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Visuals and Modules

Chapter 17: Vector Calculus

Vector Calculus
This comprehensive site offers information on almost every aspect of elementary vector calculus.

Section 17.1: Vector Fields

Vector Field Analyzer
A similar Java applet that plots the vector fields of sample functions and lets you analyze the flow and other properties of the vector field.

Section 17.2: Line Integrals

Visualizing Circulation of Vector Fields
This site shows how line integrals over a closed curve in a plane can be visualized as ordinary integrals with respect to the arc length parameter.

Section 17.5: Curl and Divergence

Flows of Vector Fields
A Java applet that plots the vector fields of several functions and shows the effect of curl and divergence.

From Points to Regions
A guide showing how the divergence of a vector field combined with integration can be used to determine characteristics of an entire region in one, two, and three dimensions.

Divergence in Two and Three Dimensions
A tutorial using population growth and migration to explain divergence in a vector field in two and three dimensions.

Section 17.6: Parametric Surfaces and Their Areas

Surface Area for Parametric Surfaces
This online graphing tool allows the user to generate parametric surfaces.