizing rules for cell division, we develop a discrete dynamical system for the growth of a population of bacteria. - Bacteria growth model exercises
Exercises on developing discrete dynamical systems for the growth of a population of bacteria. - Bacteria growth model exercise answers
Answers to selected exercises on developing discrete dynamical systems for the growth of a population of bacteria. - Exponential growth and decay modeled by discrete dynamical systems
Overview of exponential growth and decay in discrete time. Exploration of their qualitative properties as well as solutions to the dynamical system.