# Divergence; Laplacian - HP 48gII User Manual

Graphing calculator.

function (x,y,z) does not exist. In such case, function POTENTIAL returns an
error message. For example, the vector field F(x,y,z) = (x+y)i + (x-y+z)j +
xzk, does not have a potential function associated with it, since, f/ z
h/ x. The calculator response in this case is shown below:

## 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.,
divF
Function DIV can be used to calculate the divergence of a vector field. For
example, for F(X,Y,Z) = [XY,X
ALG mode, as follows:

### Laplacian

The divergence of the gradient of a scalar function produces an operator
called the Laplacian operator. Thus, the Laplacian of a scalar function (x,y,z)
is given by
2
φ
The partial differential equation
Function LAPL can be used to calculate the Laplacian of a scalar function. For
example, to calculate the Laplacian of the function (X,Y,Z) = (X
use:
f
g
F
x
y
2
2
2
+Y
+Z
,YZ], the divergence is calculated, in
2
2
φ
φ
φ
2
2
x
x
2
= 0 is known as Laplace's equation.
h
z
2
φ
2
x
2
2
+Y
)cos(Z),
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