Vector Calculus

Many quantities which are of interest in physics are both directed quantities (vectors) and can take on a continuous range of values, making calculus methods necessary. Several operations from the mathematical field of vector calculus are of particular importance in solving physical problems.

Basic vector calculus operationsVector calculus identitiesDivergence theoremStokes' theorem

Index

Vector concepts
 
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Vector Calculus Operations

Three vector calculus operations which find many applications in physics are:

1. The divergence of a vector function

2. The curl of a vector function

3. The Gradient of a scalar function


These examples of vector calculus operations are expressed in Cartesian coordinates, but they can be expressed in terms of any orthogonal coordinate system, aiding in the solution of physical problems which have other than rectangular symmetries.

Index

Vector calculus
 
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The Del Operator

The collection of partial derivative operators

is commonly called the del operator. It shows up in important vector calculus operations.

Gradient

Divergence

Curl

LaPlacian

Index

Vector calculus
 
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