Apllying Generalized Stokes Theorem

82 Views Asked by At

I'm having no difficulties to understand the theorical concepts about the Generalized Stokes Theorem, but I'm having trouble to applying it.

Let $M$ the semiellipsoid in $\mathbb{R}^{3}$ defined by $4x^{2}+y^{2}+4z^{2}=4$ and $y\geq 0$. Show that M is, in fact, an oriented 2-manifold and describe the boundary of $M$. Well, to describe $\partial M$ is easy.

How can I find the induced orientation for $\partial M$ by the orientation of $M$? Actually, is there any method to find a orientation?

If I know that I can verify the Stokes Theorem, but I'm not getting.