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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Helmholtz-Hodge Decomposition

So I was recently getting familiar with the Helmholtz-Hodge Theorem, briefly (but decently) described by https://en.wikipedia.org/wiki/Helmholtz_decomposition and I was wondering whether there exists ...
5
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1answer
80 views

Plotting a parametrically defined vector field

Let's say that you have a three dimensional surface defined by two parameters. E.g. $$ S(\theta,\phi) = \{\cos{\theta}\sin{\phi},\sin{\theta}\sin{\phi},\cos{\phi}\} $$ Additionally, you have some ...
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0answers
45 views

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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1answer
54 views

NDSolve and vectors [closed]

I think I can't find solution of equation below because I need use scalars, not vectors as I have tried. But I don't know how I can do express the problem with scalars. I have read Wolfram Language ...
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2answers
118 views

How to find the limit of a function of two variables

I was wondering if there is a method to find the limit of a function of two variables at a point. I tried the following: ...
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0answers
19 views

scaling parameters for vector-valued Non-linear optimization

I am trying to minimize a non-linear vector-valued function in Mathematica. As a test case, I try to minimize a function whose solution I know apriori. The problem is that one of the solutions is ...
3
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1answer
54 views

Integrating a gradient and matching terms automatically

I am trying to integrate a function $\nabla w(x,y)$ indefinitely knowing both components of $\nabla w(x,y)$. I have a function dw[x_,y_] that I have defined. I then ...
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1answer
87 views

Manipulating curl and div of a vector in spherical coordinates

I'm trying to show that an E field satisfies the two Maxwell equations: $\mathsf{Curl}[E]=-dB/dt$ and $\mathsf{Curl}[B]=(w/k)^2 dE/dt$ I define $\qquad ...
3
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1answer
154 views

Errors Solving Elliptic PDES with FEM

I am trying to solve the equation below governing transversely isotropic plane strain in cartesian coordinates with the given boundary conditions based on code found here using Mathematica 10.1 on OSX ...
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1answer
65 views

Cross product of three vectors

I am following the answer of Jens from following post: How do I simplify a vector expression? vec /: Cross[vec[x_], HoldPattern[Cross[y__]]] := I want to create ...
3
votes
1answer
92 views

Angle between two vectors in spherical coordinates [closed]

I have two vectors: H = {1, 0, π/4}; EA = {1, 0, 0}; Which I want to be in {r, Phi, Theta} - which would should give an angle between the two vectors as ...
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4answers
136 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: ...
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2answers
127 views

Finding vector of same direction with smallest integer coordinates

To determine Miller Indices of crystal lattice planes I would need a stable algorithm which determines the smallest set of integer coordinates of a vector which has same direction as a given vector ...
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2answers
132 views

Finding scalar potential function [duplicate]

Consider the vector field defined by: $$\vec F(x,y)=\langle 2xy-\sin x,x^2+e^{3y}\rangle$$ We can check to see if the vector field is conservative with the following calculations: $$\begin{align*} ...
3
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0answers
140 views

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) ...
6
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1answer
97 views

Line Integral Difficulty

I am having difficulty with the following question: Compute the line integral of $$f(x,y)=\frac{xy}{1+x+2y},$$ along the unit quarter-circle in the first quadrant from (1,0) to (0,1). My problem ...
7
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2answers
167 views

How to expand dot product by applying properties

I would like to expand a dot product which includes vectors $ \vec{v_1}, \vec{v_2}, \dots $ and constants $ c_1, c_2, \dots $ So that: $$ c_1 \vec{v_1} \cdot \left(c_2 \vec{v_2}+ c_3 \vec{v_3}+\dots ...
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1answer
99 views

Divergence of $1/r^2$: Mathematica yields 0, while the correct answer is a DiracDelta

In spherical coordinates, the divergence of a point charge is $4 \pi \delta (r)$, the three-dimensional Dirac delta function. In ...
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1answer
49 views

How can I tell mathematica that $a, \space b, \space \omega$ are constants? [closed]

I want to differentiate the following vector: $$=\frac{1}{\sqrt{a^2\omega^2\sin^2(\omega t)+b^2\omega^2\cos^2(\omega t)}}\begin{pmatrix}-a \omega \sin(\omega t)\\b \omega \cos (\omega ...
5
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1answer
82 views

Comparing unit normal definition in calculus with FrenetSerretSystem

I'm trying to compare the unit normal definition in calculus texts (i.e., $\vec N=\vec T'/||\vec T'||$) where $\vec T$ is the unit tangent vector, with the unit normal vector returned by the ...
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1answer
94 views

How to I plot a vector and a line on the same graph?

For example I want to plot the vector <7, 20> on the same plot as the line {t, 6t+10}
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1answer
85 views

How to plot a linear vector tangent to a bezier surface?

I have a bezier surface and its parameters are u and v. The partial differentiation with u as variable gives me a vector in the direction of u. I need to plot this vector. I plugged in a particular ...
3
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1answer
101 views

Finding the attractors of the vector field constructed as the gradient of an interpolated 3D scalar field

I have a list of data existing as {{{x, y, z}, f},...} from which I construct a 3D interpolation function using Interpolation[ ]. I am able to construct a vector field from the gradient of this scalar ...
2
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1answer
157 views

Curl expression does not evaluate [closed]

I am using Mathematica 8 on OS X. I am trying to compute the cylindrical curl of a symbolic vector following Mathematica documentation. ...
5
votes
0answers
209 views

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 ...
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0answers
24 views

Show[cp1,cp2, …] but PlotLabel in cp2 does not show up [duplicate]

I am visualizing the extrema of $f(x,y)=x^3+3y^2$ constrained to the level curve $g(x,y)=xy=-4$, found by using the Lagrange Multiplier Method. ...
5
votes
3answers
281 views

Extrema of a function of three variables

To identify and classify the critical points of the function $f(x,y,z)=x^3+xz^2-3x^2+y^2+2z^2$, I used the Hessian matrix method. ...
7
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1answer
435 views

Dipolar magnetic field lines inside a cylinder

I'm drawing the magnetic field lines of a rotating dipole (magnetic field distorded by emission of radiation). Currently, my Mathematica 7.0 code is fully working, but I'm having a constraint which I ...
2
votes
0answers
78 views

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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0answers
98 views

How to obtain the magnetic field of the following set up [closed]

This is the experimental set up: A ferromagnetic cylindrical disk (of irrelevant dimensions) has either sides set at different electric potentials (left side at 0 volts and right side at 1 volt). A ...
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1answer
58 views
0
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0answers
48 views

vector product defined on kronecker delta [duplicate]

I have some vectors such as : a={{0}, {0}, {0}}; b={{1}, {1}, {1}}; c={{1}, {1}, {0}}; I wanted to product a by ...
1
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3answers
111 views

Combine 2 plots in one [closed]

$f: R^2 -> R,$ $f(x,y)=x²-y²$ ...
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1answer
127 views

Divergence in spherical coordinates as can be done in W|A

Is there any widget kind of thing that can work out calculations of vector analysis in not-Cartesiian coordinates, i.e spherical and cylindrical? Like the calculators found here: ...
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0answers
58 views

Abstract Vectors [duplicate]

Is there a way to deal with abstract vectors in the following sense: Say I have a function f[y]. Now I want to evaluate ...
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2answers
100 views

Plotting vectors using derivatives

This question stems from a previous question I asked here: Multiple Integral of equation including dx prime? An equation describing a gravitational field of a cuboid is given as: $V(X,Y,Z) = -G\rho ...
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1answer
64 views

Integrating the second derivative of a 3D curve

I have a 3D curve K2[s_] := c1[s] + 0.4*(j[s]*Sin[500*Pi*s/97.8] - v[s]*Cos [500*Pi*s/97.8]) where j and v are frame vectors. I want to find the integral of ...
3
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1answer
179 views

compute the gradient in high dimension

The following code is used to compute the gradient of a given 2D data. ...
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1answer
57 views

It is possible to calculate a two vector integral

I have this problem: calculate the integral of: -1+Sqrt[2*d+1] with d being a distance of two points in a 60$\times$60 box ...
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1answer
65 views

What is wrong with my following vector plot

I am trying to plot the following: ...
11
votes
1answer
448 views

How can I define or use a new coordinate system in Mathematica?

I want to use the dipole coordinate system as defined in this paper: http://arxiv.org/abs/physics/0606044 I see that Mathematica can do all kinds of vector analysis using different kinds of ...
2
votes
1answer
85 views

Can I define a “total Curl” operator similar to a “total derivative (Dt)” operator? [duplicate]

I am trying to take the curl of a vector field. A={A1,A2,A3} B=Curl[A,{x,y,z}] This yields {0,0,0} because Mathematica ...
2
votes
1answer
169 views

StreamPlot of a square-root - Issue

When I plot ...
2
votes
1answer
1k views

Inverse gradient operator

I found a nice paper about inverse vector operators here. I have successfully implemented a Mathematica function for most of them, however I can't figure out how to do inverse gradient (page 7 in the ...
1
vote
1answer
211 views

How to rotate vectors in vector plot?

I'm writing an exam for my calculus students and am seeking help with using Mathematica on a particular problem. Here's my idea: I want to give a multiple choice problem that has four choices of ...
0
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0answers
62 views

Transform NMinimze into LinearProgramming formulation

I have the following maximization problem that I currently try to solve with Minimize/NMinimize. Unfortunately, this kind of solution method takes really long for large systems of equations and ...
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2answers
143 views

Symbolic matrice or vectors in Mathematica?

Suppose I would like to define an expression, containing and array or matrix of symbolic elements. Like this ...
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0answers
127 views

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 ...
2
votes
1answer
175 views

How to simplify an expression using a differential equation as an assumption?

I have a fluid dynamics flow described by a 3D velocity field such as u = {ux[x, y, z], uy[x, y, z], uz[x, y, z]} I want to calculate ...