gradient

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Cartesian coordinates

\boldsymbol\nabla f(x,y,z) =\frac {\partial f }{ \partial x}\mathbf{\hat x} + \frac{\partial f }{ \partial y}\mathbf{\hat y} + \frac{\partial f }{ \partial z}\mathbf{\hat z}

Curvilinear coordinates

Cylindrical coordinates

\boldsymbol\nabla f(\rho, \theta, z) = \frac{\partial f }{ \partial \rho}\boldsymbol{\hat \rho} + \frac{1 }{ \rho}\frac{\partial f }{ \partial \phi}\boldsymbol{\hat \phi} + \frac{\partial f }{ \partial z}\mathbf{\hat z}.

Spherical coordinates

\boldsymbol\nabla f(r, \theta, \phi) = \frac{\partial f }{ \partial r}\mathbf{\hat r} + \frac{1 }{ r} \frac{\partial f }{ \partial \theta}\boldsymbol{\hat \theta} + \frac{1 }{ r\sin\theta}\frac {\partial f }{ \partial \phi}\boldsymbol{\hat \phi}
Retrieved from "http://www.mathematics.thetangentbundle.net/wiki/Vector_calculus/gradient"
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