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.
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questions with no upvoted or accepted answers
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Symbolically evaluating gradients/Hessians
I'm taking a machine learning course, which involves taking a lot of analytical gradients and Hessians. It would be ideal if I could perform these calculations in Mathematica. However, I am only aware ...
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8
votes
0
answers
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Visualizing the Lagrange Multiplier Solution
This question is based on work in Susan Colley's Vector Calculus, 4th ed.
The question is to find and classify critical points of $f(x,y,z)=3xy-4yz+5xz$ subject to the constraint $g(x,y,z)=3x+y+2z=13$...
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How to verify the convexity of a function?
I have an optimization problem with the following objective function in $(x,y)$
$$
A\log \left(\sum_{i=1}^n x_i\right)+\log\left(1-\frac{f}{n}\left(\sum_{i=1}^n\frac{x_i}{y_i}\right)\right)
$$
where $...
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0
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Is there a 3D version of ListStreamPlot[] (analogous to ListVectorPlot3D[])
Is there is straightforward way to visualize streamlines given a series of discrete samples of a 3D vector field? There is a generalization of ListVectorPlot --> <...
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4
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391
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Complex boundary conditions and NDEigensystem
I am having difficulties implementing a Neumann value when numerically solving the Navier equation using NDEigensystem.
The Navier equation is given by
$\nabla^2 \vec u + (p^2 - 1) \nabla(\nabla\...
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3
votes
0
answers
145
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Summation variables aren't recognised as dummy variables
I'm trying to write this expression
in Mathematica, and calculate the following quantity
However, when I tried the following
...
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3
votes
0
answers
274
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Finding possible lattice planes of a crystal structure
After generating a crystal structure from a crystallographic data and duplicating it to a larger crystal system I would like to find possible lattice planes of this crystal.
It is well-known that the ...
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2
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0
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79
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12.1 VectorPlot - How to show differing magnitudes in the new implementation
I'm graphing vector fields for a class. Magnitude is important at least initially. In 12.0 and earlier VectorPlot plotted the different magnitudes as length. In 12.1 VectorPlot represents magnitude by ...
2
votes
1
answer
157
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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 ...
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2
votes
0
answers
118
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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)^...
- 21
2
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0
answers
61
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Find vectors describing two interconnected pyramids in Euclidean space
I need the help of competent linear algebra specialists in Mathematica.
In the Euclidean space, two tetrahedrons are turned at different angles. Their vertices coincide with the beginning of the base ...
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2
votes
0
answers
64
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How to get results in terms of vector operations?
Is there a simple way to simplify an expression in terms of vector operations?
For example, when I evaluate this;
...
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2
votes
0
answers
261
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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 ...
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2
votes
0
answers
203
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Extracting the curl-free component of a vector field
I am trying to extract the curl-free component of a discrete vector field. My plan is to take the Fourier transform of the vector field and then extract the radial component in Fourier space. The ...
2
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0
answers
785
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Symbolic derivatives with vectors and matrices
I'm currently trying to solve some problems using symbolic vectors and matrices of arbitrary size. However, I have some problems with understanding and verifying the results:
I defined the vectors as ...
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2
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0
answers
341
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Derivative of vector dot product with respect to a vector
I have the expression:
Transpose[gvecI, {2, 1}].x (m[1] + m[2])
gvecI and x are [3x1] ...
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1
vote
0
answers
63
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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 ...
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1
vote
0
answers
81
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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
...
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1
vote
0
answers
47
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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 ...
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1
vote
0
answers
87
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StreamPlot works slow with analitical functions
I'm day to day user in Mathematica, that's I will be happy to any kind of help in code optimisation.
So, I try to plot gradient for beatings between two laser modes and plot intensity, phase and phase ...
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1
vote
0
answers
108
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How to plot integral of a gradient function
For $f : \mathbb{R} \longrightarrow \mathbb{R}$ continously differentiable and $\phi \in [0,\pi/2]$ let
$$F(x) = \int \frac{f'(x)-\cot \phi}{1+ f'(x) \cot \phi} d x$$
be a clockwise 'rotation' of $f$.
...
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1
vote
0
answers
165
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How to write a program on gradients and the path for steepest ascent?
I'm given two functions
f[x ,y ]=Cos[x]*Cos[y]/(6+x^2+y^2)
and
df[x ,y ]=Grad[F[x,y],{x,y}]
I was given a note that
...
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1
vote
0
answers
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How to reproduce `JacobianMatrix` function
I want to use the JacobianMatrix function in package VectorAnalysis, but I get the following warning message after running the ...
1
vote
0
answers
61
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Obtain the vector potential and magnetic vector of infinite wire carrying charge
I'm working on the question above, but I'm really stuck for days. my goal is to implement the following Problem in Mathematica. Any help would be appreciated.
I want to evaluate the following ...
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1
vote
0
answers
120
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Error when trying to solve elastic PDEs using FEM: "Compile::argcompten: The comparison, LessEqual, is invalid for tensor arguments."
I'm trying to solve the following linear elastic problem:
The pairs of numbers beside each node is the coordinates in meters. The loads are in Newtons.
The part of codes that probably have no ...
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1
vote
0
answers
39
views
keep variables in the correct position when TensorExpand
I would like to expand a tensor expression of 3-d vectors. However, the code runs really slow, the problem is asked here:
Why is TensorExpand so slow for vector operations?
However, I found that by ...
- 1,121
1
vote
0
answers
586
views
Integrating over a sphere
We are trying to integrate a vector function over a sphere. To do this we changed it to spherical coordinates and then tried to integrate it. Unfortunately we get the error message shown on the image ...
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1
vote
0
answers
124
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How does this `Tagset` /: defined function work?
This came up in an assignment problem.
I am tasked to use
1)
▽ /: ▽[f_] := {D[f, x], D[f, y], D[f, z]}
2)
...
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1
vote
0
answers
189
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Using NMinimize to solve the Multi Commodity Flow problem
I have the following optimization problem and I was hoping to solve it with NMinimize. Unfortunately, I don't get the desired result. I would like to get an optimal vector for $d_{e}$.
This is how ...
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1
vote
0
answers
247
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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 ...
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0
votes
0
answers
25
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Why won't this magnetic field plot?
I have been having some longstanding trouble in getting a 2D vector plot of a magnetic field to show up. For context, I am working with Lienard-Wiechert potentials and as such trying to plot the curl ...
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0
votes
0
answers
132
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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):
...
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0
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0
answers
106
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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=...
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58
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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 ...
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0
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52
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How to input a specific three-variable function into this definition?
I have the following expression:
...
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0
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58
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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 ...
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0
votes
0
answers
45
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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
...
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0
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0
answers
61
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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 &...
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votes
0
answers
61
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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}}
...
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0
votes
0
answers
86
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How would you write a electric field in cylindrical coordinates?
I am new to Mathematica and I am trying to automate the process of finding electric and magnetic fields for TE and TM modes in a cylindrical superconducting cavity. I could not find documentation ...
0
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0
answers
79
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Is it possible to generate a random vector space in Mathematica?
The idea is that I’d like to try to use Mathematica to work through proofs. So if a proof says, “Let there be a vector space V…”, I would like to see a concrete representation of that vector space in ...
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High-dimensional second-order differential matrix equations
I am working on Lagrangian derived high-dimensional motion equations for a robot in matrix form. The structure of such an equation is known:
$M(q)\ddot{q}+C(q,\dot{q})\dot{q}+G(q)=0$
where $q=[\dot{\...
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50
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Scaling vectors by their norm in VectorPlot3D
I'm trying to generate a 3D vector plot in which the length of the vector is really it's norm. This is my code:
...
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0
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41
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Picking elements from separate lists and multiplying them
So I'm doing some instruction items about surface integrals. I've written the following code. it calculates curl and partial derivatives of the surface. I now want to create the following function, ...
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0
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Eliminate doesn't work
I tried to define r by the polynomials a,b,c only. The result which I want is r=4/3 a.
But this eliminate doesn't work! It is continue running without stop and without any output.
Eliminate[{a == x[1] ...
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0
answers
94
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Functions of several variables composition
If we have two functions $G,F:\mathbb R^2\to\mathbb R^2$ then the mechanism
$F\circ G(x,y)=F(G(x,y))$ gives us a new map $F\circ G:\mathbb R^2\to\mathbb R^2$ called its composition.
In a "...
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65
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How do you get a partial derivative of a vector to another vector?
I have a translation function between Cartesian and Polar coordinates:
xi[xPrime_] := {xPrime[[1]]*Cos[xPrime[[2]]], xPrime[[1]]*Sin[xPrime[[2]]]}
I now want to ...
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93
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0
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0
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65
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0
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343
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Curl in Polar Coordinates
I was trying to figure out Curl in other coordinates. The Curl documentation (https://reference.wolfram.com/language/ref/Curl.html ) didn't really say how Mathematica interpreted the input.
Anyway, I ...
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