### Highlighted pages

- Introduction to partial derivatives

The concept of partial derivatives is introduced with an illustration of heating costs. Interactive graphics demonstrate the properties of partial derivatives. - 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. - 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. - 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. - Subtleties of differentiability in higher dimensions

A description of some of the tricky ways where a function of multiple variables can fail to be differentiable. Example two variable functions are illustrated 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

- 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* - Integrals and the Fundamental Theorem of Calculus
*Added Oct. 27, 2015* - More new items

### Highlighted applets

A bacteria population that doubles every time step illustrates a discrete dynamical system.

The gradient and directional derivative are illustrated by a level curve plot of a mountain range. The applet interactively computes the gradient and the directional derivative at different points and directions.

### 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.