# Tagged Questions

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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### 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 ...
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### 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 components:...
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### Singularities using VectorPlot

I am trying to plot a vector function of a fluid flow given by $\vec{V} = (\frac{-\cos(\theta)}{r^2},-\frac{\sin(\theta)}{r^2})$ I am trying to plot it in Mathematica using the command below, I ...
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### 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. ...
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### 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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### 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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### 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 ...
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### 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 ...
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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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### 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 ...
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### 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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### 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: ...
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### Normal and Tangent of Acceleration in 3D

I am trying 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 of ...
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### 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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### 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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### 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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### How do you show a cone inside of a sphere?

I have a sphere of radius 5 and a cone (i.e. z=√(x^2+y^2)) inside of it. I can show them separately, but I'd like to show them together. I've tried a few tricks with opacity, implicit specifications, ...
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### Finding a vector field from a set of points

I have a data set of the type $\{x,y,z\}$ where $(x,y)$ is a point and $z$ is the "value" or magnitude at that point. This gives me a triangular sort of shape since $(x,y,z)$ is not defined along the ...
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### 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. ...
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### 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? ...
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### Why I get the “Set::write: ”Tag Times in is Protected." error?

Why I get the error below with this code: ...
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### Vector Analysis: Why are the Grad, Laplacian and Div being evaluated to zero

For the non linear partial differential equation below, why are the Gradient, Laplacian and Divergence being evaluated to zero despite using the VectorAnalysis ...
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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 ...
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### Laplacian or Grad of an InterpolatingFunction

For obtaining a Schlieren image from an equation for density, I need to calculate the first derivative of density and make a contour plot. The below code snippet calculates the first derivative w.r.t ...
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When I plot ...