# Tagged Questions

Questions on spherical coordinates, a three-dimensional coordinate system where a point is represented in terms of its distance from the origin, and its latitude and longitude angles (or complements thereof).

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### analytic solution poisson equation spherical coordinates

I'm trying to analitically solve a poisson equation $\nabla^{2}p(r,\theta,\phi)=f(r,\theta)$ in spherical coordinates; the boundary condition is $p(\infty,\theta,\phi)$=0. I'm quite used to the ...
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### How can I evaluate this integral over a sphere, with surface area element instead of volume element?

$$\int_S (x^2 + y^2)d\sigma,$$ where S is the sphere of radius 1 centered at (0,0,0) and $\sigma$ is surface area. I would like some hints on how to proceed. This is tricky, since I am not being ...
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### Help with limits of integration in spherical coordinates

$$\int_\Omega F(\theta,\phi) \sin(\phi) \, d\Omega$$ where $\Omega$ represents the (outer) surface of a spherical cap on a unit sphere. Specifically, let the center of the spherical cap be in some ...
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### Manifolds, coordinate systems, books

Which books, say Lee's Introduction to Smooth Manifolds or Munkres' Analysis on Manifolds explains how the theory of a differentiable manifolds can be used to solve a problem that is expressed in a ...
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### Convert $x^2+y^2+z^2=49$ to spherical coordinates

I really need your help to convert this $x^2+y^2+z^2=49$ to spherical coordinates. I tried it and I got $(R\sin\phi\cos\theta)^2+(R\sin\phi\sin\theta)^2+(R\cos\phi)^2=49$. But it says that it is ...
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