The vector-calculus tag has no wiki summary.
7
votes
2answers
2k views
How to make Jacobian automatically in Mathematica
If we have two vectors, a and b, how can I make Jacobian matrix automatically in Mathematica?
$$ a=\left(
\begin{array}{c}
\text{x1}^3+2\text{x2}^2 \\
3\text{x1}^4+7\text{x2}
\end{array}
...
7
votes
3answers
873 views
Finding unit tangent, normal, and binormal vectors for a given r(t)
For my Calc III class, I need to find $T(t), N(t)$, and $B(t)$ for $t=1, 2$, and $-1$, given $r(t)=\{t,t^2,t^3\}$.
I've got Mathematica, but I've never used it before and I'm not sure how to coerce ...
4
votes
1answer
255 views
How to change coordinates of a differential operator?
I'm doing a basic quantum mechanics problem and am trying to learn how to do it in Mathematica. Any help would be much appreciated.
$\vec{L} = \vec{x} \times \vec{p}$
where $\vec{x}$ has ...
5
votes
1answer
353 views
Is it possible to do vector calculus in Mathematica?
I am trying to rearrange and manipulate some vector differential equations in Mathematica. As far as I understand you have to tell Mathematica that a variable is a vector by specifying the components ...
9
votes
2answers
389 views
Creating randomly oriented planes
I would like to create randomly oriented planes.
This is how I'm attempting to do that:
I create a 2 random unit vectors, $\mathbf{v}_1$, and $\mathbf{v}_2$, in the $x$-$y$ plane
I assume that if I ...
2
votes
3answers
287 views
How do you show a cone inside of a sphere?
I have a sphere of radius 5 and a cone (i.e. z=√(x^2+y^2)) inside of it. I can show them separately, but I'd like to show them together. I've tried a few tricks with opacity, implicit specifications, ...
2
votes
1answer
206 views
Laplacian or Grad of an InterpolatingFunction
For obtaining a Schlieren image from an equation for density, I need to calculate the first derivative of density and make a contour plot.
The below code snippet calculates the first derivative w.r.t ...
1
vote
0answers
197 views
About doing an integral
For a given integer $N$ and some function $f(x,y)$ I want to be able to do an integration of the kind,
$\int_{0} ^{\infty} \prod_ {i=1}^N da_i e^{[\sum_{n=1}^{\infty} \frac{1}{n} \left[ N + ...
