basic_tools:variational_calculus:functional
Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision | ||
|
basic_tools:variational_calculus:functional [2018/03/14 15:58] iiqof |
basic_tools:variational_calculus:functional [2020/04/12 14:41] (current) jakobadmin |
||
|---|---|---|---|
| Line 2: | Line 2: | ||
| - | Let $\Omega(\mathcal{Q})$ be the set of functions $q:\mathbb{R} \to \mathcal{Q}$, 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. | ||
| Line 27: | Line 26: | ||
| - | 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 a point (i.e. a function is also a functional)... |
basic_tools/variational_calculus/functional.1521039498.txt.gz · Last modified: 2018/03/14 14:58 (external edit)
Page Tools
Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Share Alike 4.0 International
