### Highlighted pages

- 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. - 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. - An introduction to conservative vector fields

An introduction to the concept of path-independent or conservative vector fields, illustrated by interactive graphics. - The idea of the curl of a vector field

Intuitive introduction to the curl of a vector field. Interactive graphics illustrate basic concepts. - 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.

### 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.

Animation of the mapping of rectangle by a nonlinear change of variables.

### 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.