# Tagged Questions

$$\iiint\limits_H (x^2+y^2) \, dx \, dy \, dz \\ H=\{(x,y,z) \in R^3: 1 \le x^2+y^2+z^2 \le9, z \le 0 \}$$ I'm using Spherical coordinate system: $$x=r\cos \theta \cos\phi$$ $$y=r\cos \theta ... 1answer 47 views ### Minimum of a potential function I'm looking for extremes (minimum) of$$V = \frac{\alpha}{|\vec{r}_1-\vec{r}_2|} + \beta (\vec{r}_1 + \vec{r}_2)\cdot \vec{e}_z where $\vec{r}_i = ... 2answers 57 views ### Integral using spherical coordinates I am trying to compute the volume of the following set : intersection of cylinder$x^2 + y^2 \leq R$and sphere$x^2 + y^2 + z^2 \leq 4R^2$. I am having trouble setting up the integral properly ... 1answer 43 views ### Del on Riemannian manifolds I was supposed to figure out what$grad(div(e_r))$is, where$e_r$is the unit vector in spherical coordinates. In the following I assume$g:=diag(1,r^2,r^2sin^2(\theta))$be the metric tensor. My ... 1answer 459 views ### integral of a spherically symmetric 3-dimensional function over all space I'm very sorry because it may be a very basic question but I'm not able whether to solve it for sure, nor to find an answer in stackexchange or elsewhere. I have to calculate$ \int \int ...
For a function $f(r, \vartheta, \varphi)$ given in spherical coordinates, how can the Fourier transform be calculated best? Possible ideas: express $(r,\vartheta,\varphi)$ in cartesian coordinates, ...