The vector-calculus tag has no wiki summary.
9
votes
2answers
404 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 ...
8
votes
3answers
641 views
How do I plot the unit normal field for a surface?
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?
8
votes
2answers
3k 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?
$$ a=\left(
\begin{array}{c}
\text{x1}^3+2\text{x2}^2 \\
3\text{x1}^4+7\text{x2}
\end{array}
...
7
votes
3answers
1k views
Finding unit tangent, normal, and binormal vectors for a given r(t)
For my Calc III class, I need to find $T(t), N(t)$, and $B(t)$ for $t=1, 2$, and $-1$, given $r(t)=\{t,t^2,t^3\}$.
I've got Mathematica, but I've never used it before and I'm not sure how to coerce ...
6
votes
2answers
139 views
How to declare a 3D vector variable?
How can I do vector calculations without telling Mathematica the vector entries?
I have very many arbitrary linear combinations in $\mathbb{R}^3$ which I want to perform some general calculations on ...
6
votes
2answers
378 views
Singularities using VectorPlot
I am trying to plot a vector function of a fluid flow given by
$\vec{V} = (\frac{-\cos(\theta)}{r^2},-\frac{\sin(\theta)}{r^2})$
I am trying to plot it in Mathematica using the command below, I ...
6
votes
1answer
130 views
Smoothing/Averaging 2D Vector Fields
I have a list of 2D vectors defined by {{x,y},{u,v}} and would like to smooth or average the vectors. For example here are 2 vector fields, the second has noise ...
5
votes
1answer
378 views
Is it possible to do vector calculus in Mathematica?
I am trying to rearrange and manipulate some vector differential equations in Mathematica. As far as I understand you have to tell Mathematica that a variable is a vector by specifying the components ...
4
votes
1answer
152 views
3
votes
1answer
271 views
How to change coordinates of a differential operator?
I'm doing a basic quantum mechanics problem and am trying to learn how to do it in Mathematica. Any help would be much appreciated.
$\vec{L} = \vec{x} \times \vec{p}$
where $\vec{x}$ has ...
3
votes
1answer
250 views
Plotting a complicated vector field
If we consider the vector $\left ( A \cdot \nabla \right) \: B$, we have in Cartesian coordinates
$$\left ( A \cdot \nabla \right) \: B = \left ( A \cdot \nabla B_x \right ) e_x + \left ( A \cdot ...
3
votes
2answers
599 views
How to substitute numeric values in a symbolic Jacobian matrix?
I have a multi-variate function from $\mathbb{R}^n\to\mathbb{R}^n$. Choosing any desired initial vector, we can produce the corresponding function value, which is a vector as follows. The main problem ...
3
votes
1answer
115 views
Extending D for four-derivatives
I'm currently trying to consistently define rules for extending D[] to four-derivatives. As 'backend' I'm using the package TRACER (http://library.wolfram.com/infocenter/MathSource/2987/), which can ...
2
votes
3answers
292 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
2answers
218 views
Finding a vector field from a set of points
I have a data set of the type $\{x,y,z\}$ where $(x,y)$ is a point and $z$ is the "value" or magnitude at that point. This gives me a triangular sort of shape since $(x,y,z)$ is not defined along the ...
2
votes
2answers
158 views
Why are these flow lines cut short?
I want to plot some flow lines for a certain vector field, but Mathematica doesn't seem to plot the entire flow line, only a small piece of it. How can I fix this?
...
2
votes
1answer
391 views
Lie-Bracket of two vector fields
I'm new to Mathematica (installed couple of hours ago) and I need to compute a few Lie brackets between two vector fields $f$ and $g$.
$$ f\left(\mathbf{x}\right) =
\left(
\begin{array}{c}
...
2
votes
1answer
209 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 ...
2
votes
1answer
211 views
Vector Analysis: Why are the Grad, Laplacian and Div being evaluated to zero
For the non linear partial differential equation below, why are the Gradient, Laplacian and Divergence being evaluated to zero despite using the VectorAnalysis ...
2
votes
2answers
100 views
CoordinateTransform from Cartesian to Spherical
I have a set of coordinates on the sphere in terms of cartesian coordinates. I would like to convert them to spherical data points. However, when I try to convert the point {0, 0, 1} it tells me that ...
2
votes
1answer
419 views
Calculation of Jacobians for a finite element method simulation
I'm attempting to calculate symbolic expressions for the (Newton's method) Jacobian of a Galerkin finite element method using Mathematica. It would seem that this is a perfect application for symbolic ...
2
votes
0answers
100 views
Derivatives of list elements
Could someone explain the odd behavior of the Derivative function when drawing arguments from lists? We have,
...
2
votes
0answers
111 views
Changing Curl to use Colatitude
How do you change Curl in Mathematica so that it uses theta as latitude rather than as colatittude? Changing theta to ...
1
vote
2answers
194 views
Doing vector manipulations on Mathematica
This is hopefully a simpler version of this previous unanswered question of mine.
Let me just focus on the two expressions $F_2^{(s)}$ and $F_3^{(s)}$ given in A.3 and A.4 of page 19 of this paper. ...
1
vote
1answer
187 views
1
vote
1answer
86 views
Difference between vector's Dimensions
What's the difference between
projection= Table[Conjugate[autoVett[[k]].someVector1], {k, 1, r}]
Dimensions[projection]
that gave me as results ...
1
vote
0answers
206 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 + ...
0
votes
1answer
91 views
Projection of a set of 4D points to the 3D space
Consider the following set of points in the 4D space:
...
0
votes
1answer
872 views
Why I get the “Set::write: ”Tag Times in is Protected." error?
Why I get the error below with this code:
...
-1
votes
0answers
56 views
Doing vector manipulations in Mathematica (Part 2) [closed]
Inspired by the answer from Simon Woods, here, Doing vector manipulations on Mathematica, I thought of doing the intended vector manipulation in the following way but it didn't work!
...
