Illustration of how the polar coordinate transformation maps a rectangle onto on the Cartesian plane and changes area.
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. - 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. - 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. - 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. - The components of the curl
Illustration of the meaning behind the components of the curl.
Recent pages
- A birth-death process
Added April 13, 2022 - A stochastic process introduction
Added April 13, 2022 - An introduction to neural coding and decoding
Added April 3, 2022 - More new items
Highlighted applets
Illustration of how the polar coordinate transformation maps a rectangle onto on the Cartesian plane and changes area.
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.