# 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
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### 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 (...
1answer
37 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 $\max\{5-X_1a, 3-X_2a,0\}$?
2answers
139 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 $t_f$ ...
2answers
143 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 ...
2answers
64 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 ...
0answers
96 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 ...
2answers
72 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 ...
1answer
37 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 ...
2answers
68 views

### Add function to Manipulate

I have a Manipulate plot and want to add another function, in addition to the existing a and ...
1answer
53 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 ...
0answers
40 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 ...
1answer
92 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 $\boldsymbol{r}\left(s\right)=\left(x\left(s\right),y\left(s\right)\right)$ ...
1answer
97 views

### Empty graph when using parametric plot 3D

I want to plot a parametric 3D plot from the following ParametricNDSolve code: ...
2answers
73 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? ...
1answer
135 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, ...
1answer
93 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 ...
1answer
65 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?
1answer
59 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: ...
2answers
59 views

2answers
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### 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 :- ...
3answers
153 views

5answers
356 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 ...
3answers
95 views

### How can I make a projection of ParametricPlot3D onto 2D surface without shading?

I have a Parametric Plot that has very high and low values. I used this answer Project RegionPlot3D to 2D using hue/color function to show third dimension to project the surface onto the 2D plane. ...
1answer
74 views

### How can I plot Trajectory of 3d parametric plot?

x1 and y1 are constants. I have plotted ParametricPlot3D. ...
2answers
84 views

### ParametricNDSolve for a system of 4 non-linear ODEs and plotting the solutions

I have four coupled first-order non-linear differential equations, denoted as: A1[x], A2[x], ...
2answers
182 views

### Problem with FindFormula for experimental dataset [closed]

I have a dataset whose mathematical model is unknown. There is my code. ...
1answer
104 views

### Combine different kinds of plots [duplicate]

how can i combine thats plots: ...
1answer
45 views

### Parametric field Plot

i want to plot this field: G(x,y,z) = (0,0,-b^3(x^2+y^2)cos(b^2(x^2+y^2))) with the parameter b>0. Is it possible to do that? if yes,how can i do that?
0answers
159 views

### Simplify Vs FullSimplify

I performed an integral and received an extremely long answer. I tried running FullSimplify on the answer, and after 72 hours gave up. Does ...
1answer
358 views

### Calculate Radius of Curvature

I have a list of coordinates that make a near-parabolic graph, which I managed to fit and calculate the curvature. However, the curvature only outputs a equation. Is there any way to calculate the ...
1answer
69 views

### Find Arc Curvature From List of Coordinates and NonLinearModelFit

I have coordinates as a list, and I can fit it almost perfectly with an equation. I'm just curious as to how I can find the curvature of this arc. I've tried using ArcCurvature, but I'm not sure how ...