The dynamics of an undamped pendulum illustrate a two-dimensional state space of a continuous dynamical system.
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. - The idea of the divergence of a vector field
Intuitive introduction to the divergence of a vector field. Interactive graphics illustrate basic concepts. - 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. - Parametrization of a line
Introduction to how one can parametrize a line. Interactive graphics illustrate basic concepts. - 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
- 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
The dynamics of an undamped pendulum illustrate a two-dimensional state space of a continuous dynamical system.
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.