Math Insight

Pages similar to: Length, area, and volume factors

• 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.
• Using Green's theorem to find area
  A trick to use Green's theorem to calculate the area of a region
• Determinants and linear transformations
  A description of how a determinant describes the geometric properties of a linear transformation.
• Double integrals as volume
  Explanation of how double integrals could be used to represent volume.
• Double integrals as area
  Explanation of how double integrals could be used to represent area.
• The idea behind Green's theorem
  Introduction to Green's theorem, based on the intuition of microscopic and macroscopic circulation of a vector field.
• Area calculation for changing variables in double integrals
  A derivation of how a mapping that changes variables in double integrals transforms area.
• 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.
• The idea behind the divergence theorem
  Introduction to divergence theorem (also called Gauss's theorem), based on the intuition of expanding gas.
• Volume calculation for changing variables in triple integrals
  A derivation of how a mapping that changes variables in triple integrals transforms volume.
• Introduction to double integrals
  The definition of a double integral is motivated through a hair density example.
• Double integrals as iterated integrals
  A description of how to convert double integrals into two single integrals.
• Double integral examples
  Examples of integrating double integrals over rectangles and triangles.
• Examples of changing the order of integration in double integrals
  Examples illustrating how to change the order of integration (or reverse the order of integration) in double integrals.
• Double integrals where one integration order is easier
  Illustration of a region where integrating a double integral in one order is must easier than integrating in the other order.
• 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.
• The arc length of a parametrized curve
  Introduction to the arc length of a parametrized curve. The arc length definition is illustrated with interactive graphics.

Back to: Length, area, and volume factors