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

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1
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3answers
66 views

Combine 2 plots in one [on hold]

$f: R^2 -> R,$ $f(x,y)=x²-y²$ ...
0
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1answer
44 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: ...
1
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0answers
54 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 ...
0
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2answers
58 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 ...
0
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1answer
47 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
92 views

compute the gradient in high dimension

The following code is used to compute the gradient of a given 2D data. ...
-1
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1answer
48 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 ...
1
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1answer
44 views

What is wrong with my following vector plot

I am trying to plot the following: ...
10
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1answer
204 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
68 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
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1answer
105 views

StreamPlot of a square-root - Issue

When I plot ...
2
votes
1answer
330 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 ...
0
votes
0answers
87 views

Solving for a coordinate transformation for a rank 2 tensor

I am working on a project in general relativity, and I have a metric or rank 2 tensor $g_{ab}$ of the form, $$g =\left( \begin{array}{ccccc} f(x^a) & 0 & 0 & 0 & 0\\ 0 & -f(x^a) ...
1
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1answer
83 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
47 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 ...
0
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2answers
97 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 ...
1
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0answers
100 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
141 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 ...
3
votes
3answers
221 views

Hypergeometric function with a matrix argument

I am looking for the evaluation of a Hypergeometric function with a matrix argument as for example in Ploev and Edelman or as showcased in this Wikipedia article. From what I understand from ...
3
votes
1answer
124 views

Bad numerical approximations

I'm trying to do some calculations here, but for some reason Mathematica starts using numerical approximations that are no good for my work. Specifically: ...
1
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2answers
39 views

how to extract a matrix and a vector from a vector [duplicate]

I have a vector like this: V = {a*exp1+b*exp2+c*exp3, a*exp4+b*exp5+c*exp6, a*exp7+b*exp8+c*exp9} and I want to get : ...
-1
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1answer
114 views

Plotting vector field [closed]

I am trying to plot the gradient vector field of the function: $$sin\sqrt{x^2+y^2}$$ This is my code: ...
-1
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1answer
138 views

Finding the maximum of a gradient vector

Im trying to find the maximum of my gradient vector G[x,y], I've tried several options including FindMaximumValue, FindMaximum etc. but i couldn't find it. The full function is shown below, any help ...
-2
votes
1answer
459 views

How to compute the curl of a vector field?

Can anyone help me out with this? I am trying to get Mathematica to evaluate curl of a vector field. The vector field is ...
5
votes
2answers
258 views

Working with abstract vectors

I often need to compute derivatives or integrals involving N-dimensional vectors (where the dimension could be equal to 2 or 3 but is not particularly relevant for the sake of the derivation). The ...
3
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1answer
710 views

Plot a function based on Derivative - Gradient field

I'm trying to plot the gradient field of a function in such a way that is possible to change it easily, only editing the function. Consider the code: ...
0
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0answers
75 views

How can I do symbolic vector differentiation in mathematica? [duplicate]

I want to do this calculation using Mathematica and I do not know how. I want to finf gradient of a vector function I Have this $$ f:R^n\to R $$ $$ \nabla_xf(x)=\nabla_x(x^tBx) $$ I want to get ...
9
votes
1answer
1k views

How do I plot a proper streamline plot, including spacings and line endings?

Mathematica includes two nice built-in tools to visualize vector fields, VectorPlot and StreamPlot. The latter is a useful tool, ...
0
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1answer
360 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
228 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
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1answer
92 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
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1answer
171 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
149 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
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0answers
120 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
201 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
53 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
737 views

Normal and Tangent of Acceleration in 3D

I need to figure out how 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 ...
1
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1answer
133 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
660 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
252 views

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

Consider the following set of points in the 4D space: ...
1
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2answers
305 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
431 views

Checking if an expression is equal to zero

I have 6 points in $\mathbb R^3$ as follows: ...
2
votes
2answers
552 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
0answers
290 views

Derivatives of list elements

Could someone explain the odd behavior of the Derivative function when drawing arguments from lists? We have, ...
6
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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
459 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
161 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 ...
6
votes
2answers
2k 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 ...
16
votes
4answers
8k 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
348 views

How to find this convolution?

How can I use Mathematica to find the convolution $f*f$ for ...