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Questions tagged [vector-calculus]

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Questions on dealing with vector calculus functions of Mathematica such as Grad, Div, Curl, Laplacian and their representations in various coordinate systems.

313 questions
Newest Active Bountied Unanswered
46 votes
3 answers
51k views

If we have two vectors, $a$ and $b$, how can I make Jacobian matrix automatically in Mathematica? $$ a=\left( \begin{array}{c} x_1^3+2x_2^2 \\ 3x_1^4+7x_2 \end{array} \right);b=\left( \begin{array}{...
George Mills's user avatar
  • 963
33 votes
4 answers
28k views

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 ...
a98's user avatar
  • 433
26 votes
4 answers
2k views

I have a usual mathematical background in vector and tensor calculus. I was trying to use the differential operators of Mathematica, namely Grad, ...
Hosein Rahnama's user avatar
  • 1,737
21 votes
2 answers
7k views

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 ...
Holger Schmitz's user avatar
  • 378
19 votes
4 answers
8k views

The question is pretty much in the title; I'm about to teach my multivariable calculus students about orientations on surfaces, and I would like to be able to show them pictures. Any ideas?
Paul Siegel's user avatar
  • 291
17 votes
1 answer
3k views

I want to use the dipole coordinate system as defined in this paper: http://arxiv.org/abs/physics/0606044 I see that Mathematica can do all kinds of vector analysis using different kinds of ...
jvriesem's user avatar
  • 437
16 votes
3 answers
8k views

How can I do vector calculations without telling Mathematica the vector entries? I have very many arbitrary linear combinations in $\mathbb{R}^3$ which I want to perform some general calculations on (...
Foo Bar's user avatar
  • 345
15 votes
2 answers
8k views

Mathematica includes two nice built-in tools to visualize vector fields, VectorPlot and StreamPlot. The latter is a useful tool, ...
Emilio Pisanty's user avatar
  • 10.5k
14 votes
4 answers
3k views

I would like to expand a dot product which includes vectors $ \vec{v_1}, \vec{v_2}, \dots $ and constants $ c_1, c_2, \dots $ So that: $$ c_1 \vec{v_1} \cdot \left(c_2 \vec{v_2}+ c_3 \vec{v_3}+\dots ...
atom44's user avatar
  • 307
13 votes
2 answers
1k views

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 ...
BeauGeste's user avatar
  • 2,907
11 votes
1 answer
58k views

Why I get the error below with this code: ...
Aurelius's user avatar
  • 361
10 votes
3 answers
1k views

About the setting: We have a 3D simulation box with side $l$ and our catesian coordinate system is set with its origin at the centre of the box. We have a number $N$ of spherocylinders of aspect ...
user avatar
10 votes
2 answers
4k views

I am trying to plot a vector function of a fluid flow given by $\vec{V} = (\frac{-\cos(\theta)}{r^2},-\frac{\sin(\theta)}{r^2})$ I am trying to plot it in Mathematica using the command below, I ...
l3win's user avatar
  • 735
10 votes
1 answer
2k views

I'm drawing the magnetic field lines of a rotating dipole (magnetic field distorded by emission of radiation). Currently, my Mathematica 7.0 code is fully working, but I'm having a constraint which I ...
Cham's user avatar
  • 4,203
10 votes
0 answers
412 views

Is it possible to do matrix calculus in Mathematica, like in http://www.matrixcalculus.org/ ? One of the main limitations I've found in Mathematica is that symbols are assumed to be scalars by ...
yewang's user avatar
  • 327

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