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basic_tools:variational_calculus:functional

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 basic_tools:variational_calculus:functional [2018/03/15 14:31]iiqof basic_tools:variational_calculus:functional [2020/04/12 14:41] (current)jakobadmin Both sides previous revision Previous revision 2020/04/12 14:41 jakobadmin 2018/03/15 14:31 iiqof 2018/03/14 16:00 iiqof 2018/03/14 15:58 iiqof 2018/03/10 17:28 iiqof Clarification2018/03/10 17:05 iiqof created Functional Page 2020/04/12 14:41 jakobadmin 2018/03/15 14:31 iiqof 2018/03/14 16:00 iiqof 2018/03/14 15:58 iiqof 2018/03/10 17:28 iiqof Clarification2018/03/10 17:05 iiqof created Functional Page Line 3: Line 3: 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.