Pages similar to: Volume calculation for changing variables in triple integrals
- Introduction to changing variables in triple integrals
Introduction to the concepts behind a change of variables in triple integrals. - Area calculation for changing variables in double integrals
A derivation of how a mapping that changes variables in double integrals transforms area. - Triple integral change of variables story
Story illustrating the process of changing variables in triple integrals. - 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 variable examples
Examples of changing variables in triple integrals. - Determinants and linear transformations
A description of how a determinant describes the geometric properties of a linear transformation. - Illustrated example of changing variables in double integrals
An example illustrating with interactive graphics how changing variables transforms regions in the plane. - 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. - The cross section method for determining triple integral bounds
Explanation of the cross section method for turning a triple integral into a double integral combined with a single integral in order to compute the limits of integration. - Double integrals as volume
Explanation of how double integrals could be used to represent volume. - 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. - Double integral change of variable examples
Examples of calculating double integrals through changing variables. - 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. - Volumes by cross sections
Calculating the volume of a solid by integrating the area of its cross sections. - Volume of surfaces of revolution
Calculating the volume of created by rotating a plane region around some axis. - Matrices and determinants for multivariable calculus
Brief description of matrices and determinants, at the level needed for multivariable calculus. - The scalar triple product
Definition of the scalar triple product and derivation of its formula. Include interactive graphic to illustrate its properties. - Scalar triple product example
Example showing how to calculate the scalar triple product.