Operatore di Laplace: differenze tra le versioni
Contenuto cancellato Contenuto aggiunto
Riga 89:
</math>
:<math> \nabla^2 = {1 \over r} {\partial \over \partial r} \left( r {\partial f \over \partial r} \right)
+ {1 \over r^2} {\partial^2 f \over \partial \theta^2} + {\partial^2 f \over \partial z^2 } </math>
e nelle [[coordinate sferiche]] assume la forma:
:<math> \nabla^2 f = {1 \over r^2} {\partial \over \partial r} \left( r^2 {\partial f \over \partial r} \right) + {1 \over r^2 \sin \theta} {\partial \over \partial \theta} \left( \sin \theta {\partial f \over \partial \theta} \right)
Riga 100:
:<math> = {1 \over r} {\partial^2 \over \partial r^2} \left( rf \right) + {1 \over r^2 \sin \theta} {\partial \over \partial \theta} \left( \sin \theta {\partial f \over \partial \theta} \right) + {1 \over r^2 \sin^2 \theta} {\partial^2 f \over \partial \phi^2} </math>
In [[coordinate curvilinee]]
:<math>\nabla^2 = \nabla \xi^m \cdot \nabla \xi^n {\partial^2 \over \partial \xi^m \partial \xi^n} + \nabla^2 \xi^m {\partial \over \partial \xi^m } </math>
dove si utilizza la [[notazione di Einstein]].
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