### Pages similar to: Divergence and curl example

- Divergence and curl notation

Different ways to denote divergence and curl. - The components of the curl

Illustration of the meaning behind the components of the curl. - Subtleties about curl

Counterexamples illustrating how the curl of a vector field may differ from the intuitive appearance of a vector field's circulation. - 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 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. - Vector field overview

An overview introducing the basic concept of vector fields in two or three dimensions. - Calculating the formula for circulation per unit area

A sketch of the proof for the formula for the component of the curl of a vector field. - The idea behind Green's theorem

Introduction to Green's theorem, based on the intuition of microscopic and macroscopic circulation of a vector field. - The definition of curl from line integrals

How the curl of a vector field is defined by line integrals representing circulation. - Stokes' theorem examples

Examples illustrating how to use Stokes' theorem. - A path-dependent vector field with zero curl

A counterexample showing how a vector field could have zero curl but still fail to be conservative or path-independent. - 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. - The integrals of multivariable calculus

A summary of the integrals of multivariable calculus, including calculation methods and their relationship to the fundamental theorems of vector calculus. - 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 three-dimensional conservative vector fields

How to find a potential function for a given three-dimensional conservative, or path-independent, vector field. - Introduction to changing variables in double integrals

Introduction to the concepts behind a change of variables in double integrals. The transformation is illustrated with interactive graphics. - 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. - Finding a potential function for conservative vector fields

How to find a potential function for a given conservative, or path-independent, vector field. - Vectors in two- and three-dimensional Cartesian coordinates

A introduction to representing vectors using the standard Cartesian coordinate systems in the plane and in three-dimensional space.