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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Problem with filling area of parametric equation

Hello, I have following code, which represents parametric equation. It should draw a border (d1, red color) and area of the curve d2 (fill that curve, blue color) for "o > 0, w > 0", ...
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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(...
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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? ...
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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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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 ...
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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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How can I plot these three equations? [closed]

There are 3 parametric equations given I have to plot the sphere. I tried with ParametricPlot3D, but it does not show any graph. Then, I also tried using ...
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Parametric3D inconsistencies

i wanted to plot a surface of the form ...
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Plot and Table in the same line

I would like to plot this with different y1 but isn't working!! ...
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2 answers
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How to plot this 3D ParametricRegion?

I want to plot this 3D ParametricRegion by using Region, ...
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InverseFunction fails at some parameter

Currently, I am faced with the difficulty of evaluating the inverse of the function below for certain negative decimal values of the parameter q. Specifically for ...
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Plotting functions defined via NIntegrate. Too slow

I have the following two functions xs[u,v] and ys[u,v] defined through numerical integration of $\alpha$ and $\beta$ and $\theta$...
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How can I make sure if the given curve is monotonic with respect to $x$ and $y$?

I have two functions $ f(x,y) $ and $ g(x,y) $ over the domains $ 1<x< 2$ and $0<y<\pi$. I use ContourPlot to ses those values of $(x,y)$ for which $g(...
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ParametricRegion is not showing complete region

I am trying to plot a region using the following code ...
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Creating Multiple Parametric Plots on the Same Graph

I know how to create multiple parametric plots on the same graph via the following command: ...
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Make this parametric plot y-axis symetrical

I'm trying to make this plot symetrical by y-axis (even). But not sure what to do. ...
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How to use NIntegrate with symbolic parameters? [closed]

I am trying to evaluate an integral that has two symbolic parameters, $x$ and $y$ in it $$-\int_0^1\frac{\log (u)}{\sqrt{1-u^2}} \exp \left(\frac{2 u}{u+1}xy-\frac{u^2 (x-y)^2}{1-u^2}\right) \; du$$ ...
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Plot colour coded contours as a parameter varies in a certain range

The following is a code for plotting the 0.1 contour of a complicated function $f(B,\zeta_1,\zeta_2,k_3,k_4,q)$ in the $B$-$\zeta_1$ plane, while keeping $\zeta_2$, $k_3$, $k_4$ and $q$ constant. ...
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Problem with solving a linear ODE with a parameter

I have been struggling with the following ode for several weeks, but I fail to solve it. So I post this question and my attempts and expect someone here could give some suggestions. First, define an ...
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Evaluated -> True in Parametric Plot with Legends and Labels causes error

Why does using Evaluated -> True in Parametric Plot (with PlotLegends and PlotLabels) causes a Part and Mapthread error? I use the same type of code in my Non-Parametric Plot but it doesn't cause ...
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A question about ParametricRegion/Region

If $\left(x_{0},y_{0}\right)\in\left(0,\infty\right)\times\left(0,\infty\right)$, then it easy to get $\left(u_{0},v_{0}\right)\in\left(0,\infty\right)\times\left(0,1\right)$ though the parametric ...
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Which options do I have for a ParametricFunction

I wanna know which options do I have with a ParametricFunction, which i got from solving an ODE with ParametricNDSolve? Can I find for example the Minimum for this function, which dependes form the ...
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Possible bug: Wrong differentiation of ParametricFunction inside Parallelize?

In the note RootSearch problem when called from within ParallelDo I described the problem with Ted Ersek's RootSearch package and came to the conclusion that it is ...
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Plot implicit function with intermediate variable

Cross-posted in Wolfram Community. Here, I intend to plot a 3D picture of with two implicit functions where $x, y, t, \xi, \eta$, are variables. Of course, these variables can be constrained to ...
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Is Function broken is this example?

This program f[x_] := g[Function[a, x]]; g[fn_] := Module[{h}, h[a_] := fn[a]; h[0]]; f[999] returns Function[0, 999][0] but ...
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Get parametervalues from ParametricPlot?

From an examplary plot plot = ParametricPlot[{1 Cos[s] , 2 Sin[s]}, {s, 0, 2 Pi}] I know how to get the plotted points ...
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Find the area enclosed by the x = t^2 − 2t, y = √ t and the y axis [closed]

How do I find the area for these parametric equations : x=t^2-2t y=sqrt(t) and y axis Please help
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2 votes
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ParametricPlot inside of ParametricPlot [closed]

I don't know why the following is not working! The code has a function y[x] then I have g[t] then I want to plot ...
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I have a variable error and was curious to see if it's due to piecewise functions?

So I have a displacement function sigx as a function of "t" (time) and sig.pre (pre-stress). At some time "dx": force "fo" goes to 0, and the same displacement function ...
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What parametric equations could be used to replicate these surface plots seen on 3d printed vases?

I came across this interesting link and am curious to know what generic equations were used to create these waves on the vase surface? It was mentioned that special dates could be incorporated into ...
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1 vote
2 answers
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How to Plot an Equation, based on another plot [closed]

I've been struggling with this problem That I have an equation with two variables. One of them has a defined interval. Like this: ...
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2 votes
1 answer
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Table of surface Parametric draw

I'm trying to reproduce this kind of graph for a spherical cap, with different span ratios. I tried with this: ...
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How to solve \[Theta]23 from the following equation?

How do I solve [Theta]23 from the following equation? ...
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1 answer
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Parametric Optimization In Mathematica

I want to solve the following problem: $$ \max_q \dfrac{q}{a}\left[ (-\log(1-q))^{-a} - (-\log(q))^{-a} \right] $$ subject to $1\geq q \geq 0$ for each $a\neq 0$. Here is the code I used: ...
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use of parametric ndsolve with a constraint

I want to solve differential equation $$ \frac{y''[x]}{(1+y'[x]y'[x])^{3/2}} = -a -y[x]/ \sqrt{2} + x/ \sqrt{2} $$ subject to boundary condition $y(-1) = y(1) = 0$ for some value of $a$. $a$ is found ...
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How to get a specific component of an equation without hardcoding? [closed]

Say I define an equation line[t_] = {t, 2t, 3t}. What code will define x[t] = t, y[t] = 2t, ...
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1 vote
1 answer
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How to table ParametricPlot with parametric value

I can plot this code ...
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6 votes
2 answers
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Olympic Athletics Track

Writing: ...
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2 votes
2 answers
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Unpacking a Mathematica expression returned by DSolve

I was trying to solve a system of differential equations in Mathematica and had troubles understanding what the solution looked like. So I wanted help to unpack it. I had a system of two coupled ...
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1 vote
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Singularity or stiff system in ParametricNDSolve

I have following parameters and equations(it's a complex one, please check it :) ): ...
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2 votes
1 answer
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Does mathematica cache the interpolating function from ParametricNDSolve?

I want to evaluate the solution of a system of non-linear ODEs using ParametricNDSolve. The output of ParametricNDSolve is a ParametricFunction object. Let's call it $f_\theta(t)$, where $\theta$ is a ...
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Shading a surface bound by a curve in 3D

Foundation Input: unit circle The exercise deals with transformations of the unit circle, $(\cos \theta, \sin \theta)$. We start with the unit circle with Hue coloring over the angular range of $(-\pi,...
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How to use ParametricPlot3D with ParametricFunction objects? [duplicate]

My code produces the iconic figure showing the error threshold of the quasispecies model. ...
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2 answers
144 views

Use solutions of FindRoot in subsequent calculations

I want to solve the equation $b e^a = 2$ in $b$, for values of $a$ ranging from $0$ to $10$ and each time $a$ to be increased by $0.1$. So I have: ...
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3 votes
1 answer
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Solution for inequality equation - "Cannot be solved with the methods available to Reduce"

I am trying to solve the following inequality for $v$: $b>e^{\frac{-v}{\alpha}}\cdot \alpha + v$. (Where I know: $b>0$, $v \in [0, 1]$, and $\alpha >0$). However the following doesn't work: <...
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1 vote
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Solving 2nd order coupled differential equations using shooting method

I'm trying to solve these two coupled 2nd order differential equations: with the following boundary conditions: where $r_{*}$ is the value of the $r$ at midpoint. I was trying to solve these ...
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1 vote
1 answer
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How to pass results of computations to a function definition?

Here is the following code that works, F[{x_,y_,z_}]:={16(y-x), x(45-z)-y, x*y-4z); x = Array[a,3]; F[x] and the answer is, ...
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How to calculate the derivative of the solution of ParametricNDSolveValue?

Consider the following code: ...
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How to derive all KKT points of a parametric optimization problem

Suppose we have a symbolic optimization problem where all parameters and decision variables are nonnegative like the following problem. I would be thankful to know if there is any method to find all (...
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Issue with Piecewise Parametric Plotting

I am trying to make a parametric plot of a piecewise function that is defined locally. For some odd reason, Mathematica will only plot the first two pieces of the piecewise function. If I plug in ...
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