Questions tagged [parametric-functions]
Questions about explicit functions expressed in terms of independent variables, i.e. parameters. Including approaches for rewriting functions using different parameterizations.
752 questions
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Visualizing multiple paths to infinity in the complex plane using Mathematica [closed]
Hello everyone — I’m reading about the extended complex plane and the “point at infinity,” and I find the geometric picture quite helpful. According to this text, in the complex plane $z \in \mathbb{C}...
- 867
1
vote
0
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111
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Parametric Plot 3D Surface Model
I'm trying to recreate this plot. Its over the interval $
u, v \in[0,2 \pi]$
My attempt is horrific.
...
- 5,094
3
votes
3
answers
690
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Making a threaded pipe end
I am trying to make something that involves a threaded end to both pipes attached to a hollowed out ellipsoid. I am having problems with:
Making it smooth. I tried various things but it is likely due ...
- 687
3
votes
2
answers
202
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Is there a better way to define the Gradient, Divergence and Laplacian of a curvilinear coordinate system?
I am trying to write a code to compute the gradient, divergence and the Laplacian of any curvilinear geometry.
For any curvilinear coordinate system defined in (\xi,\theta), let X be the mapping ...
- 121
5
votes
2
answers
520
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Explicit function for converting HUE to RGB
How to extract function for converting HUE to RGB without manually rewriting it by using Piecewise. (preferably without using interpolation, I accept it being ...
- 32.8k
9
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2
answers
546
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Numerical simulation of dynamical systems on torus: periodicity of variables
Suppose we have the following system of ODEs,
...
- 895
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4
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296
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Area bounded by Sheared Sine curve
Inspired by a high school problem: Show calculate the area bounded by the $x$-axis and a sine curve $y=\sin(x)$ which has been sheared parallel to the $x$-axis. This can be solved by noting that area ...
- 1,466
2
votes
2
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142
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Definition of periodic parametric function
The parametric plot bellow is periodic for intervals {x, 0, 1}, {y, 0, 1}. It consist of two separate functions. But the functions are identical just one is shifted....
- 32.8k
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Issue with ParametricRegion in free cloud account
This works
pr=ParametricRegion[{Sin[x]Exp[x],Cos[x]Exp[x]},{{x,0.,3.Pi}}]; Region[pr]
and produces a nice image of a logarithmic spiral
This does not
...
- 298
1
vote
2
answers
190
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ParametricRegion doesn't recognise BezierFunction as 3D
Problem
I'm trying to make a MeshRegion from a bezier surface defined from an array of control points. Consider
...
- 4,293
1
vote
3
answers
216
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How can I fit two datasets simultaneously using two different functions but with the same parameters?
There are two sets of data: firstHalf and secondHalf. Both firstHalf and secondHalf are fitted using the models modelPositive and modelNegative, respectively. Both models use the same parameters: MS, ...
- 13
1
vote
1
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ParametricNDSolve not returning the correct solution (and changes depending on the Method)
I am investigating the following parametric fourth order differential equation
$Y^{(4)}(x)-\beta^4 Y(x)=0$
on the one-dimensional domain $[0,L]$ subject to four boundary conditions $Y(0)=0$, $Y(L)=0$, ...
- 95
4
votes
3
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282
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Converting a System of Three Polynomials to a Regular Chain in Mathematica
I have the following system of equations involving three polynomials in the variables XA, XB, XC with parameters a, b, c.
...
- 143
5
votes
2
answers
411
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Numerical approximation of implicit functions
I have an expression $t \equiv t(x)$,
\begin{equation}
t = 2^{-2+\frac{a}{2}} c^{1-\frac{a}{2}} \Gamma\left(-1+\frac{a}{2}, \frac{c}{2} x^2\right)
\end{equation}
where $\Gamma\left(-1+\frac{a}{2}, \...
- 787
2
votes
2
answers
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Using eigenvalues of an differential operator to numerically solve another differential equation and use the solutions to perform integration
I am trying to use eigenvalues of a differential operator in another differential equation to find solutions of the later. Next I want to use the solutions to perform a numerical integration where I ...
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