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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18
votes
4answers
12k 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 ...
22
votes
2answers
15k 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} x_1^3+2x_2^2 \\ 3x_1^4+7x_2 \end{array} \right);b=\left( \begin{array}{...
11
votes
2answers
3k 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 ...
6
votes
2answers
1k 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 components:...
8
votes
2answers
1k 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 (...
2
votes
1answer
21k views

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

Why I get the error below with this code: ...
10
votes
2answers
3k 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, ...
3
votes
1answer
1k 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: ...
3
votes
3answers
390 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
votes
1answer
93 views

How do you manipulate this in 2D

Use Manipulate to create an interactive plot that shows the parametrically-defined curve described by {x[t], y[t]} = {t Sin[t], t^2/15} for ...
15
votes
4answers
3k 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?
4
votes
1answer
540 views

Checking if an expression is equal to zero

I have 6 points in $\mathbb R^3$ as follows: ...
11
votes
2answers
702 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 ...
4
votes
2answers
135 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 (e....
2
votes
4answers
146 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: ...
2
votes
3answers
730 views

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, ...