Questions tagged [vector-calculus]
Questions on dealing with vector calculus functions of Mathematica such as Grad, Div, Curl, Laplacian and their representations in various coordinate systems.
299
questions
1
vote
1
answer
145
views
PlotLegends` and VectorAnalysis is now obsolete on Mathematica v 12.0.0.0 Home edition [closed]
My code was working a few months ago. Now I receive the messages:
...
- 2,154
2
votes
1
answer
157
views
Plotting list data of cross product of field vectors
I have some experimental data points of electric Ey(t, value) and magnetic field Hz(t, value). I am trying to calculate the ...
CommunityBot
- 1
5
votes
3
answers
794
views
Explicitly construct tensor quantities with given symmetries
I am trying to use mathematica to generate explicitely a tensor. I know multiple thing about it. Let's call it $C_{\mu\nu\lambda\sigma}$. This guy has to be symmetric in the two first indices ${\mu,\...
- 65.3k
3
votes
2
answers
91
views
Eigenvalues and classification of critical points [closed]
I started with a function (x,y) and tried to write the code to work out the eigenvalues and classify the critical points.
The output it all good up until I try to use Which[] to classify the critical ...
- 123k
3
votes
5
answers
2k
views
How to obtain the gradient of a function as a function?
The Grad function allows me to get the gradient of a function like this:
...
- 1
2
votes
1
answer
74
views
Differentiating unit tangent vector does not work
I am new to Mathematica and I want to visualize the tangent and normal vector field of a particular embedding of the circle. In my code it is [CapitalGamma][s]. When I put the unit tangent vector (uT[...
- 61.2k
1
vote
1
answer
67
views
Plotting the electric field of the Lienard-Wiechert potentials
I am having a very rough time trying to properly define and then vectorplot the expression for the electric field of the Lienard-Wiechert potentials I have been trying to code. Up to this point, the ...
- 3,797
6
votes
3
answers
3k
views
How to calculate the surface integral of a vector field?
Suppose the oriented surface is described as, the outside of an upper hemisphere $S:x^2+y^2+z^2=1$ inside the cylinder $x^2-x+y^2=0$
The vector field is : ${\vec F}=<x^2,y^2,z^2>$
How to ...
- 23.2k
0
votes
0
answers
66
views
How to get $ (\vec{A} \cdot \nabla) \vec{b}) $ to evaluate in Wolfram language [duplicate]
I am quite new to Wolfram language, and I am trying to use it to prove the equality $$ \nabla (A \cdot B) = A \times (\nabla \times B) + B \times (\nabla \times A) + (A \cdot \nabla)B + (B \cdot \...
- 18.1k
1
vote
2
answers
223
views
Map water runoff flows near Ellicott City, Maryland
Ellicott City, Maryland was the site of a flash flood several years ago due to the local topography. How can we use the Wolfram Language to show the direction water flows at many points near that city?...
- 45.4k
1
vote
3
answers
147
views
Drawing circles on top of a vector field drawn using VectorPlot
I am using the command
VectorPlot[{{y, -x}}, {x, -4, 4}, {y, -4, 4}]
to plot the vector field $\vec{V}=y\hat{i}-x\hat{j}$. On top of this, I need to draw circles ...
- 62.8k
2
votes
1
answer
134
views
Inactive form for PDE and symmetry
I would like to solve the following non-linear Poisson equation (as a toy problem for a more complicated problem)
...
- 39.1k
2
votes
0
answers
261
views
Computing quadratic differential trajectories with Mathematica
There was a question about a particular case of this, Quadratic differentials; seemingly it contained too little information, so let me try again. This will be also a second take on my previous ...
- 1
4
votes
2
answers
350
views
How are Symbolic Vectors Defined?
It is my understanding that undefined symbols are considered scalars, so I can't index variables that aren't defined.
It is possible to define a symbol as a vector of symbols as follows, allowing ...
- 13.5k
0
votes
0
answers
32
views
How do I prevent, or get rid of the <code>Abs^\[Prime]</code> in the output of a partial of a Normalize[vector]? 12.0.0 for Microsoft Windows [duplicate]
12.0.0 for Microsoft Windows
How do I prevent, or get rid of the Abs^[Prime] in the output of a partial of a Normalize[vector]?
The code below shows the problematic ...
- 1,447
1
vote
1
answer
58
views
'not a variable' error when applying D function [closed]
I am trying to apply differentiation, D, operator in Mathematica to a vector. Importantly, I want to carry out the operation with respect to another vector. Basically, I am computing a Jacobian matrix....
- 45.4k
0
votes
0
answers
51
views
Polar to Cartesian coordinate transformations [duplicate]
I'm trying to plot the energy boundary function EBminus[r, \theta, LL, S, BB] using Polar to Cartesian coordinate transformations. The plot should be a closed curve....
- 87
1
vote
0
answers
63
views
Vector Potential Function of Vector Field with DSolve?
(This is a redux of this.)
Why doesn't this work? I have a vector field F1 whose div is 0 with a known vector potential function A2, and I try to get DSolve to solve the differential equation for A2 ...
- 263
0
votes
0
answers
132
views
Find Vector Potential from Vector Field with Div = 0?
This works to compute the scalar potential function of a vector field whose curl is 0 (using the DifferentialForms.m package):
...
- 263
2
votes
1
answer
113
views
Preventing Mathematica from applying product rule
I am programming viscous terms of compressible Navier-Stokes equations
...
- 39.1k
1
vote
2
answers
115
views
Showing each component of velocity in a helix
In this animation, I want to show each component of velocity (V_x, V_y and V_z) with arrows ...
- 61.2k
2
votes
1
answer
59
views
Simplifying expressions with dot or non-commutative product (without the help of NCAlgebra)
I have two expressions (with dot and non-commutative product):
$f=J^T.x+J.x$
$g=J^T**x+J**x$
I want to simplify them and get the following expressions:
$f=(J^T+J).x$
$g=(J^T+J)**x$
In an attempt to ...
- 2,344
1
vote
2
answers
184
views
Calculating Matrix Derivatives
I'm sorry if this is an easy question, but I'm trying to refresh my memory on calculating derivatives of matrix products and have been reading the Matrix Cookbook. I'd like to rebuild my intuition by ...
- 11.7k
0
votes
1
answer
128
views
How to stack several vector plots using StreamPlot?
I would like to plot several stream plots as is in ref/StreamPlot (Mathematica 12).
As is reported in the section: Generate a list of stream plots of varying [Lambda]:
I did not change but it does not ...
CommunityBot
- 1
1
vote
0
answers
78
views
How to define a vector operator?
I know how to define a single-variable differential operator like
Clear[Op]
Op[x_] := a D[#, {x, 1}] &
and I can do operations like
...
- 189
3
votes
5
answers
845
views
Calculating length of curve based on data points?
I had around $1000$ data points $(x,y,z)$ and when I plot them they seem to lie on a closed curve. I carefully checked the data points and the points do not repeat rather they are somewhat close to ...
- 199
3
votes
1
answer
134
views
Why isn't the vector field being plotted over the entire torus?
I am trying to plot a vector field over a torus. Here is my code and the image it produces:
...
- 61.2k
2
votes
1
answer
64
views
Solving a vector diferential equation lead to ComplexInfinity Encountered non-numerical value for a derivative at t == 0
I'm trying to solve the following Vector PDE:
I implemented the following code:
...
- 11.7k
1
vote
0
answers
47
views
Using `GradientFilter[]` and `GradientOrientationFilter[]` to reproduce Matlab's `gradient()` function
In 'gradient' function in MMA, two methods are given to reproduce Matlab's gradient() function. I thought that ...
- 123k
0
votes
0
answers
104
views
Implementing the 3D Radon transform
I am wondering how to implement the Radon transform, the 3D Radon transform, that is, given a 'density' function $f: \mathbb{R}^3\to \mathbb{R}$ The Radon transform of $f$ is $$Rf(s,w)= \int_{x\cdot w=...
- 109
0
votes
0
answers
58
views
How to express elemental operations in matrix form?
I ran the following code:
X = Array[x, {5, 4}];
W = Array[w, {4, 3}];
Y = Array[y, {5, 3}];
D[Norm[X.W-Y, "Frobenius"]^2, {W}]//MatrixForm
However, mma ...
- 1
0
votes
0
answers
52
views
How to input a specific three-variable function into this definition?
I have the following expression:
...
- 101
0
votes
0
answers
47
views
Looking to compute $e^{\phi}\Delta^2 f e^{-\phi}$ in a coordinate-free way
Let $f, \phi:\mathbb{R}^n\to\mathbb{R}$ with $\phi(x)$ looking like $\phi(x)=(x+a)^2$ for some $a\in\mathbb{R}^n$. I am interested in computing $$L_\phi(f)=e^{\phi}\Delta^2 \left(e^{-\phi}\,f\right)$$ ...
- 123k
0
votes
0
answers
57
views
Calculation of SolidAngle not recognizing region?
Basically I'm trying to calculate the solid angle of a square seen from the origin. I defined the region (in two different ways) and tried running the function but it does not give any output.
Why is ...
- 58
3
votes
2
answers
123
views
Solving an integral vectorial equation by iterations
I'm triying to solve a problem like the following:
$$
\binom{f(t)}{g(t)}=\binom{f_0(t)}{g_0(t)}+\lambda\int_0^t ds\hat{A}(s)\binom{f(s)}{g(s)},
$$
where $f_0(t),g_0(t)$ and $\hat{A}(t)$ (a $2\times2$ ...
- 491
0
votes
0
answers
45
views
Output of expressions unable to have operations be performed on the expression
I am currently trying to use the code linked in the catalog of spacetimes pdf to calculate chirstoffel symbols for a metric which follows as
n := 4
...
- 119
0
votes
0
answers
61
views
Algorithm: Permutations & Signature
Theoretical side
Simple example: If I have two sets $A_1=\{1,3\} ,A_2=\{2,3\}$
and Permutations[{1, 2, 3}]= $\left(
\begin{array}{ccc}
1 & 2 & 3 \\
1 &...
- 732
1
vote
1
answer
78
views
Derivative of quadratic form in NCAlgebra
I installed the NCAlgebra package in the hope that it contains enough rules for symbolic work with most branch-matrix expressions.
...
- 1,916
3
votes
2
answers
150
views
Set of quadratic forms and linear algebra
I have a set of quadratic forms.
$L_{1}=u_1^TJ_{1}u_1$
$L_{2}=u_2^TJ_{2}u_2$
$L_{3}=u_3^TJ_{3}u_3$
where $u_{i=1,2,3}$ - 3$\times$1 vector;
where $J_{i=1,2,3}$ - 3$\times$3 matrix;
I need to pack ...
- 45.4k
0
votes
1
answer
207
views
How do I find the unit vector in the direction of the minimal rate of change?
A ball falls on the surface $x^4 z+x^9 y^2+y^2 z^3=65$ at the point (-1,-3,2). How do I find a three-dimensional unit vector in the direction that the ball will begin to roll. I know that the ball ...
- 45.4k
1
vote
3
answers
125
views
About composition of functions (I don't want to use a vector variable function)
f2[x_, y_] := x^2 + y^3;
g[t_] := {t^2, 3*t+1}
$g$ returns a list, but $f_2$ is a two variable function.
So, we cannot compose these functions:
...
- 11
1
vote
1
answer
145
views
How to compute the divergence of a four-vector?
I have a quadri-vector which is given by
u = {(E^(-φ0[r]))*(1 - ε δφ[t,
r]), (E^(-φ0[r])) D[ε ξ[t, r], t], 0,
0}
and a quantity n which is given by
<...
- 7,872
0
votes
0
answers
61
views
Difference in covariant derivative and divergence?
defining polar Minkowski metric (with indecies down in polar coordinates) as
gdd = {{-1, 0, 0, 0},{0, 1, 0, 0},{0, 0, r^2, 0},{0, 0, 0, r^2 Sin[\[Theta]]^2}}
...
- 588
2
votes
0
answers
118
views
How can I make NDSolve aware of vectorial nature of an ODE?
I am trying to solve the equilibrium equation $\text{DIV } \mathbf P(\textbf{u}(x,y)) = \mathbf{f}$, where $\mathbf P$ is the stress tensor defined by
$$
\mathbf P = \mathbf F + (1-\det\mathbf F)^...
- 39.1k
2
votes
2
answers
94
views
How to deduce cosine theorem with vector?
I want to prove the cosine theorem of triangles with vectors under the following assumptions:
...
- 62.8k
0
votes
1
answer
81
views
Finding the Curvature of the path of a particle
How do I find the curvature of the vector when t=5?
The function is:
v[t_] := {2 t^4 + 2, 6 t^3 + 1, 3 t^2 + 4}
- 4,216
1
vote
1
answer
475
views
how to define unit vectors in mathematica
I'm struggling a little bit trying to understand how to address this problem, I would like to do this in mathematica: is just that I don't know how to do the dot product between $\mathbf{J}$ and $\...
- 62.8k
1
vote
1
answer
266
views
The square of Abs of a complex number
We all know that
4^2 + 22^2 = 500
Is there a natural way to generates 500 from the complex number ...
- 14k
3
votes
1
answer
226
views
Pattern matching with two variables - derivatives on 4-vectors
I am interested in pattern matching with two variables and not just one, and more specifically implementing derivatives on 4-vectors. In the case of interest the 4-vectors have two indices; one is in ...
- 4,216
2
votes
1
answer
210
views
Using Curl and Grad in cylindrical coordinates gives different result than in Cartesian
I am doing a quite elementary calculation to verify
$$
\vec \nabla\cdot V = \vec\nabla \times \vec A
$$
Where $V$ is just some scalar function in $\rho$, $\phi$ and $z$ and $A$ is defined as
$$
...
- 14k