### Highlighted pages

- Introduction to the multivariable chain rule

Introduction to the multivariable chain rule. The basic concepts are illustrated through a simple example. - The cross product

Introduction to the cross product with a focus on its basic properties. Includes an interactive graphic to illustrate these properties of the cross product. - An introduction to parametrized curves

An introduction to how a vector-valued function of a single variable can be viewed as parametrizing a curve. Interactive graphics illustrate the way in which the function maps an interval onto a curve. - Forming planes

A description of ways to specify a plane. Interactive graphics illustrate the concepts. - 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.

### 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

The level curves of an elliptic paraboloid are shown as the intersection of a horizontal plane with the graph.

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

### 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.