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Complete rotation in 2 and 3 dimension

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jannisp 2021-07-02 15:12:06 +02:00
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Mathematik-V-ZF.tex
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@ -180,7 +180,8 @@ $$f(a) + \frac{f'(a)}{1!}(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \frac{f'''(a)}{3!}(x
\section{Operators} \section{Operators}
$$\mathrm{div} \, \vec{u} = \frac{\partial u}{\partial x} + \frac{\partial v}{\partial y}$$ $$\mathrm{div} \, \vec{u} = \frac{\partial u}{\partial x} + \frac{\partial v}{\partial y}$$
$$\mathrm{rot} \, \vec{u} = \nabla \times \vec{u} = -\frac{\partial u}{\partial y} + \frac{\partial v}{\partial x}$$ $$\mathrm{rot} \, \vec{u_{xy}} = \nabla \times \vec{u} = (\frac{\partial v}{\partial x} - \frac{\partial u}{\partial y})$$
$$\mathrm{rot} \, \vec{u_{xyz}} = \nabla \times \vec{u} = (\frac{\partial w}{\partial y}-\frac{\partial v}{\partial z}, \frac{\partial u}{\partial z} - \frac{\partial w}{\partial x}, \frac{\partial v}{\partial x} - \frac{\partial u}{\partial y})$$
$$\nabla = \begin{pmatrix} $$\nabla = \begin{pmatrix}
\frac{\partial}{\partial x}, \frac{\partial}{\partial x},