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

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4
votes
1answer
454 views

Checking if an expression is equal to zero

I have 6 points in $\mathbb R^3$ as follows: ...
2
votes
2answers
590 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
338 views

Derivatives of list elements

Bug introduced in 8.0.0 and fixed in 9.0.0 Could someone explain the odd behavior of the Derivative function when drawing arguments from lists? We have, ...
7
votes
1answer
1k 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
496 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? ...
3
votes
1answer
164 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 ...
7
votes
2answers
2k 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 ...
17
votes
4answers
9k 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 ...
1
vote
1answer
356 views

How to find this convolution?

How can I use Mathematica to find the convolution $f*f$ for ...
2
votes
3answers
594 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
826 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 ...
4
votes
1answer
1k 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} ...
6
votes
2answers
1k 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 ...
13
votes
4answers
2k 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
1k 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
429 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 ...
1
vote
1answer
14k views

Why I get the “Set::write: ”Tag Times in is Protected." error?

Why I get the error below with this code: ...
1
vote
1answer
913 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
394 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
votes
2answers
1k 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 ...
19
votes
2answers
11k 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} ...
2
votes
2answers
491 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 ...
10
votes
2answers
628 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 ...