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

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0
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1answer
575 views

Symbolic matrix simplification and solving

I am trying to expand or solve an equation that contains matrices for a certain matrix, but it is not working: ...
1
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1answer
311 views

Rotating a set of 3D points against an arbitrary axis

I want to rotate a list of 3D points around unit vector (1,0,1) by the angle of Pi. How can I accomplish it?
1
vote
1answer
97 views

Simplify ignores DiracDelta contribution from Coulomb sources

Executing the following line, Simplify[Div[Grad[-1/Sqrt[{x, y, z}.{x, y, z}], {x, y, z}], {x, y, z}]] yields 0. However, this is incorrect, since ...
0
votes
1answer
223 views

replace is not happening for specific vector valued expression

Given x[t_] := {Subscript[x, 1][t], Subscript[x, 2][t]} following replace works fine x[t] /. x[t] -> 0 0 but following ...
5
votes
1answer
166 views

Integration over a convex combination of a region: $\int_{\Omega} (w_1 z_1 + w_2 z_2)^{1-\sigma} d (z_1, z_2)$ where $\Omega = \{ z_1 + z_2 = 1\}$

Take $w,z\in R^{n}$. I am interested in integrating (as generically if possible) $$\int_{\Omega}(w \cdot z)^{1-\sigma} d z$$ Where the domain of $\Omega$ is $1$ dimension, and includes the convex ...
1
vote
0answers
133 views

Simple Jacobians, Gradients, etc. with arbitrary length vectors/matrices?

Is there any way (or a package built for it) can do simple operations with vectors and matricies of arbitrary size, but conforming extents? For the simplest example to test, given an arbitrary vector ...
1
vote
1answer
249 views

Blank VectorPlot

I'm trying to draw a VectorPlot of a function that admittedly probably is not very well suited for such a plot. But at the moment I just get a white sheet and I ...
2
votes
0answers
58 views

Draw Vector Tangent to Point on Parameterized Curve [duplicate]

I define the vector function $\vec{r}(t)$ by r[t_] = {t, Cos[t], Sin[t]} The command r'[t] gives the vector tangent to the ...
3
votes
1answer
935 views

Normal and Tangent of Acceleration in 3D

I am trying to find the normal and tangent of acceleration. I know the formula for the tangent of acceleration is $((Acceleration . Velocity)/(Velocity.Velocity))*Velocity$ and the normal of ...
1
vote
1answer
138 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 ...
8
votes
2answers
1k 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 ...
0
votes
1answer
297 views

Projection of a set of 4D points to the 3D space

Consider the following set of points in the 4D space: ...
1
vote
2answers
329 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. ...
4
votes
1answer
504 views

Checking if an expression is equal to zero

I have 6 points in $\mathbb R^3$ as follows: ...
2
votes
2answers
692 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
396 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
563 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
170 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 ...
9
votes
2answers
3k 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 ...
18
votes
4answers
11k 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
384 views

How to find this convolution?

How can I use Mathematica to find the convolution $f*f$ for ...
2
votes
3answers
654 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, ...
4
votes
1answer
954 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 ...
14
votes
4answers
3k 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
2k 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
464 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
18k 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
967 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
412 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 ...
20
votes
2answers
13k 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} x_1^3+2x_2^2 \\ 3x_1^4+7x_2 \end{array} \right);b=\left( ...
2
votes
2answers
554 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 ...
11
votes
2answers
668 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 ...