The vector-calculus tag has no wiki summary.
0
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2answers
145 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. ...
3
votes
1answer
138 views
2
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2answers
92 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
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0answers
88 views
Derivatives of list elements
Could someone explain the odd behavior of the Derivative function when drawing arguments from lists? We have,
...
6
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1answer
113 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 ...
2
votes
2answers
152 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?
...
7
votes
3answers
849 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 ...
3
votes
1answer
111 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
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0answers
106 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 ...
5
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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 ...
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 ...
1
vote
1answer
175 views
2
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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, ...
3
votes
1answer
235 views
Plotting a complicated vector field
If we consider the vector $\left ( A \cdot \nabla \right) \: B$, we have in Cartesian coordinates
$$\left ( A \cdot \nabla \right) \: B = \left ( A \cdot \nabla B_x \right ) e_x + \left ( A \cdot ...
2
votes
1answer
352 views
Lie-Bracket of two vector fields
I'm new to Mathematica (installed couple of hours ago) and I need to compute a few Lie brackets between two vector fields $f$ and $g$.
$$ f\left(\mathbf{x}\right) =
\left(
\begin{array}{c}
...
8
votes
3answers
592 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?
6
votes
2answers
339 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 ...
2
votes
1answer
205 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 ...
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 ...
0
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1answer
648 views
Why I get the “Set::write: ”Tag Times in is Protected." error?
Why I get the error below with this code:
...
1
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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 + ...
2
votes
1answer
407 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
1answer
205 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 ...
3
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2answers
559 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 ...
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2answers
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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}
...
2
votes
2answers
213 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 ...
