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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:
Laplacian, curl, divergence, grad
Date:
2004-03-30
Version:
3
Review Date:
2006-03-30
Status:
official


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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


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grad

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):
grad(F) = (\partial(F)/\partial(x_1), ... ,\partial(F)/partial(x_n))
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):
curl ( F ) = ( 1 , 0 , 0 ) × ( ( 1 ) ) + ( 0 , 1 , 0 ) × ( ( 2 ) ) + ( 0 , 0 , 1 ) × ( ( 3 ) )
Signatures:
sts


[Next: Laplacian] [Previous: grad] [Top]

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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