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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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8 votes
2 answers
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How to make Region from Spline curve

Let bsf = BSplineFunction[{{1, 1}, {-0.5, -0.7}, {-0.4, -1}, {1, 0}}, SplineClosed -> True, SplineDegree -> 3] Than ...
lesobrod's user avatar
  • 1,809
3 votes
2 answers
163 views

Symbolic solution of trigonometric equation

I am dealing with complicated trigonometric equations. Generally, I would like to calculate θ or at least Sin[θ]. My code is as ...
blahblah's user avatar
  • 111
6 votes
2 answers
326 views

How to plot mutiple spiric sections of a torus in a single plot?

Spiric Sections are the cross-sections of a circular torus (radius $ a $) cut by a plane parallel to its axis. It has been extensively discussed in the wikipedia page. I want to show the cross-...
user444's user avatar
  • 2,644
2 votes
1 answer
85 views

How to avoid overlapping mesh lines ParametricPlot3D?

I have the following plot obtained using ParametricPlot3D: obtained via the following code: ...
annuk89's user avatar
  • 65
2 votes
1 answer
103 views

Plot3D for a problem where the initial value of the independent variable is a parameter in ParametricNDSolve

I would like to obtain a Plot3D from a ParametricNDSolve routine; I encounter a problem similar to Initial time as parameter in ParametricNDSolve, ParametricNDSolve with variable initial conditions ...
annuk89's user avatar
  • 65
0 votes
1 answer
126 views

How to execute this code? [closed]

I want to plot the following equation: ...
vijay's user avatar
  • 47
7 votes
2 answers
219 views

3D plotting of parametric curved surface

Imagine I want the 3D plot of a solid object that has height $H$ and a circular base of radius $R$. The radius of the horizontal cross-section of the object at height $z$ above the base reduces with $...
sam wolfe's user avatar
  • 4,903
4 votes
1 answer
181 views

Kernel quits while using ParametricNDSolve

I'm trying to reproduce the plots (Figure 1 and Figure 2) of this paper. The plots are obtained by solving the Eqs. 4.3 and 4.4. The boundary conditions described in section 3.3 for Eqn. 4.3 are ...
Entangled Quark's user avatar
1 vote
0 answers
88 views

Enclosing ParametricPlot3D to create a solid volume

I'm creating a 3D parametric hourglass shape that I hope to fill, making the center solid to use as a 3D volume, because I can't set parameters to it in COMSOL for simulations right now. I know that a ...
Char's user avatar
  • 539
1 vote
1 answer
141 views

Find the polar plane of the ellipsoid and integrate the Ellipsoid cap

I am working on writing a code to find the polar plane of an ellipse, and subsequently calculate the cap formed by subtending the point $p$ (red) onto a random ellipse. I think I have managed to ...
MKF's user avatar
  • 613
0 votes
0 answers
20 views

Is it possible to find a closed-form expression for determinant of the $k+1$-dimensional three-diagonal matrix whose entries obey particular rules?

I have this $k+1$ dimensional three-diagonal matrix in which $k=0,1,2,3,...$. I want to compute its determinant. Of course, for each fixed $k$ it is easy to compute the determinant. My question. Since ...
charmin's user avatar
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0 votes
0 answers
37 views

Efficient Triple Numerical Integral Computation with Variable Limit Functions

I have a triple integral expression where the limits of integration depend on other integral parameters. Here is the functions where $0<p<1$: ...
Frey's user avatar
  • 325
0 votes
0 answers
40 views

Parametric Region with Interpolating Function

How can I create a ParametricRegion from InterpolatingFunctions? Let's say we have: ...
MathX's user avatar
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3 votes
2 answers
120 views

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_\...
PhyGeom's user avatar
  • 31
1 vote
1 answer
79 views

ParametricNDSolveValue, NMaximize: Dealing with complex results in maximization problem

I analyze a system of differential equations in several variables including mus[t], mui[t], and w[t]. Time runs from t=0 to t=T. The two initial values mus[0] and mui[0] can freely be chosen; their ...
beginners's user avatar
9 votes
2 answers
510 views

Expand a 2d curve into a 3d path curve with a fixed axis of rotation?

Given a string of fonts, such as "ABC", give a space line, how to rotate around the line while expanding the string into several curves.
babyK's user avatar
  • 155
0 votes
1 answer
62 views

How can I simplify this out put?

Based on this answer, I tried to find the condition to function $y = \dfrac{a x+ b}{c x +d}$ where $ad \neq 0$ and $a d - b c \neq 0$ increasing on $(-d/c, +\infty)$. I tried ...
John Paul Peter's user avatar
7 votes
3 answers
159 views

How can I find values of m so that the function $\frac{-m+x^2+x-4}{4 x-m}$ increasing in the interval $(1,2)$?

I am trying to find value of marameters $m$ so that the function $f(x) = \dfrac{-m+x^2+x-4}{4 x-m}$ increasing in the interval $(1,2)$? I tried ...
John Paul Peter's user avatar
1 vote
2 answers
110 views

Iterated integral numerically

I am trying to calculate a double integral. However, after a long time, Mathematica does not give me any outputs. Has someone any ideas how to calculate this? ...
Marco's user avatar
  • 163
1 vote
0 answers
31 views

Issue with Integration of a Parameter-Dependent Function in Mathematica [closed]

The following Mathematica code is given: ...
Kώστας Κούδας's user avatar
1 vote
2 answers
136 views

How to impose a change of variable in a differential equation?

I have this differential equation in terms of the variable $y$ deq[y_]=y^2 U''[y] + (a y^2 + b y + c) U'[y] + (d y + f) U[y]=0 and I want to make the change of ...
PhysFan's user avatar
  • 63
0 votes
1 answer
129 views

Is it possible to get rid of `Root` and have an explicit closed-form solution for the given equation?

I want to solve the given equation for m>0 where all parameters are Reals and a<0. ...
PhysFan's user avatar
  • 63
2 votes
1 answer
99 views

Maximize a function of $x$ and $y$ where $x^2 +y^2 \leq 1$

I have the following function: $f(x,y) = x(y^2-x^2)- \frac{(x^2 +y^2)^2}{2\rho}+\frac{3x^2(y^2-4x^2)}{\rho}$ where $\rho>0$ is a constant. My goal is to find the maximum value of this function ...
wanderer's user avatar
  • 135
4 votes
1 answer
153 views

Cassini oval plotting related isues

PART 1 The parametric equation mentioned in the webpage, Eggs, melons, and peanuts - Cassini Oval, for the Cassini oval is given by ...
user444's user avatar
  • 2,644
1 vote
1 answer
101 views

Plotting a parameteric function

I aim to plot the amoeba of f=x1^3 + x2^3 - 4 x1 x2 + 1 . Following this thread, I have solved f==0 and tried to plot the log of ...
Shasa's user avatar
  • 1,043
7 votes
3 answers
413 views

How to plot a surface given implicitly by 3 equations in 5 coordinate variables?

I have 3 implicit equations in 5 variables: $f_1(S, y_h, y_d, x_h, J)=0$, $f_2(S, y_h, y_d, x_h, J)=0$, and $f_3(S, y_h, y_d, x_h, J)=0$. These equations determine a 3D surface in $S-y_h-y_d$ ...
yuhao chen's user avatar
3 votes
1 answer
164 views

Finding the parametric equation of two intersecting surfaces

I was given two equations of surfaces: an ellipsoid (x/2)^2+(y/4)^2+(z/5)^2=1 and a plane z=3. So I graphed their intersection ...
bb_823's user avatar
  • 133
3 votes
2 answers
189 views

Area of ​a parametrically defined function

I can’t solve the problem; I need to find the area of ​​a parametrically defined function. According to the graph, part of the area has a negative sign. ...
Vladimir's user avatar
  • 337
0 votes
0 answers
57 views

Get curve equation from parametrization

I am quite new to Mathematica and I have been wondering how to do this one very specific thing. I have two functions $x(t)$ and $y(t)$ that are the parametrization of a curve, how would I get the ...
Memat's user avatar
  • 101
2 votes
2 answers
120 views

Convert list of variables to list of parametrized functions

I have a list of differential equations of some variables eqns = {f[x,y,x',y'],g[x,y,x',y']} e.g., f[x,y,x',y'] = x x' + y y'. ...
Joalito's user avatar
  • 123
0 votes
0 answers
99 views

Plotting function defined via NIntegrate is too slow

I have the following functions as solutions of a system of differential equations (for calculation, I used ParametricNDSolveValue) ...
derdin1's user avatar
  • 63
0 votes
1 answer
98 views

Speed Up Plotting of Mathieu Equations

I am trying to plot Mathieu Functions, running for an hour without a result. Here is my code: First define the relevant physical constant: ...
ZHENGYAO HUANG's user avatar
4 votes
3 answers
308 views

Plotting multiple parametric 3D curves without using the Show command

How can I plot multiple parametric 3D curves on a single graph without the need to combine them using Show? Additionally, is there a way to clearly distinguish ...
emnha's user avatar
  • 2,111
1 vote
1 answer
117 views

How to invert this function when the argument e is small?

I need to find an analytical solution the following equation for e in terms of n and p ...
Dotman's user avatar
  • 486
2 votes
4 answers
128 views

Plot the surface $xy+z=1$, plane $x+y+z=1,$, and their curve of intersection in different colors

Plot the surface $x y + z = 1$, plane $x+y+z=1$, and their curve of in intersection in different colors.
Parker James's user avatar
3 votes
1 answer
230 views

Parametric Plotting 6D Dimensions to 3D for Visualizing a Solution

I am trying to find out when: $$f(x,y,z,α,β,γ):= z\cos(β)\cos(γ)+y(\cos(γ)\sin(α)\sin(β)+\cos(α)\sin(γ))+x(−\cos(α)\cos(γ)\sin(β)+\sin(α)\sin(γ)),$$ where $α,β, \text{and } γ$ can be any value in $[-2\...
Teg Louis's user avatar
0 votes
0 answers
37 views

ParametricNDSolve with known solution at one limit

The ODE I wish to understand is the following: ...
Anthony's user avatar
  • 231
2 votes
1 answer
141 views

Convert R code to Mathematica code of Poisson log-likelihood for the epidemic curve

I want to define a function that simulates the model for a given combination of parameters and calculates the Poisson log-likelihood for the epidemic curve of reported cases: ...
Athanasios Paraskevopoulos's user avatar
1 vote
0 answers
54 views

Stiffness problem which abruptly stops the evaluation

We have a Lagrangian and we found the EOM. We need to solve the EOM and find the Phase-space plot. However, we are facing a stiffness problem which abruptly stops the evaluation (...
user444's user avatar
  • 2,644
0 votes
1 answer
130 views

Find parameters in an SIR model

...
Athanasios Paraskevopoulos's user avatar
-5 votes
3 answers
108 views

Why can't the problem of constancy be solved?

Clear["Global`*"] f[x_] := a E^x - Log[x] ForAll[x, 1 < x < 2, f'[x] > 0] Resolve[%, Reals] Why can't the problem of constancy be solved?
csn899's user avatar
  • 4,461
3 votes
2 answers
190 views

Given the parity of a function, how can I find the value of a parameter?

Given that the function g [x] is an even function g[x_] := (x + a) Log[(2 x - 1)/(2 x + 1)] How to find the value of parameter a? I tried the following method but ...
csn899's user avatar
  • 4,461
3 votes
3 answers
198 views

How to find the range of values for this absolute value function?

The function is: f[x_] := Abs[2 x - k] + Abs[2/k x + 1/k^2] The range of parameter k is: 0 < k <= 1 How to find the ...
csn899's user avatar
  • 4,461
2 votes
1 answer
115 views

Eigenfunction condition of time-independent Schrödinger equation

I'm trying to get the eigenfunctions and eigenvalues of the following one-dimensional Schrodinger equation: $$ -\frac{1}{2}\frac{d^2}{dx^2}\psi(x)+V(x)\psi(x)=E\psi(x)\,,$$ where the external ...
Crazydemon92's user avatar
1 vote
3 answers
293 views

Finding maximum value of a function with parameter

How can I find the maximum value (and the corresponding $x$) of the following function with parameter $t$: $$ f(x) = |x^2-tx + 2t|$$ on a closed interval $x\in[0,1]$? I tried using ...
csn899's user avatar
  • 4,461
3 votes
2 answers
179 views

Complicated system of two non linear equations in three variables

I have a system of two equations in three variables. The two expressions involved in the system are obtained diagonalizing the following matrix with Eigensystem[]: <...
Anna's user avatar
  • 33
1 vote
1 answer
90 views

Fitting Parameters to the Heat Equation [closed]

As part of my research, I have been trying to use a model of heat conduction through a 2D layer given an input steady-state Gaussian power profile and a heat loss term to the environment. All but one ...
Jack LeGrow's user avatar
3 votes
1 answer
173 views

Is it possible to ask Mathematica to obtain the function describing the upper and lower boundaries of a combinations of functions?

Assume that I have three one-variable non-periodic functions $f(x),g(x),h(x)$ for $x>0$. The question is: is it possible to ask Mathematica to obtain the function describing the upper and lower ...
math2021's user avatar
  • 749
0 votes
1 answer
41 views

Find the fitting values of unknown parametres by ParametricNDSolveValue

I have this ODE: eq = E^(2 a x[t]) + (2 + 13 E^(2 (a - b) x[t]) x'[t]^2== 6 a E^(2 (a - b) x[t]) ((2 a - b) x'[t]^2+ x''[t] ) I want to solve for ...
Dr. phy's user avatar
  • 287
0 votes
2 answers
99 views

Number of solutions of an equation with parameter (Mathematica)

Some nonlinear equations can have many solutions for a given parameter and I would like to know how the number of solutions varies with respect to a parameter $a$. I would like to solve: $ax^2+x-1=e^...
Jakub Wróbel's user avatar

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