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.
722
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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_\...
1
vote
1
answer
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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 ...
9
votes
2
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478
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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.
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1
answer
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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
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7
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2
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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
...
1
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2
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103
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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?
...
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31
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Issue with Integration of a Parameter-Dependent Function in Mathematica [closed]
The following Mathematica code is given:
...
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2
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116
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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 ...
0
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1
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98
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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. ...
2
votes
1
answer
95
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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 ...
4
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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
...
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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 ...
7
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3
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405
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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$ ...
3
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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 ...
3
votes
2
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186
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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.
...
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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 ...
2
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2
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116
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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'. ...
0
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0
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98
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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)
...
0
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1
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94
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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:
...
4
votes
3
answers
304
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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 ...
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1
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116
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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
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4
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117
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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.
3
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1
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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\...
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0
answers
37
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ParametricNDSolve with known solution at one limit
The ODE I wish to understand is the following:
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2
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1
answer
139
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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:
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1
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0
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51
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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 (...
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3
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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?
3
votes
2
answers
186
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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 ...
3
votes
3
answers
191
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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 ...
2
votes
1
answer
107
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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)\,,$$ where the external ...
1
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3
answers
264
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Finding maximum value of a function with parameter
How can I find the maximum value (and the corresponding $x$) of the following function with parameter $t$:
$$ f(x) = |x^2-tx + 2t|$$
on a closed interval $x\in[0,1]$?
I tried using ...
3
votes
2
answers
175
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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[]:
<...
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1
answer
85
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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 ...
3
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1
answer
171
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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 ...
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1
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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 ...
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2
answers
93
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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^...
0
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0
answers
146
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Factorization of 5th polynomial with Wolfram-Mathematica
I have a very complicated 5th-degree polynomial form. Using the factor function in Wolfram is impossible to make it because of the high degree. I just want to know that is it possible to factor as I ...
3
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3
answers
169
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Parametric Plot in different graphs
i would like to plot the function of a parametric differential system below ideal in separate graphs. My code is
...
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3
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174
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How to use plot parametric function with discrete data?
You can easily create a ParametricPlot using the syntax ParametricPlot[{fx, fy}, {t, tmin, tmax}] when you have the functions fx ...
2
votes
1
answer
186
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How to plot Hyperbolic using parametric form with Animation?
Animate[ ParametricPlot[{Cos[\[Theta]], Sin[\[Theta]]}, {\[Theta], 0, a + 0.0001}, PlotRange -> {{-1, 1}, {-1, 1}}], {a, 0, 2 Pi}, AnimationRunning -> False]
...
3
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1
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Manipulating expression ParametricPlot
How can I make Mathematica plot the curve being traced by the focii of the ellipse?
I know the traced curve would be drawn in an instant, when I switch the variable from u to t, but I want the curve ...
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1
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Plot of non-homogeneous diffusion equation
Let the initial and boundary value problem for the diffusion heat equation
\begin{align*}
u_t(x,t)&=u_{xx}(x,t)-\alpha u_x(x,t), \quad 0<x<+\infty,t>0\\
u(x,0)&=f(x), \quad x\...
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Is it possible to ask Mathematica to order this expression in terms of descending absolute values of the arguments of the exponential functions?
I have the given expression which is a sum of exponential functions with some parameters $a,t,u,y$ where $a>0$.
Question
Is it possible to ask Mathematica to order this expression in terms of ...
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6
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846
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How to wrap a cylinder?
i'm trying to wrap a cylinder in a torus, the best i've done is the following code:
...
0
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1
answer
46
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Unable to access solutions of coupled linear differential equations using ParametricNDSolve [closed]
I have the following code that tries to solve for 4 coupled differential equations Ap1[x], Ath[x], ...
0
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2
answers
70
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Accessing solutions of coupled differential equations solved using ParametricNDSolve [closed]
I have the following linear coupled differential equations (y , z) that I wish to solve with a varying parameter a
...
2
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1
answer
81
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Why does Series give two different results for given function?
I want to do Series of this function x^12 Cos[y x]^2 Sin[y x]^6 Sin[(-1 + Sqrt[3]) y x]^2 around ...
0
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0
answers
33
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ParametricNDSolve Skipping Over Periodic Input Function
I am attemting to model some expermental data with the differential equation $\frac{dm}{dt} = D(m) + F(\omega t)$ via Mathematica's ParametricNDSolveValue function. ...
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199
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Solving Helmholtz Equation in 2D for Circular Disk with DEigensystem, NDEigensystem
I would like to solve the Helmholtz equation with Dirichlet boundary conditions in two dimensions for a circular disk with a radius of 1.
$\Omega =$ some boundary e.g. a circle
$
\nabla^2 u(x,y) + k^...