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basic_tools:variational_calculus:functional

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basic_tools:variational_calculus:functional [2018/03/14 16:00]
iiqof
basic_tools:variational_calculus:functional [2020/04/12 14:41]
jakobadmin
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 Let $\Omega(\mathcal{Q})$ be the set of functions $q:​\mathbb{R^n} \to \mathcal{Q}$,​ then a //​functional//​ S is a map  Let $\Omega(\mathcal{Q})$ be the set of functions $q:​\mathbb{R^n} \to \mathcal{Q}$,​ then a //​functional//​ S is a map 
-$$ + 
-S:\Omega \to \mathbb{R}; S[q] \mapsto \alpha \in\mathbb{R} +$$ S:\Omega \to \mathbb{R}; S[q] \mapsto \alpha \in\mathbb{R} ​.$$ 
-$$ +
  
 So we can see how a functional is a //function of functions// as we said before, this is the reason why the notation $S[\cdot]$ instead of $S(\cdot)$, to remind that it is more that the eyes meet.  So we can see how a functional is a //function of functions// as we said before, this is the reason why the notation $S[\cdot]$ instead of $S(\cdot)$, to remind that it is more that the eyes meet. 
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-But there can be other functionals:​ maximum/​minimum value of a function, ​value at point $x$...+But there can be other functionals:​ maximum/​minimum value of a function, ​evaluation of the function ​at point (i.e. a function is also a functional)...
basic_tools/variational_calculus/functional.txt · Last modified: 2020/04/12 14:41 by jakobadmin