# 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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### How to Solve Partial Derivative with Summation (for Linear Regression)?

I'm demonstrating linear regression so I would like to calculate derivatives 1 & 2 using Mathematica, something like this This is based on the textbook notation in Johnston's Econometric Methods ...
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### ArcTan action in more than two dimensional space [closed]

There is a four-dimensional vector, (w, x, y, z). Can ArcTan, ArcTan[w, x, y, z] be applied? Or what is the alternative to it?
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### Integration by parts for Green's first identity

How should one implement $$\int _{\Omega }\nabla u\cdot \nabla v\,d\Omega \ =\ \int _{\Gamma }v\,\nabla u\cdot {\hat {\mathbf {n} }}\,d\Gamma -\int _{\Omega }v\,\nabla ^{2}u\,d\Omega\,,$$ Symbolically ...
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### Map water runoff flows near Ellicott City, Maryland

Ellicott City, Maryland was the site of a flash flood several years ago due to the local topography. How can we use the Wolfram Language to show the direction water flows at many points near that city?...
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### How are Symbolic Vectors Defined?

It is my understanding that undefined symbols are considered scalars, so I can't index variables that aren't defined. It is possible to define a symbol as a vector of symbols as follows, allowing ...
33 views

### How do I prevent, or get rid of the <code>Abs^\[Prime]</code> in the output of a partial of a Normalize[vector]? 12.0.0 for Microsoft Windows [duplicate]

12.0.0 for Microsoft Windows How do I prevent, or get rid of the Abs^[Prime] in the output of a partial of a Normalize[vector]? The code below shows the problematic ...
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1 vote
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### 'not a variable' error when applying D function [closed]

I am trying to apply differentiation, D, operator in Mathematica to a vector. Importantly, I want to carry out the operation with respect to another vector. Basically, I am computing a Jacobian matrix....
1 vote
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### Vector Potential Function of Vector Field with DSolve?

(This is a redux of this.) Why doesn't this work? I have a vector field F1 whose div is 0 with a known vector potential function A2, and I try to get DSolve to solve the differential equation for A2 ...
123 views

### Preventing Mathematica from applying product rule

I am programming viscous terms of compressible Navier-Stokes equations ...
1 vote
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### Showing each component of velocity in a helix

In this animation, I want to show each component of velocity (V_x, V_y and V_z) with arrows ...
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### Simplifying expressions with dot or non-commutative product (without the help of NCAlgebra)

I have two expressions (with dot and non-commutative product): $f=J^T.x+J.x$ $g=J^T**x+J**x$ I want to simplify them and get the following expressions: $f=(J^T+J).x$ $g=(J^T+J)**x$ In an attempt to ...
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### Calculating Matrix Derivatives

I'm sorry if this is an easy question, but I'm trying to refresh my memory on calculating derivatives of matrix products and have been reading the Matrix Cookbook. I'd like to rebuild my intuition by ...
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### How to define a vector operator?

I know how to define a single-variable differential operator like Clear[Op] Op[x_] := a D[#, {x, 1}] & and I can do operations like ...
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### Calculating length of curve based on data points?

I had around $1000$ data points $(x,y,z)$ and when I plot them they seem to lie on a closed curve. I carefully checked the data points and the points do not repeat rather they are somewhat close to ...
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### Why isn't the vector field being plotted over the entire torus?

I am trying to plot a vector field over a torus. Here is my code and the image it produces: ...
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### Solving a vector diferential equation lead to ComplexInfinity Encountered non-numerical value for a derivative at t == 0

I'm trying to solve the following Vector PDE: I implemented the following code: ...
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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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### How to compute the divergence of a four-vector?

I have a quadri-vector which is given by u = {(E^(-φ0[r]))*(1 - ε δφ[t, r]), (E^(-φ0[r])) D[ε ξ[t, r], t], 0, 0} and a quantity n which is given by <...
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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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### Finding the Curvature of the path of a particle

How do I find the curvature of the vector when t=5? The function is: v[t_] := {2 t^4 + 2, 6 t^3 + 1, 3 t^2 + 4}
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