# Chapter 13 - Vector Analysis Applications; The Del Operator; Gradient - HP 48gII User Manual

Graphing calculator.

Chapter 13
Vector Analysis Applications
This chapter describes the use of functions HESS, DIV, and CURL, for
calculating operations of vector analysis.

### The del operator

The following operator, referred to as the 'del' or 'nabla' operator, is a vector-
based operator that can be applied to a scalar or vector function:
[ ]
When applied to a scalar function we can obtain the gradient of the function,
and when applied to a vector function we can obtain the divergence and the
curl of that function. A combination of gradient and divergence produces the
Laplacian of a scalar function.

The gradient of a scalar function φ(x,y,z) is a vector function defined by
φ
φ
.
=
Function HESS can be used to obtain the gradient of a
function.. The function takes as input a function of n independent variables
φ(x
, x
, ...,x
), and a vector of the functions ['x
1
2
n
returns the Hessian matrix of the function, H = [h
of the function with respect to the n-variables, grad f = [ ∂φ/∂x
∂φ/∂x
], and the list of variables ['x
n
visualize in the RPN mode.
2
X
+ XY + XZ, we'll apply function HESS to this scalar field in the following
example:
Thus, the gradient is [2X+Y+Z, X, X].
[ ]
[ ]
=
+
+
i
j
x
y
' 'x
1
', 'x
',...,'x
']. This function is easier to
1
2
n
Consider as an example the function φ(X,Y,Z) =
[ ]
k
z
'...'x
']. The function
2
n
∂x
] = [∂φ/∂x
ij
i
j
∂φ/∂x
1
2
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