Using cobwebbing to visualize how a linear approximation to a function captures its behavior around equilibria.
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. - 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. - Introduction to the multivariable chain rule
Introduction to the multivariable chain rule. The basic concepts are illustrated through a simple example. - 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. - Level sets
A introduction to level sets. Illustrates level curves and level surfaces with interactive 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
Using cobwebbing to visualize how a linear approximation to a function captures its behavior around equilibria.
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.