# 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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### Symbolic Vector calculus

Can mathematica perform symbolic vector calculus? Say I want to find $$\mathbf{v} = \mathbf{a} \exp(\mathbf{b}\cdot\mathbf{x})$$ $$\nabla \cdot \mathbf{v} = \mathbf{b}\cdot \mathbf{v}$$ If I try ...
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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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### 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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### Help with code on integration

I'm trying to do a surface integral through a vector field of a disc. The problem says there is a vector field $\langle 0, y, -z\rangle$ and the disc is $x^2 + z^2 \le 1, y = 1$. The answer is $\pi$ ...
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### Parametric Surface Integral Boundary Code?

I am having trouble using MMA to calculate 2 parametrized surface integrals. I'd be grateful for any fixes people can offer. I usually calculate surface integrals with the following code, which works, ...
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### Parametric equations and eq. of tangent plane

I have written the following code to determine the equation of a plane tangent to a surface at a given point: ...
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### Help on center of mass code

I have reviewed questions on MMMA Stack Exchange and found no help. Here's my problem and my code, which only partially works. I can't figure out my mistake. Help? Find the mass and COM of a wire in ...
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### Exploring curl of a gradient of a scalar function

Suppose I want to explore $\nabla \times \nabla V$ where $V$ is some scalar function. It basically results in a zero. But I would only know why if I solve it on paper. I wanted to use Mathematica for ...
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### How to plot integral of a gradient function

For $f : \mathbb{R} \longrightarrow \mathbb{R}$ continously differentiable and $\phi \in [0,\pi/2]$ let $$F(x) = \int \frac{f'(x)-\cot \phi}{1+ f'(x) \cot \phi} d x$$ be a clockwise 'rotation' of $f$. ...
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### Issue with the Laplacian in Cylindrical Coordinates

I am using Mathematica 12.1.1 and am unable to get the correct result for a simple laplacian in 3D Cylindrical Coordinates. I want to reproduce the following result on Mathematica: But, I am only ...
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### Can Mathematica evaluate vector gradients?

Can Mathematica compute vector gradients such as $$\nabla \lVert x \rVert ^2_2 = 2x$$ $$\nabla \lVert Ax - b \rVert = A^T (Ax - b)$$
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### How to write a program on gradients and the path for steepest ascent?

I'm given two functions f[x ,y ]=Cos[x]*Cos[y]/(6+x^2+y^2) and df[x ,y ]=Grad[F[x,y],{x,y}] I was given a note that ...
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### Understanding and visualizing Bessel function with complex argument

I have a vector field in polar coordinates $(r,\phi)$, which I wish to visualize and better understand. It represents the Electric field vectors for a given field distribution inside a circular ...
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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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### Triple Integral boundaries and solution

So I'm working on triple integrals, specifically on those where I have a region bounded by various surfaces. (In other words, the ranges for each integrals are not given, but must be calculated.) I ...
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### Scalar potential function from 3D vectorial field [duplicate]

I am new at this forum and a beginner with Mathematica. Today I was studying multivariable calculus and I came with this problem. For example, in 2D case I have this code: ...
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### A mistery in the documentation of the StreamDensityPlot command, and Is Abs' the same as Sign?

I was trying to decipher the documentation example ...
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### JacobianMatrix Command Not Working Properly [duplicate]

This is what I get when using the command: ...