2007 | OriginalPaper | Buchkapitel
Appendices
Erschienen in: Introduction to Classical Geometries
Verlag: Birkhäuser Basel
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To extend the concept of differentiability to a function of several variables,
F
: ℝ
n
→ℝ, at a point
P
0 of its domain, we must recall that the value of a differentiable function at a point close to
P
0
,
P
0
+
$$ \bar h $$
, can be approximated by the value of the function at the point,
F
(
P
0), plus the value of a linear transformation, called precisely the
derivative at
P
0
, applied to the increment
$$ \bar h $$
, where
$$ \left\| {\bar h} \right\| $$
is sufficiently small.