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.
Highlighted pages
- 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 divergence of a vector field
Intuitive introduction to the divergence of a vector field. Interactive graphics illustrate basic concepts. - 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. - Spherical coordinates
Illustration of spherical coordinates with interactive graphics. - 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.
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
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.
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.