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Divergence
The divergence of a vector function, F(x,y,z) = f(x,y,z)i + g(x,y,z)j
+h(x,y,z)k, is defined by taking a “dot-product” of the del operator with
the function, i.e.,
. Function DIV can be used to calculate
the divergence of a vector field. For example, for F(X,Y,Z) =
[XY,X
2
+Y
2
+Z
2
,YZ], the divergence is calculated, in ALG mode, as follows:
DIV([X*Y,X^2+Y^2+Z^2,Y*Z],[X,Y,Z])
Curl
The curl of a vector field F(x,y,z) = f(x,y,z)i+g(x,y,z)j+h(x,y,z)k,is defined
by a “cross-product” of the del operator with the vector field, i.e.,
. The curl of vector field can be calculated with function
CURL. For example, for the function F(X,Y,Z) = [XY,X
2
+Y
2
+Z
2
,YZ], the curl
is calculated as follows: CURL([X*Y,X^2+Y^2+Z^2,Y*Z],[X,Y,Z])
Reference
For additional information on vector analysis applications see Chapter 15
in the calculator’s user’s guide.
FdivF •∇=
FF ×∇=curl
SG49A.book Page 2 Friday, September 16, 2005 1:31 PM