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# OpenMath Content Dictionary: veccalc1

Canonical URL:
http://www.openmath.org/cd/veccalc1.ocd
CD Base:
http://www.openmath.org/cd
CD File:
veccalc1.ocd
CD as XML Encoded OpenMath:
veccalc1.omcd
Defines:
Date:
2004-03-30
Version:
3
Review Date:
2006-03-30
Status:
official


This document is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

The copyright holder grants you permission to redistribute this
document freely as a verbatim copy. Furthermore, the copyright
holder permits you to develop any derived work from this document
provided that the following conditions are met.
a) The derived work acknowledges the fact that it is derived from
this document, and maintains a prominent reference in the
work to the original source.
b) The fact that the derived work is not the original OpenMath
document is stated prominently in the derived work.  Moreover if
both this document and the derived work are Content Dictionaries
then the derived work must include a different CDName element,
chosen so that it cannot be confused with any works adopted by
the OpenMath Society.  In particular, if there is a Content
Dictionary Group whose name is, for example, math' containing
Content Dictionaries named math1', math2' etc., then you should
not name a derived Content Dictionary mathN' where N is an integer.
However you are free to name it private_mathN' or some such.  This
is because the names mathN' may be used by the OpenMath Society
for future extensions.
compilation of derived works, but keep paragraphs a) and b)
intact.  The simplest way to do this is to distribute the derived
work under the OpenMath license, but this is not a requirement.
society at http://www.openmath.org.


This CD contains symbols to represent functions which are concerned with vector calculus.

## divergence

Role:
application
Description:

This symbol is used to represent the divergence function. It takes one argument which should be a vector of scalar valued functions, intended to represent a vector valued function and returns a scalar value. It should satisfy the defining relation: divergence(F) = \partial(F_(x_1))/\partial(x_1) + ... + \partial(F_(x_n))/\partial(x_n)

Commented Mathematical property (CMP):
divergence(F) = \partial(F_(x_1))/\partial(x_1) + ... + \partial(F_(x_n))/\partial(x_n)
Signatures:
sts

Role:
application
Description:

This symbol is used to represent the grad function. It takes one argument which should be a scalar valued function and returns a vector of functions. It should satisfy the defining relation: grad(F) = (\partial(F)/\partial(x_1), ... ,\partial(F)/partial(x_n))

Commented Mathematical property (CMP):
Signatures:
sts

 [Next: curl] [Previous: divergence] [Top]

## curl

Role:
application
Description:

This symbol is used to represent the curl function. It takes one argument which should be a vector of scalar valued functions, intended to represent a vector valued function and returns a vector of functions. It should satisfy the defining relation: curl(F) = i X \partial(F)/\partial(x) + j X \partial(F)/\partial(y) + j X \partial(F)/\partial(Z) where i,j,k are the unit vectors corresponding to the x,y,z axes respectively and the multiplication X is cross multiplication.

Commented Mathematical property (CMP):
curl(F) = i X \partial(F)/\partial(x) + j X \partial(F)/\partial(y) + j X \partial(F)/\partial(Z)
Formal Mathematical property (FMP):
$\mathrm{curl}\left(F\right)=\left(1,0,0\right)×\partial \left(\left(1\right)\right)+\left(0,1,0\right)×\partial \left(\left(2\right)\right)+\left(0,0,1\right)×\partial \left(\left(3\right)\right)$
Signatures:
sts

## Laplacian

Role:
application
Description:

This symbol is used to represent the laplacian function. It takes one argument which should be a vector of scalar valued functions, intended to represent a vector valued function and returns a vector of functions. It should satisfy the defining relation: laplacian(F) = \partial^2(F)/\partial(x_1)^2 + ... + \partial^2(F)/\partial(x_n)^2

Commented Mathematical property (CMP):
laplacian(F) = \partial^2(F)/\partial(x_1)^2 + ... + \partial^2(F)/\partial(x_n)^2
Signatures:
sts

 [First: divergence] [Previous: curl] [Top]

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