### Highlighted pages

- The idea behind Green's theorem

Introduction to Green's theorem, based on the intuition of microscopic and macroscopic circulation of a vector field. - Parametrized curve and derivative as location and velocity

Description of a parametrization of a curve as the position of a particle and the derivative as the particle's velocity. Illustrated with animated graphics. - The idea of the divergence of a vector field

Intuitive introduction to the divergence of a vector field. Interactive graphics illustrate basic concepts. - Introduction to differentiability in higher dimensions

An introduction to the basic concept of the differentiability of a function of multiple variables. Discussion centers around the existence of a tangent plane to a function of two variables. - The components of the curl

Illustration of the meaning behind the components of the curl.

### 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

- Visualizing the solution to a two-dimensional system of linear ordinary differential equations

An interactive plot of the the solution trajectory of a 2D linear ODE, where one can explore the behavior of the solution in the phase plane and versus time.*Added Sept. 20, 2016* - The determinant of a matrix

The calculation of the determinant of a matrix, a single number that gives useful information about the matrix.*Added Jan. 14, 2016* - Applications of integration
*Added Oct. 27, 2015* - More new items

### Highlighted applets

Using cobwebbing to visualize how a linear approximation to a function captures its behavior around equilibria.

The dynamics of an undamped pendulum illustrate a two-dimensional state space of a continuous dynamical system.

### 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.