### Highlighted pages

- An introduction to the directional derivative and the gradient

Interactive graphics about a mountain range illustrate the concepts behind the directional derivative and the gradient of scalar-valued functions of two variables. - 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. - 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. - 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.

### 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 magnetic bead moving along a helix with tangent vector and vector corresponding to a magnetic field.

Illustration of the Cartesian coordinates of a movable three-dimensional point

### 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.