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
- Developing an initial model to describe bacteria growth
By analyzing some data and hypothesizing rules for cell division, we develop a discrete dynamical system for the growth of a population of bacteria. - 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. - 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. - 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. - 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.
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.
Illustration of the Cartesian coordinates of a movable three-dimensional point
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.