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

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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.

Gradient

The gradient of a scalar function φ(x,y,z) is a vector function defined by
φ
φ
.
=
grad
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
], the gradient
ij
i
j
∂φ/∂x
1
2
Page 13-1
...

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