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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13
votes
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
1k views

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 ...
2
votes
1answer
401 views

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 ...
0
votes
1answer
12k views

Why I get the “Set::write: ”Tag Times in is Protected." error?

Why I get the error below with this code: ...
1
vote
1answer
857 views

Calculation of Jacobians for a finite element method simulation

I'm attempting to calculate symbolic expressions for the (Newton's method) Jacobian of a Galerkin finite element method using Mathematica. It would seem that this is a perfect application for symbolic ...
2
votes
1answer
378 views

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 ...
3
votes
2answers
1k views

How to substitute numeric values in a symbolic Jacobian matrix?

I have a multi-variate function from $\mathbb{R}^n\to\mathbb{R}^n$. Choosing any desired initial vector, we can produce the corresponding function value, which is a vector as follows. The main problem ...
18
votes
2answers
9k 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} ...
2
votes
2answers
431 views

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 ...
10
votes
2answers
596 views

Creating randomly oriented planes

I would like to create randomly oriented planes. This is how I'm attempting to do that: I create a 2 random unit vectors, $\mathbf{v}_1$, and $\mathbf{v}_2$, in the $x$-$y$ plane I assume that if I ...