### 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. - A line or a plane or a point?

Examples showing how the graph of an equation depends on the underlying dimension, becoming a line or a point or a plane. - The idea behind Green's theorem

Introduction to Green's theorem, based on the intuition of microscopic and macroscopic circulation of a vector field. - The idea of the divergence of a vector field

Intuitive introduction to the divergence of a vector field. Interactive graphics illustrate basic concepts. - Level sets

A introduction to level sets. Illustrates level curves and level surfaces with 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

- Plotting line graphs in R

Basic commands to plot line graphs with one or more series in R*Added Jan. 16, 2017* - For-loops in R

How to use a for-loop in R*Added Jan. 12, 2017* - 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* - More new items

### Highlighted applets

Illustration of spherical coordinates illustrating the effect of changing each of the three spherical coordinates on the location of a point.

Illustration of how the polar coordinate transformation maps a rectangle onto on the Cartesian plane and changes area.

### 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.