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] 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 | ||
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| - | 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. | ||
basic_tools/variational_calculus/functional.txt · Last modified: 2020/04/12 14:41 by jakobadmin
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