The dynamics of an undamped pendulum illustrate a two-dimensional state space of a continuous dynamical system.
Highlighted pages
- Subtleties about divergence
Counterexamples illustrating how the divergence of a vector field may differ from the intuitive appearance of the expansion of a vector field. - Level sets
A introduction to level sets. Illustrates level curves and level surfaces with interactive graphics. - The idea of the divergence of a vector field
Intuitive introduction to the divergence of a vector field. Interactive graphics illustrate basic concepts. - Spherical coordinates
Illustration of spherical coordinates with interactive graphics. - An introduction to conservative vector fields
An introduction to the concept of path-independent or conservative vector fields, illustrated by interactive graphics.
Recent news
Redesigned for small screens
by Duane Q. Nykamp on May 31, 2012Interactive Gallery of Quadric Surfaces
by Duane Q. Nykamp on March 14, 2012- More recent news
Recent pages
- A simple spiking neuron model
An introduction to the Fitzhugh Nagumo model of a spiking neuron, including basic phase plane analysis.
Added May 2, 2013 - The dynamics of competition between two species
Added April 27, 2013 - An infectious disease model with immunity
Added April 22, 2013 - More new items
Highlighted applets
The dynamics of an undamped pendulum illustrate a two-dimensional state space of a continuous dynamical system.
Animation of the mapping of rectangle by a nonlinear change of variables.
Welcome to Math Insight
The Math Insight web site is a collection of pages and applets designed to shed light on concepts underlying a few topics in mathematics. The focus is on qualitative description rather than getting all technical details precise. Many of the pages were designed to be read even before students attend lecture on the topic, so they are intended to be somewhat readable introductions to the basic ideas.
You can browse the pages organized into threads, which are sequences through a subset of pages organized by particular topics. An index can help you find pages discussing a particular term. You can also search through the pages, applets, and image captions. A few pages allow you to change the notation system used to render the mathematics.
We hope Math Insight can help you understand key mathematical concepts. We welcome comments on how we can improve it.