# Divergence; Curl; Reference - HP 50g User Manual

Graphing calculator.

## 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
divF
F
the divergence of a vector field.
For example, for F (X,Y,Z) =
2
2
2
[XY,X
+Y
+Z
,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.,
curl
F
F
. The curl of vector field can be calculated with function
2
2
2
CURL. For example, for the function F (X,Y,Z) = [XY,X
+Y
+Z
,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.
Page 13-2

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F2229aa - 50g graphing calculator