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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How should I interpret the results I'm getting from Grad? [closed]
When I type the following in Mathematica:
$Assumptions = (a | b | c | d) ∈ Vectors[3, Reals];
Grad[(b - a)\[Cross](d - c), {a}]
I obtain:
...
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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 ...
CommunityBot
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Complex boundary conditions and NDEigensystem
I am having difficulties implementing a Neumann value when numerically solving the Navier equation using NDEigensystem.
The Navier equation is given by
$\nabla^2 \vec u + (p^2 - 1) \nabla(\nabla\...
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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} + \...
CommunityBot
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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 ...
CommunityBot
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How to add a vector variable to a vector value?
If we have a three dimensional vector variable:
$Assumptions = a ∈ Vectors[3];
and a three dimensional vector value for example:
...
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Quadratic form derivative in Mathematica
How can I correctly differentiate quadratic form by vector in Mathematica, i.e.:
$$Q=\omega^T I_{p} \omega$$
$$\frac{\mathrm{d}Q}{\mathrm{d}\omega} = \;?$$
...
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Symbolic derivatives with vectors and matrices
I'm currently trying to solve some problems using symbolic vectors and matrices of arbitrary size. However, I have some problems with understanding and verifying the results:
I defined the vectors as ...
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How to expand dot product by applying properties
I would like to expand a dot product which includes vectors $ \vec{v_1}, \vec{v_2}, \dots $ and constants $ c_1, c_2, \dots $
So that:
$$ c_1 \vec{v_1} \cdot \left(c_2 \vec{v_2}+ c_3 \vec{v_3}+\dots ...
- 41.5k
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Derivative of vector dot product with respect to a vector
I have the expression:
Transpose[gvecI, {2, 1}].x (m[1] + m[2])
gvecI and x are [3x1] ...
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Derivative of a norm
I learned not use the Norm[] function when computing vector derivative, so I use the dot product instead:
In: D[x.x, x]
Out: 1.x + x.1
What does the result mean? ...
- 41.5k
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Working with abstract vectors
I often need to compute derivatives or integrals involving N-dimensional vectors (where the dimension could be equal to 2 or 3 but is not particularly relevant for the sake of the derivation). The ...
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