Content License: Creative Commons Attribution Non Commercial Share Alike 4.0 International (CC-BY-NC-SA-4.0)Credit must be given to the creatorOnly noncommercial uses of the work are permittedAdaptations must be shared under the same termsDownloadsRotationNickDefinition¶rotf=∇⃗×f=(∂∂x1⋮∂∂xn)×(f1⋮fn)\text{rot}f = \vec \nabla \times f = \begin{pmatrix}\frac{\partial}{\partial x_{1}}\\ \vdots \\ \frac{\partial}{\partial x_{n}}\end{pmatrix} \times \begin{pmatrix}f_{1} \\ \vdots \\ f_{n}\end{pmatrix}rotf=∇×f=⎝⎛∂x1∂⋮∂xn∂⎠⎞×⎝⎛f1⋮fn⎠⎞(1)Übung¶Untersuchen von f(x,y,z)=(2x2yzy2+xz−xy2zx2y−xyz2−2yz)f(x,y,z) = \begin{pmatrix} 2x^{2}yz \\ y^{2}+xz-xy^{2}z \\ x^{2}y-xyz^{2}-2yz\end{pmatrix}f(x,y,z)=⎝⎛2x2yzy2+xz−xy2zx2y−xyz2−2yz⎠⎞(2) auf Divergenz und RotationLösungDivergenz ist 0rotf=(x2−xz2−2z−x+xy2−2xy+yz2+2x2yz−y2z−2x2z)\text{rot}f = \begin{pmatrix} x^{2}-xz^{2}-2z-x+xy^{2} \\ -2xy+yz^{2}+2x^{2}y \\ z-y^{2}z-2x^{2}z \end{pmatrix}rotf=⎝⎛x2−xz2−2z−x+xy2−2xy+yz2+2x2yz−y2z−2x2z⎠⎞Mathematik I: AnalysisDivergenzMathematik I: AnalysisApproximationen