Pages similar to: The idea behind the divergence theorem
- 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. - Length, area, and volume factors
A summary of the expansion factors that arise from mappings in integrals of multivariable calculus. - The idea of the divergence of a vector field
Intuitive introduction to the divergence 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. - Divergence and curl notation
Different ways to denote divergence and curl. - Divergence and curl example
An example problem of calculating the divergence and curl of a vector field. - Introduction to triple integrals
An introduction to the definition of triple integrals as well as their formulation as iterated integrals. - Triple integral examples
Examples showing how to calculate triple integrals, including setting up the region of integration and changing the order of integration. - Triple integral change of variables story
Story illustrating the process of changing variables in triple integrals. - Triple integral change of variable examples
Examples of changing variables in triple integrals. - Introduction to a surface integral of a scalar-valued function
How to define the integral of a scalar-valued function over a parametrized surface. - Introduction to a surface integral of a vector field
How to define the integral of a vector field over a parametrized surface, illustrated by interactive graphics. - Scalar surface integral examples
Examples of calculating the integral of scalar functions over parametrized surfaces. - Vector surface integral examples
Examples of calculating the integral of vector fields over parametrized surfaces. - 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. - Proper orientation for Stokes' theorem
The importance of orientating the surface and its boundary correctly when using Stokes' theorem. - Stokes' theorem examples
Examples illustrating how to use Stokes' theorem. - Divergence theorem examples
Examples of using the divergence theorem. - The fundamental theorems of vector calculus
A summary of the four fundamental theorems of vector calculus and how the link different integrals. - The shadow method for determining triple integral bounds
Explanation of the shadow method for turning a triple integral into a double integral combined with a single integral in order to compute the limits of integration.