# 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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### 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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### 12.1 VectorPlot - How to show differing magnitudes in the new implementation

I'm graphing vector fields for a class. Magnitude is important at least initially. In 12.0 and earlier VectorPlot plotted the different magnitudes as length. In 12.1 VectorPlot represents magnitude by ...
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### Plotting list data of cross product of field vectors

I have some experimental data points of electric Ey(t, value) and magnetic field Hz(t, value). I am trying to calculate the ...
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### How to express elemental operations in matrix form?

I ran the following code: X = Array[x, {5, 4}]; W = Array[w, {4, 3}]; Y = Array[y, {5, 3}]; D[Norm[X.W-Y, "Frobenius"]^2, {W}]//MatrixForm However, mma ...
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### How to input a specific three-variable function into this definition?

I have the following expression: ...
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### Calculation of SolidAngle not recognizing region?

Basically I'm trying to calculate the solid angle of a square seen from the origin. I defined the region (in two different ways) and tried running the function but it does not give any output. Why is ...
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### Output of expressions unable to have operations be performed on the expression

I am currently trying to use the code linked in the catalog of spacetimes pdf to calculate chirstoffel symbols for a metric which follows as n := 4 ...
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### Scaling vectors by their norm in VectorPlot3D

I'm trying to generate a 3D vector plot in which the length of the vector is really it's norm. This is my code: ...
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### Picking elements from separate lists and multiplying them

So I'm doing some instruction items about surface integrals. I've written the following code. it calculates curl and partial derivatives of the surface. I now want to create the following function, ...
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### Eliminate doesn't work

I tried to define r by the polynomials a,b,c only. The result which I want is r=4/3 a. But this eliminate doesn't work! It is continue running without stop and without any output. Eliminate[{a == x ...
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### Functions of several variables composition

If we have two functions $G,F:\mathbb R^2\to\mathbb R^2$ then the mechanism $F\circ G(x,y)=F(G(x,y))$ gives us a new map $F\circ G:\mathbb R^2\to\mathbb R^2$ called its composition. In a "...
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### How do you get a partial derivative of a vector to another vector?

I have a translation function between Cartesian and Polar coordinates: xi[xPrime_] := {xPrime[]*Cos[xPrime[]], xPrime[]*Sin[xPrime[]]} I now want to ...
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### Vector calculus expression formatting

I have the following example vector calculus code ...