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Vector Calculus

Vector Fields - Intro

In mathematics, a vector field is a mathematical tool used to describe the velocity and acceleration of particles in a fluid, the speed and direction of a moving object, the distribution of heat over a surface, or the strength and direction of some physical force. A vector field in three-dimensional space is represented by a line segment, called a vector, that has a definite magnitude and direction at each point. The vector is commonly depicted by a line with an arrow, as in the diagram at right. The vector itself is often referred to as the "field". The magnitude of the vector is called the "length" of the vector, and the direction is given by the angle the vector makes with the positive "x"-axis. The vector is said to be "normalized" if its length is equal to 1. The scalar (or dot) product of two vectors is a numerical value that determines the angle between them. Dot products are used to calculate the magnitude of a vector or the angle between two vectors.

Matt Just

Vector Fields - Intro

Line Integrals and Vector Fields - Overview

Line Integrals and Vector Fields - Example 1

Line Integrals and Vector Fields - Example 2

Line Integrals and Vector Fields - Example 3

Line Integrals and Vector Fields - Example 4

Conservative Fields and Potential Functions - Overview

Conservative Fields and Potential Functions - Example 1

Conservative Fields and Potential Functions - Example 2

Conservative Fields and Potential Functions - Example 3

Conservative Fields and Potential Functions - Example 4

Green's Theorem - Overview

Green's Theorem - Example 1

Green's Theorem - Example 2

Green's Theorem - Example 3

Green's Theorem - Example 4

Surface Integrals - Overview

Surface Integrals - Example 1

Surface Integrals - Example 2

Surface Integrals - Example 3

Surface Integrals - Example 4

Stokes' Theorm and Divergence Theorem - Overview

Stokes' Theorm and Divergence Theorem - Example 1

Stokes' Theorm and Divergence Theorem - Example 2

Stokes' Theorm and Divergence Theorem - Example 3

Stokes' Theorm and Divergence Theorem - Example 4