# 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).

0answers
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### Biot-Savart Law to construct vector potential for divergence free vector field on $\mathbb{R}^3$

I would like to confirm a method I am trying to use which uses the Biot-Savart Law to construct a vector potential $\underline{w}$ for a divergence free vector field $\underline{v}$ on $\mathbb{R}^3$. ...
1answer
35 views

### Euclidean norm on integer lattice

Does the Euclidean $L^2$ norm (and distance) make any sense on an integer lattice in $\mathbb{R}^n$? And what is the preferable way of calculating a type of norm in such spaces?
1answer
55 views

1answer
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### coupled vector equations

So I am trying to solve some problems from Hughston and Tod's Introduction to General Relativity. I need help with the following system of equations: $$aX_i+bY_i=P_i$$ $$\epsilon_{ijk} X_jY_k=Q_i$$ ...
3answers
41 views

### Vector Equation involving cross product

I am trying to solve a problem from Vector Analysis, which should be fairly easy, but somehow I can't solve it. Solve for $X_i$ $$kX_i+\epsilon_{ijk}X_jP_k=Q_i$$ Also I am trying to solve the ...
2answers
54 views

### Curl of a Point Vortex Flow and its Circulation

I have the following 2D vector field $U=(u,v)=\frac{1}{x^2+y^2}(y,-x)$. When taking the curl of this field it returns zero. But when I take the circulation of the field defined as \Gamma=\oint_C U\...
1answer
53 views

### Divergence theorem in curvilinear coordinates

Suppose I have a tensor \begin{gather} \stackrel{\leftrightarrow}{A} = \begin{bmatrix} a_{11}(\vec{r}) & a_{12}(\vec{r}) & a_{13}(\vec{r})\\ a_{21}(\vec{r}) & a_{22}(\vec{r}) & a_{23}(...
0answers
20 views

### Integral of divergence over a closed surface

I am reading a paper, where an integral of a divergence over a closed surface is used without proof. $\oint_S \nabla \cdot \vec{v}(\vec{r}) = 0$, where $\vec{v}$ is tangential to the surface (\$\vec{...