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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1answer
36 views

Remove specific terms from Mathematica output

I have a very complicated output from Mathematica - which may run to several pages - and I want to keep only some of the terms. The expression I am working with is a double summation. It results in (...
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1answer
27 views

How to find the expected value of a parametric function?

Suppose $a \ge 0$ is a parameter and $X_1$ is an uniform random variable in $[1,4]$ and $X_2$ is an uniform random variable in $[1/2,1]$. How to find the expected value of $\max\{5-X_1a, 3-X_2a,0\}$?
2
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2answers
117 views

Minimization using NMinimize

I have a system of ODEs say $$x'(t)=2 x(t)-x(t)y(t)-3 x(t) g(t),$$ $$y'(t)= y(t)-2 x(t)y(t)- x(t) g(t)$$ with ICs $x(0)= 1, y(0)=1/2$, say, for $t_0 \leqslant t \leqslant t_f$, where $t_0$ and $t_f$ ...
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2answers
128 views

Plot f(x),f(y),alpha where f(x) and f(y) are the solutions of a two ODEs system depending on a parameter α [closed]

My question is in the title. For example, the system could be: $$\begin{align*}\frac{dx}{dt}&=-y+x[\alpha-(x^2+y^2)]\\\frac{dy}{dt}&=x+y[\alpha-(x^2+y^2)]\end{align*}$$ And I want to plot this ...
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0answers
82 views

Repeated calling of a ParametricNDSolve result in a faster way?

I recently learned of ParametricNDSolve and found that I need to compute it once and then call its result sol at different ...
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2answers
59 views

Unexpected results when plotting an output of Solve [closed]

My aim I want to find the solution of a cubic equation as a function of a parameter. In my code, the cubic equation is to be solved for the variable th with ...
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2answers
70 views

Colour each graph differently

I have a Manipulate function, which allows me to compile plots on a single plot (see below). I am trying to make each line on the compiled plot to be a different ...
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2answers
99 views

Drawing evenly spaced arrows and opaque sheet between curves?

I have a question about drawing arrows/sheets between curves. Suppose I have two 3-d parametric curves like shown below: ...
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1answer
30 views

Parametric Maximization of a function with indicator function

How is it possible to determine the maximum and maximizer of the following function? where I(x>0) = 1 if x>0, otherwise 0 ...
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2answers
64 views

Add function to Manipulate

I have a Manipulate plot and want to add another function, in addition to the existing a and ...
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1answer
45 views

ParametricNDSolve Value and Manipulate with 3 parameters

I am trying to solve a set of coupled differential equations, using ParametricNDSolveValue, where there are 3 parameters. The parameters are ...
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2answers
1k views

Plotting Limit Cycle

I have Lotka Volterra Equations where the prey equation is modified. The Equations are x'[t]=a*x[t]*(1-x[t]/k)-b*x[t]*y[t] y'[t]=-c*y[t]+d*x[t]*y[t] To plot the ...
4
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1answer
80 views

Solve numerically 2D parametric boundary problem

For a personal project, I want to solve the following problem: Let $f\left(\boldsymbol{r}\right)$ be a 2D function, and let $\boldsymbol{r}\left(s\right)=\left(x\left(s\right),y\left(s\right)\right)$ ...
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0answers
37 views

Fit data to a model of two-variable differential equations

I am trying to fit some data to the solution of a differential equation. I am using ParametricNDSolve to create a model which should fit the data using ...
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2answers
183 views

Solving equations involving the modified Bessel function

I want to solve this equation Solve[s^2/y^2 (x - y + 2 g BesselI[1, s/y]) == 2 g y BesselI[1, s/y], s] and substitute s in ...
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1answer
88 views

Empty graph when using parametric plot 3D

I want to plot a parametric 3D plot from the following ParametricNDSolve code: ...
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5answers
24k views

Find eigen energies of time-independent Schrödinger equation

I'm trying to get the eigenvalues of a one dimensional time-independent Schrödinger equation, $-\frac{h^2}{2m_0}\frac{d^2\psi}{dx^2}+U(x)~\psi=Ei~\psi$ where U(x) is some potential and Ei is the ...
3
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1answer
129 views

Label curves with corresponding parameter [closed]

How can Plotlegend label each curve with the corresponding value of parameter param in the code below? ...
2
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1answer
222 views

Can DSolve give results in parametric form?

Can DSolve give results in parametric form? For example the cycloid equation is: DSolve[{(x'[t])^2 == r/x[t] - 1}, x[t], t] And the solution is usually given in ...
2
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1answer
128 views

How to make this moving surface a continuous and derivable function?

I'm having troubles in defining a function of three variables: $t$, $x$, $y$, from a moving bumpy surface that should be derivable relative to its three variables. Here's the animated surface code, ...
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2answers
71 views

How to simplify this sum of random waves?

Is there a way to simplify the random functions and their calls, in the code below? ...
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1answer
79 views

Randomly oscillating surface is not working well

I'm trying to built some random moving surface from a plane perturbed with random oscillators, and my current code isn't doing what I need yet, as seen from the ...
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1answer
51 views

I have a function $R \to C$, I want to plot it as the way we can plot parametric equations in the $R^2$. How to do it?

I have a real variable $t$ and a function $f(t)$ giving complex values. How to plot the function for $t$ in a given real interval? Also is there a way to do it in Wolfram Alpha website?
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1answer
159 views

Parametric Plot - Opacity Changing Along Line

How would one have the trajectory in a parametric plot go from a higher to lower opacity? Suppose the following code for example: ...
2
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1answer
50 views

How to insert variable height in this random bumps function?

I'm trying to insert a "time" variable that control the height of the random smooth bumps, but I'm yet unable to do it right, as shown with the code below: ...
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2answers
55 views

How to find maximum of two or more parametric functions?

I have two parametric functions in which I know the range of parameters and I want to find the maximum of these two functions by conditions on the value of the variable. Suppose $f(x)=x-c$ and $g(x)=r....
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1answer
41 views

Plotting ParametricNDSolve Value

I am trying to solve a set of coupled differential equations, where I would create plots for a(t) and e(t), where the parameter RAST can be varied. However, every time I try to plot, I get blank plots....
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2answers
109 views

ParametricPlot3D as a ContourPlot

I want to plot the amplitude of a complex-valued function of one complex variable. I want to do this in the plane defined by the real and imaginary parts of the complex variable as a ...
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2answers
87 views

Range errors when plotting solutions of systems of equations

I would like to plot the points $(a,b,c)$ that simultaneously satisfy the equations $$a^2+b^2=1,\qquad ac+b\frac{1+bc}{a}=0,\qquad c^2+\frac{(1+bc)^2}{a^2}=1.$$ I attempted to do this with ...
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1answer
82 views

How to solve the Summation equation by FindRoots [closed]

I want to find out the value of alpha and lambda where u lies between 0 and 1.
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2answers
79 views

control net of the torus

I want to make a complete control net of a torus. However, the net is not closed. Can anyone solve this problem? ...
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0answers
114 views

Plot the Corner Control Points

I face some problem of plotting the control points at the corner. I only want to plot the control points at the corner only. I do not know how to plot the corner control points from all the control ...
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2answers
159 views

Plot3D Equation of motion of a particle in a surface

I'm new in this forum. This semester I've been trying to learn how to use Mathematica for my Classical Mechanics course, but I'm still a novice concerning this software. In particular today I was ...
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2answers
300 views

Using fewer mesh lines, 3D graphics

I want to make the Final use fewer mesh lines, the ideal version will look like the second image. Where the triangle shape is more clear and clean. Can anyone give me some advice on how to fix my code?...
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1answer
81 views

Solve system of 5 unknowns and 5 nonlinear equations

I attached below the system of 5 equations that I am not able to solve using FindRoot. I also tried without defining the equations as functions but It didn't work. ` ...
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0answers
53 views

Animate ellipse drawing

$(x/3)^2+(y/5)^2=1$, $x=3\sin[t]$, $y=5 \cos[t]$ I want to draw a phase trajectory with time-lapse using manipulate or animate. Manipulate[ParametricPlot[(x/3)^2 + (p/5)^2 == 1, {x, -3, 3}, {p, -5, 5}]...
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2answers
48 views

How to Solve a function f[x[y],y] == 0 in Mathematica? i.e. a function of 2 variables, where one is dependent on other

I am new to Mathematica and am trying to solve an equation to calculate amplitude as a function of frequency numerically. The parameters are as follows :- ...
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3answers
128 views

Equipotential surfaces using ParametricPlot

So I'm trying to plot lines on which the following function is a constant $$ \frac{\left(-\Sigma (r,0.99,\theta )+2 r^2-0.99^2 r \sin ^2(\theta )\right)^2}{\Delta (r,1,0.99) \Sigma (r,0.99,\theta )^3}+...
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1answer
48 views

Not respected assumptions

I' m writing a function with the following line: ...
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0answers
31 views

Minimize doesn't work with more parameters

In the code I wrote there is a ParametricNDSolve with four parameters. I want to minimize an error function with Minimize. If I consider ParametricNDSolve with just one parameter everything works, and ...
2
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2answers
80 views

Is there a way to an implicit equation into parametric form?

For example, take the implicit equation for the unit circle $\qquad x^2 + y^2 = 1$. Is there a function Parameterize[x^2 + y^2 == 1] that would return a vector ...
0
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1answer
120 views

How can I solve this Integral?

I have a two variables function. I have to numerically or parametric integrate this function with respect to one of the variables (\tau) and assume the other variable (t) is constant. Note, however, ...
2
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1answer
72 views

How can I fill in a section of an ellipse converging on a focus rather than the center?

I am trying to plot a simple display of Kepler's second law - equal areas of an ellipse swept out in an equal amount of time. The problem is that I need my sections area sections to have a focus as ...
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1answer
32 views

How to calculate Sum of a function over a list

tlist = Table[i, {i, 1, 10}] tlist:{1, 2, 3, 4, 5, 6, 7, 8, 9, 10} f = E^(-((2 t)/T)); ...
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1answer
195 views

How to calculate specific area on surface of sphere?

I am trying to calculate the solid angle subtended by arbitrary-shaped loops on a sphere's surface. First, I parametrize circular loops by: $$\theta(t,k_{x0},r) = k_{x_0} + r \cos(t);$$ $$\phi(t,k_{...
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0answers
28 views

Using NonlinearModelFit from ParametricNDSolveValue with three parameters

Here is the very desired Parametricfunction , calculated using ParametricNDSolve, from physical arguments. From this, an interpolating function dens is settled. ...
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0answers
44 views

Find parameter ranges of a function whose value is within a window by sampling points

Problem: I want to find the ranges of the parameters for a function $f(x,y,z)$ when $0.9 < f(x,y,z) < 1.1$. All parameters are bounded $x , y, z \in [0,1]$. In the real problem the function ...
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5answers
350 views

Replace elements of a list based on a function

I have a function of k (written in the form of a table/list to get values) for 16 integer values from 1 to 16: f = Table[3*k*k, {k, 1, 256}] I want to replace ...
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0answers
18 views

Assign multiple parameters after function evaluation

I want to conduct sensitivity analysis on an ODE (say with two independent variables x,y) with many parameters. The issue I have boils down to trying to do it all at once in a module. My attempt ...
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0answers
41 views

generating a Poisson Gap sampled schedule

I have a grid of 256 points (0,1,....M-1), which I then want to distribute in sinusoid weighted Poisson Gap. tpts = Table[t, {t, 0, 255}]; I define two functions ...

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