Animation of the mapping of rectangle by a nonlinear change of variables.
Highlighted pages
- 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 partial derivatives
The concept of partial derivatives is introduced with an illustration of heating costs. Interactive graphics demonstrate the properties of partial derivatives. - The idea behind Stokes' theorem
Introduction to Stokes' theorem, based on the intuition of microscopic and macroscopic circulation of a vector field and illustrated by interactive graphics. - Forming planes
A description of ways to specify a plane. Interactive graphics illustrate the concepts. - 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 news
Redesigned for small screens
by Duane Q. Nykamp on May 31, 2012Interactive Gallery of Quadric Surfaces
by Duane Q. Nykamp on March 14, 2012- More recent news
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
Animation of the mapping of rectangle by a nonlinear change of variables.
Illustration of magnetic bead moving along a helix with tangent vector and vector corresponding to a magnetic field.
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.