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.
313 questions
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Plotting incident ray - normal ray - reflected ray, as vector fields. What am I missing?
Following up on the evaluation of a conic surface (which will later be extended to an aspherical surface) representing an optical surface:
I have the sagitta equation for the surface, from which I ...
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How do I plot the normal vector to a surface in a given point and use it in other vector operations?
Im working with a conic surface (representing an optical surface) given by:
ZagA = ((1/r)(x^2+y^2))/(1+Sqrt[1-(1+k)(1/r)^2(x^2+y^2)])
I'm making it an evaluable ...
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Vectorizing Ray Tracing Equations for NDSolve and use of WhenEvent in Mathematica
I'm trying to solve the ray tracing equations for a sound pulse (Boone,1963). I have formulated the system of ODEs and successfully solved it for both the ray position
...
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How to derive this vector analysis equation?
How to use mathematica to derive this vector equation:
\begin{equation}
\nabla \times (\mathbf{A} \times \mathbf{B}) = (\mathbf{B} \cdot \nabla) \mathbf{A} - (\mathbf{A} \cdot \nabla) \mathbf{B} + \...
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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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Plotting a vector field on a cylinder
Assume a parametric equation for a cylinder
$$\mathrm{cyl} (\theta, z) = (r \cos\theta, r \sin\theta,z)$$
and a vector field given by
$$\mathrm{vecField} (\theta, z)=\frac{\sin(\alpha)}{r}\partial_\...
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Creating a 3D Gradient Vector Field Plot in Mathematica
I am new to Mathematica and currently learning how to visualize mathematical functions and their gradients. I am trying to reproduce a specific image that illustrates the gradient of a two-variable ...
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Perturbing a tensorial expression
I am new to Mathematica. I am trying to simplify an expression of the some form like:
$$
n_i \sigma_{ij} n_j - \gamma n_i \hat{\sigma_{ij}} n_j = 2 + v_i x_i + \kappa E_{ij} \chi_{ji}
$$
There are ...
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Vector calculus in generalised orthogonal frame of reference
I want to write Navier-Stokes equations in generalised orthogonal frame of reference in Mathematica. I therefore want to expand gradient and other vector calculus operations using metric factors such ...
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Recursive application of Grad in scalars
I am looking for an efficient way to apply Grad recursively to a scalar function. The code I have so far is in the structure below. I define the scalar function outside the loop, take its derivatives ...
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Cavity resonator modeling with Wolfram Mathematica
I am attempting to determine eigenfrequencies and the corresponding electric field distribution in a rectangular cavity resonator with perfectly conducting walls. In the simplest case of a rectangular ...
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How to create a vector as a tensor object for different euclidean bases?
The components of a tensor are always displayed with respect to one or multiple basis vectors.
For a tensor of rank 1, a vector, in 3D-euclidean space, we resort to three orthonormal basis vectors.
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Defining my own set of orthogonal curvilinear coordinates
I want to use Vector Analysis functions (Grad, Div,Curl etc) with the following set of simple Toroidal coordinates $(r, \theta, \phi)$:
$x = (R+r \cos\theta)\sin\phi$, $y = (R+r \cos\theta)\cos\phi$, $...
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