Pages similar to: The cross section method for determining triple integral bounds
- 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. - 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. - Introduction to changing variables in triple integrals
Introduction to the concepts behind a change of variables in triple integrals. - Volume calculation for changing variables in triple integrals
A derivation of how a mapping that changes variables in triple integrals transforms volume. - 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 variable examples
Examples of changing variables in triple integrals. - 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. - Illustrated example of changing variables in double integrals
An example illustrating with interactive graphics how changing variables transforms regions in the plane. - Matrices and determinants for multivariable calculus
Brief description of matrices and determinants, at the level needed for multivariable calculus. - Multivariable chain rule examples
Examples demonstrating the chain rule for multivariable functions. - 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. - Double integrals as volume
Explanation of how double integrals could be used to represent volume. - 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 as area
Explanation of how double integrals could be used to represent area. - 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 a line integral of a scalar-valued function
Introduction with interactive graphics illustrating the line integral of a scalar-valued function and informally deriving the formula for calculating the integral from the parametrization of the curve.