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 Post subject: Stoke's theorem Posted: Sat Jan 16, 2016 1:45 am
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Location: Ioannina, Greece
In the Euclidean space $\mathbb{R}^3$ the plane $z=-\frac{1}{2}$ cuts the unit sphere $S^2=\big\{{(x,y,z)\in\mathbb{R}^3\;|\; x^2+y^2+z^2=1}\big\}$ in two surfaces $S$ and $T$. Let $S$ be the surface which passes through the point $(0,0,1)$. Let the vector field $\overline{F}(x,y,z)=\Bigg({\begin{array}{c} x-y\\ y-z\\ z-x \end{array}}\Bigg)\,,\quad (x,y,z)\in\mathbb{R}^3\,.$ Verify Stokes' theorem for the field $\overline{F}$ and the surface $S$.

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Grigorios Kostakos

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