Stoke's theorem
- Grigorios Kostakos
- Founder
- Posts: 461
- Joined: Mon Nov 09, 2015 1:36 am
- Location: Ioannina, Greece
Stoke's theorem
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 \(S\).
Grigorios Kostakos
Create an account or sign in to join the discussion
You need to be a member in order to post a reply
Create an account
Not a member? register to join our community
Members can start their own topics & subscribe to topics
It’s free and only takes a minute
Sign in
Who is online
Users browsing this forum: No registered users and 0 guests