# Questions tagged [vector-calculus]

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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I'm taking a machine learning course, which involves taking a lot of analytical gradients and Hessians. It would be ideal if I could perform these calculations in Mathematica. However, I am only aware ...
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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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### Summation variables aren't recognised as dummy variables

I'm trying to write this expression in Mathematica, and calculate the following quantity However, when I tried the following ...
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### How to get results in terms of vector operations?

Is there a simple way to simplify an expression in terms of vector operations? For example, when I evaluate this; ...
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### Finding possible lattice planes of a crystal structure

After generating a crystal structure from a crystallographic data and duplicating it to a larger crystal system I would like to find possible lattice planes of this crystal. It is well-known that the ...
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### Cavity resonator modeling with Wolfram Mathematica

I am attempting to determine eigenfrequencies and the corresponding electric field distribution in a rectangular cavity resonator with perfectly conducting walls. In the simplest case of a rectangular ...
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### Difference in covariant derivative and divergence?

defining polar Minkowski metric (with indecies down in polar coordinates) as gdd = {{-1, 0, 0, 0},{0, 1, 0, 0},{0, 0, r^2, 0},{0, 0, 0, r^2 Sin[\[Theta]]^2}} ...
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### How would you write a electric field in cylindrical coordinates?

I am new to Mathematica and I am trying to automate the process of finding electric and magnetic fields for TE and TM modes in a cylindrical superconducting cavity. I could not find documentation ...
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### Is it possible to generate a random vector space in Mathematica?

The idea is that I’d like to try to use Mathematica to work through proofs. So if a proof says, “Let there be a vector space V…”, I would like to see a concrete representation of that vector space in ...
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