Pages similar to: Illustrated example of changing variables in double integrals Area calculation for changing variables in double integrals A derivation of how a mapping that changes variables in double integrals transforms area. 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. 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. Triple integral change of variables story Story illustrating the process of changing variables in triple integrals. 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. Triple integral examples Examples showing how to calculate triple integrals, including setting up the region of integration and changing the order of integration. 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. 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. Introduction to double integrals The definition of a double integral is motivated through a hair density example. 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. 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. Determinants and linear transformations A description of how a determinant describes the geometric properties of a linear transformation. Double integrals as iterated integrals A description of how to convert double integrals into two single integrals. Triple integral change of variable examples Examples 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. Length, area, and volume factors A summary of the expansion factors that arise from mappings in integrals of multivariable calculus. Area and definite integrals Integrating to find the area under a curve or the area between two curves.