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Revision as of 17:42, 5 March 2009
, 17:42, 5 March 2009→Note 10: markup
| <math>|(U^\circ \to X^\circ)| ~=~ |(\mathbb{B}^2 \to \mathbb{B}^2)| ~=~ 4^4 ~=~ 256.</math>
| <math>|(U^\circ \to X^\circ)| ~=~ |(\mathbb{B}^2 \to \mathbb{B}^2)| ~=~ 4^4 ~=~ 256.</math>
|}
|}
Given any transformation of this type, <math>G : U^\circ \to X^\circ,</math> the (first order)
differential analysis of <math>G\!</math> is based on the definition of a couple of further transformations, derived by way of operators on <math>G,\!</math> that ply between the (first order) extended universes, <math>\operatorname{E}U^\circ = [u, v, du, dv]</math> and <math>\operatorname{E}X^\circ = [x, y, dx, dy],</math> of <math>G \operatorname{'s}\!</math> own source and target universes.
<pre>
<pre>
First, the "enlargement map" (or the "secant transformation")
First, the "enlargement map" (or the "secant transformation")
EG = <EG_1, EG_2> : EU% -> EX% is defined by the following
EG = <EG_1, EG_2> : EU% -> EX% is defined by the following
