# 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 do I verify a vector identity using Mathematica?

I am trying to verify well known Frenet–Serret formulas in general setting using Mathematica. I need to consider a general space curve $r(s)=(x(s),y(s),z(s))$ in $\mathbb{R}^3$ and define its unit ...
118 views

### Manipulations with tensors that keep so(3,1) symmetry manifest

I am doing some manipulations with tensors in curved background. There are, however, coordinates, where Lorentz symmetry is manifest. So, on one hand, I am dealing with particular coordinates and, on ...
695 views

### Plot a level curve and its gradient

Suppose that I have the following ellipse function, $f(x,y)=4x^2+y^2-5$. The gradient of this ellipse is calculated as $\nabla f(x,y)=[8x,2y]$. I know how to plot and join them. It is easy. I do ...
184 views

### DiracDelta convergence in 3D - Cartesian vs. spherical coordinates

Integrating DiracDelta in 3D in Cartesian coordinates works just fine i.e. gives vecf[{x, y, z}] ...
25 views

### keep variables in the correct position when TensorExpand

I would like to expand a tensor expression of 3-d vectors. However, the code runs really slow, the problem is asked here: Why is TensorExpand so slow for vector operations? However, I found that by ...
142 views

### Why is TensorExpand so slow for vector operations?

I would like to expand the following tensor expression: ...
44 views

### Integrating a vector according to elements of another vector

I have two vectors, $\bar{x},\bar{v}$ and I want to produce a third vector such that:$$u_i = \int_{x_i}^{x_i+\delta} f(v_i,t)dt \ .$$ I tried (with a simple function for example): ...
285 views

### Confused about the solution obtained from vector linearization

I am trying to linearize a vector expression $$\frac{(\mathbf{u}+d\mathbf{u})\times(\mathbf{v}+d\mathbf{v})}{\vert(\mathbf{u}+d\mathbf{u})\times(\mathbf{v}+d\mathbf{v})\vert}$$ Here is my code ...