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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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 ...
3
votes
3answers
251 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 Koev and Edelman or as showcased in this Wikipedia article. From what I understand from ...
0
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0answers
45 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 ...
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3answers
81 views
1
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0answers
104 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 ...
0
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1answer
48 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
55 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
69 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 ...
3
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1answer
111 views

compute the gradient in high dimension

The following code is used to compute the gradient of a given 2D data. ...
19
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2answers
10k views

How to make Jacobian automatically in Mathematica

If we have two vectors, a and b, how can I make Jacobian matrix automatically in Mathematica? $$ a=\left( \begin{array}{c} \text{x1}^3+2\text{x2}^2 \\ 3\text{x1}^4+7\text{x2} \end{array} ...
0
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1answer
52 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 ...
5
votes
1answer
154 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 ...
4
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1answer
1k views

Lie-Bracket of two vector fields

I'm new to Mathematica (installed couple of hours ago) and I need to compute a few Lie brackets between two vector fields $f$ and $g$. $$ f\left(\mathbf{x}\right) = \left( \begin{array}{c} ...
-1
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1answer
52 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 ...
11
votes
1answer
227 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 ...
1
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1answer
45 views
2
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1answer
72 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 ...
5
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2answers
266 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 ...
2
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1answer
476 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
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0answers
103 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
104 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
50 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
101 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 ...
2
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1answer
149 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 ...
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4answers
2k views

How do I plot the unit normal field for a surface?

The question is pretty much in the title; I'm about to teach my multivariable calculus students about orientations on surfaces, and I would like to be able to show them pictures. Any ideas?
6
votes
2answers
986 views

How to change coordinates of a differential operator?

I'm doing a basic quantum mechanics problem and am trying to learn how to do it in Mathematica. Any help would be much appreciated. $\vec{L} = \vec{x} \times \vec{p}$ where $\vec{x}$ has ...
3
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1answer
126 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: ...
17
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4answers
9k 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 ...
9
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1answer
2k 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, ...
1
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2answers
41 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
146 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
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1answer
541 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 ...
3
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1answer
846 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: ...
6
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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 ...
1
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0answers
124 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 ...
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 ...
0
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1answer
408 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
247 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
93 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
votes
1answer
187 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 ...
1
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1answer
214 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
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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 ...
0
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1answer
14k views
3
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1answer
761 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
vote
1answer
135 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
766 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 ...