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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46 views

How to initiate a matrix with indexed parameters [closed]

I couldn't find it in the documentation, so I'm posting it here. I want to create two by two matrices as follows: $$ `W = \begin{bmatrix}w_{11} & w_{12} \\ w_{21} & w_{22} \end{bmatrix}, V = \...
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Spheroidal Harmonics

There is a (scalar) field P varying on a spheroid (squashed) surface. This field is a function of four independent components ...
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1answer
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How to Create Lissajous Figures for Driven Damped Pendulum (as an animation/with Manipulate)

I wanted to know how can I generate a Lissajous plot for the forced driven pendulums (but for one pendulum in my case): (https://demonstrations.wolfram.com/ForcedPendulumsWithDamping/). I tried using ...
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convert a parametric function into a parametric polynomial [closed]

As shown in the image, I want to convert the functions Y1 and Y2 into polynomials. These functions are only dependent on X. Like the Taylor series In the Taylor series, it converts a function into a ...
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1answer
43 views

Converting a Non-Simple Closed Curve in an Image to a Parametric Equation

I would like to generate a parametric equation for a non-simple closed curve defined in a 2D image (shown below). This is the same problem as described in this question for simple curves. However, ...
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1answer
64 views

Avoiding/skipping singularity error in ParametricNDSolve

I've looked up a few examples of similar errors for ODE's with singular points, but have yet to figure out a way to solve this problem for my case. A simple patch up where the singular point is '...
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1answer
64 views

How to solve integro-differential with parameters iteratively?

I am trying to solve an integro-differential equation and tried using one of the answers that I found in a related question: Numerically solve an integro-differential equation The difference is I have ...
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1answer
60 views

Plotting multiple dependent variables with DSolve (projectile motion with air resistance)

I wrote a working code that plots what I need using DSolve and parametric plot. Here's an example of what it plots (and code is at the bottom). However, I want to be able to plot multiple graphs on ...
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How to solve this set of PDE equations? I tried ParametricNDSolve, but

I am tring to solve set of PDE equations with parameters of v[z],q[z],T[z,t,r]. Below is my ...
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Issue with ParametricNDSolve and Table

I have a differential equation, I plot it for different initial values by using ParametricNDSOlve. Code - ...
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NSolve with ParametricFunction

I have solved a SDE with ParametricNDSolve: s = ParametricNDSolve[ {p1, m1, p0, m0}, {P, m}, {r, 0, 1}, {m, k, e, Cnew} ] And now I want to treat the ...
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1answer
54 views

Plot with three functions and three parameters [closed]

I think my code doesn't have any problem but the program shows me this error and I'm confused! Plot::argr: Plot called with 1 argument; 2 arguments are expected. ...
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48 views

How can I substitute values into this set of equations?

I'm new to Mathematica and I'm trying to solve this set of trig equations (I'm not exactly sure if the syntax looks correct): ...
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1answer
62 views

3D Arrow path along a surface

I have the following two surfaces, created by the following functions ...
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1answer
48 views

Marking with Mesh, Distinct coloring, Ticksing, and Plotting table of complex function with parametric plot

Here is my todo list and what i've done: Using FrameTicks on specific points only (failed). Plotting six graphs with Table on <...
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1answer
91 views

Solving multiple differential equations parametrically

I have the following code, where I am trying to solve one set of differential equations parametrically. I then want to use this solution to solve another equation parametrically. However, I get the ...
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1answer
64 views

How to get the intersection between circle and rectangle?

Consider two figures: a rectangle with coordinates $(x_{min},y_{min}), (x_{min}+dx,y_{min}+dy)$, and a circle. The latter has a radius $R$ and is located at the center of the coordinate frame. How to ...
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1answer
30 views

Gaps in a continuous parametric plot problem

I attempted to plot a parametric plot using the following code: ...
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2answers
50 views

Solving a hyperbolic equation

I have the following equation: Tanh[-19.4*\[Zeta]]*Exp[k x] == Tanh[-19.4*\[Psi]]; \[Zeta] = 66; k x = 9.21; I want to calculate the value of ...
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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 (...
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32 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 $\max\{5-X_1a, 3-X_2a,0\}$?
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2answers
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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
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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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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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0answers
86 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
71 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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1answer
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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
65 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
50 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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38 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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1answer
84 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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1answer
91 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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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
131 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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1answer
85 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
55 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
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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
57 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
114 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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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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115 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
164 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
307 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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2answers
83 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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1answer
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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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58 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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49 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
137 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
56 views

Not respected assumptions

I' m writing a function with the following line: ...

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