# 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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### 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 ...
1 vote
147 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: ...
93 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 ...
75 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[...
1 vote
71 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 ...
66 views

1 vote
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 ...
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 ...
52 views

### How to input a specific three-variable function into this definition?

I have the following expression: ...
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 $$L_\phi(f)=e^{\phi}\Delta^2 \left(e^{-\phi}\,f\right)$$ ...
58 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 ...
124 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 $2\times2$ ...
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 ...
61 views

Theoretical side Simple example: If I have two sets $A_1=\{1,3\} ,A_2=\{2,3\}$ and Permutations[{1, 2, 3}]= $\left( \begin{array}{ccc} 1 & 2 & 3 \\ 1 &... 1 vote 1 answer 80 views ### Derivative of quadratic form in NCAlgebra I installed the NCAlgebra package in the hope that it contains enough rules for symbolic work with most branch-matrix expressions. ... 2 votes 1 answer 134 views ### Inactive form for PDE and symmetry I would like to solve the following non-linear Poisson equation (as a toy problem for a more complicated problem) ... 3 votes 2 answers 150 views ### Set of quadratic forms and linear algebra I have a set of quadratic forms.$L_{1}=u_1^TJ_{1}u_1L_{2}=u_2^TJ_{2}u_2L_{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$3 matrix; I need to pack ... 0 votes 1 answer 207 views ### How do I find the unit vector in the direction of the minimal rate of change? A ball falls on the surface$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 ... 1 vote 1 answer 147 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 <... 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}} ... 0 votes 1 answer 82 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} 1 vote 1 answer 269 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 ... 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 ... 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: ... 0 votes 0 answers 86 views ### 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 ... 1 vote 1 answer 76 views ### find a scalar potential function f for F so that f(0,0)=1 I need to find a scalar potential function f for F so that f(0,0)=1. a force field F(x,y) = <-Sinx,-2Cosy> First prove F is conservative Curl[F[x, y], {x, y}] ... 0 votes 0 answers 79 views ### 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 ... 1 vote 3 answers 151 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 ... 2 votes 1 answer 244 views ### Symbolic Vector calculus Can mathematica perform symbolic vector calculus? Say I want to find $$\mathbf{v} = \mathbf{a} \exp(\mathbf{b}\cdot\mathbf{x})$$ $$\nabla \cdot \mathbf{v} = \mathbf{b}\cdot \mathbf{v}$$ If I try ... 2 votes 1 answer 212 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$$... 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 ... 0 votes 0 answers 57 views ### 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{\...
I'm struggling with the following problem. It is necessary to find the derivative expression with respect to the vector $u$: \$r(u,v)=[(u-v)(u-v)^T]\begin{pmatrix} 1\\ 1\\ 1 \end{pmatrix}=[(u-v)\otimes ...