# 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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### In simple terms, what is a Tensor Space? [closed]

I've heard of tensor spaces, and they sound intriguing to my non-mathematically educated mind. I was wondering if anyone could give a, "Tensor Space for Dummies," rundown. If not possible to ...
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### Reconstructing a function from its gradients

I have a list of the components of the gradients, $\partial f/\partial x_i$, of a function $f(x_1,x_2,\cdots)$. Is there some neat way to reconstruct the function $f$? One approach to doing this ...
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### Vector shape and Dimensions

I think I have not understood clearly the difference between dimension and shape. I want to construct a vector remembering recurrence of the type : ...
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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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### Vector calculus expression formatting

I have the following example vector calculus code ...
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### Solving equation with Curl in angular velocity

In 3 dimensions, angular velocity is given as: $$\boldsymbol{\omega} = \frac{1}{2} \nabla \times \boldsymbol{v}$$ How can I use mathematica to solve for velocity $\boldsymbol{v}$, if I give a value ...
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### Does Laplacian use first argument “theta” for polar angle or azimuthal angle?

Only example I could find in the help for Laplacian is this My question is, is $\theta$ meant to be the polar or the azimuthal angle? Using $\theta$ for polar is ...
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### Problems encountered in plotting direction fields

I learned how to plot direction fields according to the answer of @Robert Jacobson to the question How can I plot the direction field for a differential equation?. However, when I tried to plot the ...
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### Laplacian operator examples

I was reading up in the help about the Laplacian operator. and tried to understand the one example I saw: Laplacian[Sin[r^2],{r,\[Theta]},"Polar"] results in: ...
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### Vector calculus integration identity problem

This is a follow up from another post. I was using the integration symbols available in the Basic Math Assistant palette. I am new to vector calculus operations. There is a known identity found in my ...
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### Solving Laplace equation in spherical coordinates

I was trying to solve Laplace's equation for a spherical capacitor, which is not difficult by hand, just to figure out the commands so I can eventually try something more complicated. Then, I ran into ...
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### Where to find order of arguments for default functions

Lets take for example the Laplacian. So I want to apply it in spherical coordinates, so I go the the associated documentation page (https://reference.wolfram.com/language/ref/Laplacian.html?view=all) ...
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### Curl in Polar Coordinates

I was trying to figure out Curl in other coordinates. The Curl documentation (https://reference.wolfram.com/language/ref/Curl.html ) didn't really say how Mathematica interpreted the input. Anyway, I ...