List of all pages
- Connecting network structure to dynamical properties
An exploration of the influence of network structure on the properties of dynamical processes taking place on networks. - How to determine if a vector field is conservative
A discussion of the ways to determine whether or not a vector field is conservative or path-independent. - Finding a potential function for conservative vector fields
How to find a potential function for a given conservative, or path-independent, vector field. - Finding a potential function for three-dimensional conservative vector fields
How to find a potential function for a given three-dimensional conservative, or path-independent, vector field. - An introduction to conservative vector fields
An introduction to the concept of path-independent or conservative vector fields, illustrated by interactive graphics. - A conservative vector field has no circulation
How a conservative, or path-independent, vector field will have no circulation around any closed curve. - Testing if three-dimensional vector fields are conservative
Examples of testing whether or not three-dimensional vector fields are conservative (or path-independent). - Definition: Continuous dynamical system definition
A continuous dynamical system is a dynamical system whose state evolves over state space continuously over time according to a fixed rule. - Controlling a rabbit population
A project to determine a strategy for maintaining a stable population of rabbits in an environment without predators. - Definition: Countably infinite definition
A set is countably infinite if its elements can be put in one-to-one correspondence with the set of natural numbers. In other words, one can count off all elements in the set in such a way that, even though the counting will take forever, you will get to any particular element in a finite amount of time. - Critical points, monotone increase and decrease
How to compute the intervals along which a function is increasing or decreasing. - The cross product
Introduction to the cross product with a focus on its basic properties. Includes an interactive graphic to illustrate these properties of the cross product. - Cross product examples
Examples of calculating the cross product. - The formula for the cross product
Derivation of the formula to calculate the cross product of two vectors. - The components of the curl
Illustration of the meaning behind the components of the curl. - The definition of curl from line integrals
How the curl of a vector field is defined by line integrals representing circulation. - The curl of a gradient is zero
Calculation showing that the curl of a gradient is zero. - The idea of the curl of a vector field
Intuitive introduction to the curl of a vector field. Interactive graphics illustrate basic concepts. - Subtleties about curl
Counterexamples illustrating how the curl of a vector field may differ from the intuitive appearance of a vector field's circulation. - Cylindrical coordinates
Illustration of cylindrical coordinates with interactive graphics.
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