### Pages similar to: Introduction to changing variables in double integrals

- Double integral change of variable examples

Examples of calculating double integrals through changing variables. - Area calculation for changing variables in double integrals

A derivation of how a mapping that changes variables in double integrals transforms area. - Illustrated example of changing variables in double integrals

An example illustrating with interactive graphics how changing variables transforms regions in the plane. - Introduction to changing variables in triple integrals

Introduction to the concepts behind a change of variables in triple integrals. - Triple integral change of variables story

Story illustrating the process of changing 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. - 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. - 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 double integrals

The definition of a double integral is motivated through a hair density example. - Double integrals as volume

Explanation of how double integrals could be used to represent volume. - Double integral examples

Examples of integrating double integrals over rectangles and triangles. - Triple integral change of variable examples

Examples of changing variables in triple integrals. - Double integrals as iterated integrals

A description of how to convert double integrals into two single integrals. - Length, area, and volume factors

A summary of the expansion factors that arise from mappings in integrals of multivariable calculus. - 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. - Triple integral examples

Examples showing how to calculate triple integrals, including setting up the region of integration and changing the order of integration. - Introduction to a line integral of a vector field

The concepts behind the line integral of a vector field along a curve are illustrated by interactive graphics representing the work done on a magnetic particle. The graphics motivate the formula for the line integral. - Introduction to a surface integral of a scalar-valued function

How to define the integral of a scalar-valued function over a parametrized surface. - 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.