Tagged Questions

Questions related to understanding line integrals, vector fields, surface integrals, the theorems of Gauss, Green and Stokes. Some related tags are (multivariable-calculus) and (differential-geometry).

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Vector Calculus Divergence Theorem Textbook Answer Confusion

here's a particular question I'm working on that the textbook doesn't have the same answer as me. Use The Divergence Theorem for: $F = |r|r$, where $r = <x,y,z>$, and $S$ consists of the ...
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What is this operator? (Three times curve integral)

What is this operator: https://help.libreoffice.org/File:Fo21611.png I have been seeing it in text-edit documents, but never found any explanation to it. I guess that it is a closed curve integral ...
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Computing the vector Laplacian in spherical coordinates using metric tensor

I want to compute the Laplacian of a vector in spherical coordinates using metric tensor. I started only with the first component but I have obtained a different formula! Let be $\vec{v}$ a vector ...
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Is it d^3V or dV when integrating for volume (triple integral)?

In a volume integral dxdydz is shortened to dV. I have also seen d^3V. So dcubed V. What is the correct way to write it, or are both correct?
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Torque when system is constrained to rotate about $\vec{r}$ [closed]

Let $\vec{F}, \vec{r}$ and $W$ are elements of $R^{3}$. Given $\vec{F}= -\nabla{W}$. Let system be constrained to rotate about $\vec{r}$. How can we find Torque?
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Finding the radii of an ellipse from the intersection of a plane and a sphere

I'm trying to solve the following problem, regarding Stokes Theorem: $F = z i + xj + yk$; C the curve of intersection of the plane $x + y + z = 0$ and the sphere $x^2 + y^2 + z^2 = 1$ [Hint: ...
I heard about an interesting theorem. Poincaré-Hopf Index Theorem : If $\vec{v}$ is a smooth vector filed on the compact, oriented manifold $X$ with only finitely many zeros, then the global ...