From 47b521446c95e458053999d7c1091fade2819ff7 Mon Sep 17 00:00:00 2001 From: jannisp Date: Fri, 2 Jul 2021 15:12:06 +0200 Subject: [PATCH] Complete rotation in 2 and 3 dimension --- Mathematik-V-ZF.tex | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/Mathematik-V-ZF.tex b/Mathematik-V-ZF.tex index 1d7e039..3e4ffc8 100644 --- a/Mathematik-V-ZF.tex +++ b/Mathematik-V-ZF.tex @@ -180,7 +180,8 @@ $$f(a) + \frac{f'(a)}{1!}(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \frac{f'''(a)}{3!}(x \section{Operators} $$\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} \frac{\partial}{\partial x},