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Double integral examples
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.
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.
Double integrals as iterated integrals
A description of how to convert double integrals into two single integrals.
Illustrated example of changing variables in double integrals
An example illustrating with interactive graphics how changing variables transforms regions in the plane.
Double integrals as volume
Explanation of how double integrals could be used to represent volume.
Introduction to double integrals
The definition of a double integral is motivated through a hair density example.
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.
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.
Double integrals as area
Explanation of how double integrals could be used to represent area.
Area calculation for changing variables in double integrals
A derivation of how a mapping that changes variables in double integrals transforms area.
Triple integral examples
Examples showing how to calculate triple integrals, including setting up the region of integration and changing the order of integration.
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 changing variables in triple integrals
Introduction to the concepts behind a change of variables in triple integrals.
Introduction to triple integrals
An introduction to the definition of triple integrals as well as their formulation as iterated integrals.
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.
Triple integral change of variables story
Story illustrating the process of changing variables in triple integrals.
Using the Forward Euler algorithm to solve pure-time differential equations
By pretending that the slope of a function is constant over small intervals, we following tangent lines to estimate the solution to pure-time differential equations.
The idea behind Green's theorem
Introduction to Green's theorem, based on the intuition of microscopic and macroscopic circulation of a vector field.
Using Green's theorem to find area
A trick to use Green's theorem to calculate the area of a region
Double integral examples