Gradient skalarnega polja

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Naj bo $n$ skalarno polje in je gradient tega skalarnega polja vektorsko polje

$\mbox{grad} u = \left( \frac{\partial u}{\partial x}, \frac{\partial u}{\partial y}, \frac{\partial u}{\partial z} \right)$

Primer: $u(x,y,z) = \frac{z}{x^2+y^2}\,\!$; $\mbox{grad} u(x,y,z) = \left( \frac{\partial u}{\partial x}(x,y,z), \frac{\partial u}{\partial y}(x,y,z), \frac{\partial u}{\partial z}(x,y,z) \right) = \left(\frac{-2xz}{(x^2+y^2)^2}, \frac{-2yz}{(x^2+y^2)^2}, \frac{1}{x^2+y^2}\right)$

Definicija: Definirajmo diferencialni operator nabla, ki ga označimo z $\nabla$ in pomeni:; $\nabla = \left( \frac{\partial}{\partial x}, \frac{\partial}{\partial y}, \frac{\partial}{\partial z} \right)$