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.

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Why doesn't ParametricNDSolve execute the action of WhenEvent, except the first occurrence?

I'm trying to create a ParametricFunction object using ParametricNDSolve targeting a system of equations that involves WhenEvent and DiscreteVariables. For some reason I fail to discover, the ...
1 vote
1 answer
56 views

Obtaining different answers when using NDSolve vs ParametricNDSolveValue

I am obtaining two different answers for a curve when solving the same exact system of differential equations when using NDSolve vs when using ParametricNDSolveValue. Here it is when using NDSolve: <...
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3 votes
2 answers
98 views

ListInterpolation and extrapolation: order has been reduced, [closed]

I have a following ListPlot and ListInterpolation, ...
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8 votes
5 answers
632 views

2D cross-section of ParametricPlot3D

Now I'm trying to get the two-dimensional cross-section from ParametricPlot3D, the details of this question are as follows As an example, here is a parametric equation: x=x(u,v) y=y(u,v) z=z(u,...
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How to write expression of the motion functions in Coulomb field so that it can be used as a basis in the matrix method for finding eigenvalues?

I would like to find the energy eigenvalues of the corresponding Hamiltonian (H = -1/2Laplacian -b/r * Exp[-a*r] , a, b - numbers) in the matrix way. For this, it is necessary to have a complete set ...
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2 votes
1 answer
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Failing to define a function? [duplicate]

I am trying to define a function and it apparently is not working. Here is my small working example: ...
0 votes
2 answers
57 views

How do to create 3D plot for the argument from two another arguments for maximum of the function?

How do to create 3D plot of ${t_{opt}} = {f_2}\left( {x,y} \right)$, where ${t_{opt}}$ is corresponding to maximum value of ${f_1}\left( {x,y,t} \right)$ at the limited ranges of $x,y,t$? If $t$ ...
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2 votes
3 answers
78 views

Constructing a function that returns two distinct values by Mathematica

I'm trying to enter a function in Mathematica that can take two inputs, a, and b, and return two outcomes based on those two numbers. I will assume the name of this function as Resultsf[a _,b _] the ...
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1 answer
30 views

FindRoot over parametric interpolating function

Consider the already well answered topic : Get x and z coordinate from an image and make a parametric surface of revolution. ...
4 votes
1 answer
111 views

Remove a parametrically defined curve from parametrically defined surface

I want to make a sphere with a pattern removed from it so that I can 3D print it and make a stereograhic projection art display. The equation of the curve is a lengthy Fourier series I won't include, ...
1 vote
3 answers
91 views

A peculiar behavior of `ParametricFunction`

I am trying to use ParametricNDSolve to find a desired value for a parameter in an ODE, and the output seems to misbehave. First, consider the following example ...
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3 votes
1 answer
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How to troubleshoot NIntegrate non-numerical error?

I am trying to evaluate a 2d integral (denoted as x and y here) with a function that involves a numerical integral at each point....
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1 vote
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Plotting a parametric function for a given prior distribution of parmaeters

I have a function $f(x, \alpha, \beta)$. The function is piecewise defined and not analytically integrable. I would like to do the following: draw from a distribution on $\alpha$ and $\beta$, compute $...
2 votes
1 answer
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Does the computation time for the determinant of a symbolic matrix depend only on the size of matrix? or, the form of the entries also plays a role?

I have a large ($50\times 50$) sparse matrix $M$ whose entries are symbolic, and most of them are of these exponential form: E^(-((I x)/2)) (3 + x) and ...
1 vote
1 answer
113 views

How to find a parametric equation of uniform motion?

requirement: 1.The trajectory of the parametric equation is a closed polygon. 2.Try not to use trigonometric functions and Mod.Only ...
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4 votes
2 answers
91 views

ParametricPlot for phase field error (case: Predator-Prey Model) [closed]

so I have a task that need to draw a phase field of predator-prey model, but first I tried my lecturer's coding: ...
3 votes
2 answers
259 views

Confusion surrounding Mesh for a complicated function

I have two different setting with the command Mesh, one is at All and the other one is at 2000. I just don't have the math to understand what I am seeing. ...
0 votes
1 answer
57 views

ParametricNDSolve with 2 parameters displays unexpected behavior, crosschecked with 1-parametric version of the same system

I apologize in advance for posting some lengthy code, I tried to tackle this with a simplified question yesterday here but once I implemented the suggested answer by @march deeper issues arose. I am ...
2 votes
3 answers
196 views

How to get rid of complex terms in the given expression and rewrite it as a real function?

I have an expression exp in terms of the parameter $n\in\mathbb{N}^+$ which takes the values $n=\{ 1,2,3,4,5,6,7,8,9,10 \}$. As can be seen (a picture is also ...
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2 votes
2 answers
121 views

Simplifying a sum of complex exponential terms

I have this function for $n=\{1,2,3,4,5,6,7,8,9,10\}$. Is there any hope to significantly simplify this function (make it shortened) for general $n$? I use Simplify ...
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0 votes
0 answers
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Simplifying the function for the common factors; and showing that it contains a multiplicative factor $i e^{i (6 x + 3 b + t)}$

I have the given long function for $\{x>0,b,t\}\in\mathbb{R}$ and $\{m,n\}\in\mathbb{N}$. I have two questions: This function contains many common factors in polynomial form (as can be seen in the ...
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1 answer
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How to express the given function as a factor $e^{7 i x}$ times a real function?

I have the function $f(x,b,t,m)$ for $\{x>0,t,b\}$ all reals and $m=\{1,2,3,4,5,6\}$. For each particular $m\in\{1,2,3,4,5,6\}$, I see that $f(x,b,t,m)$ has a multiplicative factor $e^{7 i x}$ ...
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2 votes
2 answers
199 views

Solve the Differential Equations of r and θ to find the r(θ)

There are some differential equations. $r''+r\theta'^{2}=0$ $r\theta''+2r'\theta'=0$ And $r=r(x)$ and $\theta=\theta(x)$. And I want to get the $r(\theta)$. I tried to solve the $r(x)$ and $\theta (x)$...
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3 votes
2 answers
126 views

MeshFunctions in ParametricPlot with BSplineFunction for parameter extraction

I would like to use MeshFunctions in ParametricPlot in combination with BSplineFunction to ...
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3 votes
3 answers
186 views

Transforming the axes of a Contour Plot

I have contours of the following function $$\Psi(\nu,\mu) = -\frac{1}{4} e^{-2 \mu} \cos{2 \nu} - \frac{1}{2} \mu$$ in terms of $(\nu,\mu)$: I need to obtain the contours for $\Psi$ in terms of a ...
0 votes
2 answers
79 views

ParametricPlot of curve with one dimensional domain

For a mapping $\gamma(x,y)$ from $\mathbb{R}^2$ to $\mathbb{R}^2$ we can plot the image of some two dimensional region with ParametricPLot as, for instance, ...
2 votes
1 answer
37 views

What's the default NormalsFunction for ParametricPlot3D?

For Plot3D, I can use the method here to compute vertex normals, ...
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4 votes
2 answers
159 views

Gradually rendering parametric surface

I want to gradually render the surface like this For parametric curves, it can be drawn gradually in the following way. After generating a graph, then extract the data for plotting, avoid some ...
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5 votes
1 answer
369 views

Obtaining the curve parallel to the function a/(x^2+b)

I would like to obtain a curve that is parallel to the function: y(x) = -a/(x^2 + b) I have tried to calculate the said curve by solving parametric equations, but ...
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0 votes
1 answer
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How to plot the solutions of the equation $f_{a,b}(x)=0$ for $x$ as $a$ and $b$ range through the whole interval $(-2,2)$?

I have a three-variable function $f_{a,b}(x)$ for $x>0$, and $-2<a,b<2$, say f[x_,a_,b_]:=b^3 Sin[x] + Cos[a/b] Question I want to plot the roots of this ...
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How to ask Mathematica to extract all $y$-dependent terms in the given function $f(x,y,z)$?

I have a very large three-variable function $f(x,y,z)$ for real variables $\{x,y,z\}$ (I had to put only part of my original function because of the limit of $30000$ characters). Is it possible to ...
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3 votes
1 answer
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MeanPredictionBands not working in ResourceFunction["MultiNonlinearModelFit"]

I have a problem creating MeanPredictionBands for a FittedModel from the ...
2 votes
1 answer
162 views

Parametric polar plot

I have a function of a parameter $x$ that gives an angle, say $\theta=f(x)$ (not easily invertible), and I want to plot another function of $x$, $g(x)$, in a polar plot. How can I do it?
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1 answer
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Solve an equation in two variables containing symbolic constants

I've been struggling to solve equations in two variables containing constant symbolic parameters. Take for example the function in two variables defined by: ...
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1 vote
4 answers
110 views

Solve a parametric equation in 2 variables

I have a function in 2 variables $F(x,y)$, which also contains the constant parameters $\epsilon_{1}$, $\epsilon_{2}$,$\beta$. It is defined as: ...
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2 votes
1 answer
61 views

Use ParametricNDSolveValue And Manipulate for ploting differential equation

Im trying to plot x[t] and y[t] but I dont know which parts of my code is wrong. Can anybody help me? here is my code: ...
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5 votes
1 answer
114 views

Optimal control via ParametricNDSolve

I'm wondering about the possibility of employing ParametricNDSolve to solve a class of constrained optimal control problems. Here's an example: The system under ...
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4 votes
3 answers
190 views

Plot with NDSolve for a range of initial values

I have a differential equation system as follow: ...
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0 votes
1 answer
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3D Parametric Plotting for N Charged Particles in a Nonuniform Electric Field

I have a code (very bottom of post) which plots a static electric field as it passed through some metal sheet with an aperture in it. I seek to observe the motion of some N charged particles (point ...
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1 vote
0 answers
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ParametricRegion in Region produces misshapen result

Prompted by an answer to question 170254, I considered ...
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1 vote
1 answer
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Value of allegedly infinite limit is different for different values of the variables

I have a $5$-variables function $f(x,y,z,u,v)$ and I want to compute the limit as $x\to\frac{3\pi}u$; using this code for general values of parameters, Mathematica gives the answer ...
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1 vote
0 answers
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Mathematica gives the answer of a limit as DirectedInfinity[Sin[x/y]]; does this mean that the limit does not exist? [closed]

I have a typical real function $f(x,y;z)$ where $z>0$ is a real variable and $x,y>0$ are two real parameters; I use Mathematica to compute the limit $$ \lim_{z\to\frac{\pi}x} f(x,y;z) $$ and ...
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3 votes
2 answers
133 views

Solve for subset of parameters in ParametricPlot

I have a discretized region $\mathscr{R}$ and two functions $x(u,v)$ and $y(u,v)$. I wish to find (numerically of course) the values of $(u,v)$ such that $$ \begin{align} \left(x(u,v),y(u,v)\right)\in ...
2 votes
1 answer
80 views

Define functions on Geographic regions

Let's plot a parametric function $(x_s(u,v), \:y_s(u,v))$ on some $uv$ domain as shown below with an annulus as example. ...
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0 answers
24 views

Change value of a single input variabe to get out put results for each case the input single value is changed

I would like to put random values like (s = 0.1, 0.7 , 0.4, 0.15, 0.18) to get the output results which are ( X and Rn ) for these values in different excel files or in the same excel file ,instead of ...
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2 votes
1 answer
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Wierd problem with Table and Evaluate

I have a very unpleasent problem with Mathematica, precisely with Table and/or Evaluate. After solving a parametric system with ParametricNDSolve, I'd like to collect the values of the solutions $f_3(...
0 votes
2 answers
157 views

Solving System of six Non-Linear Equations in Six Unknowns

I've been trying to solve the following system of equations using NSolve and the code has been running for close to 24 hours already. Is this normal? Is there a quicker way to solve these equations? ...
3 votes
1 answer
65 views

Given a function with symbols, convert symbols into function variables

Let's say that you have a function with symbols, i.e. f[x] = x^2 +a[1] I want to define a new function g[x,a[1]] = x^2 +a[1]
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2 votes
1 answer
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Nonlinear differential equations - follow- up question

I have never solved numerically differential equations and in an optimal control problem I got this one that I cannot solve: $$1-f’(x)^2+f’(x)(x +1)+f’’(x)-f’’(x)f’(x)-f’’(x)f’(x)^2=f(x)$$ The initial ...
1 vote
2 answers
97 views

Please I need help to define a function of two variables (t,x)!

Let's define the following function: f[t_, x_] = t^2 + t*x*(1 - x) such that $x \in (0,1)$ and `$t \in (0,0.02)$ The problem is when I want to define the following ...

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