# Tagged Questions

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5k 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 ...
1k views

### Fitting points to tilted, off-center ellipse

I have 24 x-y points that are supposed to form an ellipse. ...
1k views

### How to plot a certain surface? What is its parametric equation?

The surface show below is very beautiful; however, I don't know its function either as an implicit function or in parametric form. Anyone have an idea about it and how to draw it with Mathematica?
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### How to get intersection values from a parametric graph?

I have this graphed: ParametricPlot[{2.4*Cos[t] + 1.6*Cos[3 t/2], 2.4*Sin[t] - 1.6 Sin[3 t/2]}, {t, 0, 4*Pi}] It is a star, and the lines cross each other ...
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### How do I obtain the enclosed area of this particular parametric plot?

I'm trying to find a way to obtain the enclosed area of this particular plot. Can someone show me how? ...
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### How to create these famous surfaces in topology with the desired color effects?

It was said such real objects of famous topological surfaces were plotted by the cooperation between mathematician Richard Palais and artist Luc Benard, and published as the cover page of Science ...
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### Find the parameter values satisfying conditions for all roots of an equation

Hi I'm very new at Mathematica. My real problems concerns a much more difficult equation with many parameters, but I want to check that the method is good, so I made up a test equation. My test ...
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The dynamic billiard demonstration, that can be found on wolfram demonstrations (here), is only designed for an ellipsoid-shape boundary(snapshot below). The idea is to have a dynamic billiard with ...
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### Filling between parametric plots

I am new with Mathematica, but am trying to fill an area between two parametric plots ...
961 views

### Solve for the intersection point of 3 surfaces

Basically, I have three 2-torus (tilted) in 3-dimensional Euclidean space. They are expressed by parametric equations: ...
798 views

### Plotting a 2D shape along a 3D parametric function curve

Say I have a 3D curve that is parametrically defined. How would I be able to plot shapes like figure 8s whose centers are aligned along the 3D curve? Say the curve was: ...
615 views

### Visualizing Line Integrals

I have a plane curve $C$ described by parametric equations $x(t)$ and $y(t)$ and a function $f: \mathbb{R}^2 \rightarrow \mathbb{R}$. The line integral of $f$ along $C$ is the area of the "fence" ...
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### Intersection of Osculating Circle with a Parametric Curve

I have the following Parametric plot Generated from the following: ...
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### Find the value of parameter so that the equation has one solution

Let $(E_l) : x^4-4x^3+x^2(5-l^2)+4 x l^2-4l^2 = 0$ be an equation with $l$ as a parameter and $x$ as an unknown and $S_l$ the set containing all the real solutions of $(E_l)$. Then there is a unique ...
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### I need to remove a line from a ParametricPlot

What happens is that when I make this ParametricPlot: ...
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### Changing Plot order for 3D printing

Alright, I got a my first 3D print done of a pseudosphere using parametric plot and a deflated sphere using a contour plot, but when I try ...
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### How to plot this region?

Consider the $2\times 2$ matrices \begin{align} A=\begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{bmatrix} \end{align} and \begin{align} B=\begin{bmatrix} b_{11} & b_{12} \\ ...
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### ParametricPlot3D: The Mesh shows some unexpected wires to the origin. How to remove them?

In the code below a hexagonal shape is defined and plotted. The ParametricPlot3D shows the hexagonal design almost as intended. However, the mesh makes some strange "wires" to x=y=0. This is ...
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### Partial zeta curlicues

I asked a question at MSE and Raymond Manzoni provided an excellent answer that included these visuals: I made a very basic attempt at recreation with ...
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### Problem with WhenEvent

I am trying to add a time dependent fraction to a parameter in NDSolve, i.e. when 10 < t< 20, add ...
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### ParametricNDSolve and Constraint satisfaction problem

I am trying to find the values of two parameters that allow for a specific result of my differential equations, under different initial conditions. Given a system of equations: ...
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### Normal and Tangent of Acceleration in 3D

I need to figure out how to find the Normal and Tangent of acceleration. I know the formula for the tangent of acceleration is $((Acceleration . Velocity)/(Velocity.Velocity))*Velocity$ and the normal ...
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### How do you create such an animated GIF via Mathematica?

Is it possible to create such kind of GIF via Mathematica?
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### How can I get the function of a plotted trajectory? [closed]

I solved two ODEs, which are a function of t, numerically. The first ODE is the vertical equation of motion and the second one is the horizontal equation of that ...
159 views

### cycloid parametric [closed]

How do I enter 3 parametric equations for cycloids corresponding to circles with radii 1, 2, and 4. I have tried ...
364 views

### Marking specific points on a 3D curve

Here is the curve below. (written as a position vector) r = {Cos[7 Pi*t], Cos[6.2*Pi*t], 2.5*t} ParametricPlot3D[r, {t, 0, 2}] I want to know how I can mark ...
742 views

### Nonlinear least squares

I have a typical nonlinear least square problem and it seems very similar to the example provided in the section on parameter fitting at the Wolfram website. Unfortunately I always get some error ...
140 views

### Finding the intersection of curves in a one-parameter family [closed]

I have a function f[c_] := y^2 - 2 x^2 (x + 3) == c ((y + 1)^2 (y + 9) - x^2) I need to find the points of intersection between the plots of f[0] and f[2]. How ...
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### ParametricPlot3D[] Question

I know this is very similar to a previous question I asked, but there are some differences. When I graph: ...
333 views

### Speeding up solving a system of simultaneous equations

I am trying to solve the following system of equations. Solve takes a very long time to solve the following system of equations. Is there any way to speed it up? ...
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### Reading parameters from file and use them as parameter of a function [closed]

Hi all: given the code ...
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### Why is there always a horizontal tail line on the parametric curve?

I am trying to create a smooth, piecewisely continuous and differentiable curve by using Mathematica's Floor function, which is as in: ...
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### ParametricNDSolve problem

when i use ParametricNDSolve, the output is not a explicit function, for example: ...
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### Limitations of ParametricNDSolve family w.r.t objective functions

Observation: I can see even for very simple modification in case of an scalar objective involving an definite integral in time ParametricNDSolve fails. Here is an ...
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### Piecewise conditions with a parametric PDE

I'm using ParametricNDsolve to check best fit of a model (function Eb1) with some data, and I have four free parameters I want to test. I can easily construct a Parametric solution between the two ...
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### How to integrate ParametricNDSolve solution with respect to a parameter?

I have just upgraded to the new version of Mathematica because of its new built-in ParametricNDSolve function. I need to solve a first-order non-linear ordinary ...
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### How to use ParametricPlot and fill closed areas with blue and red?

The current code is : ...
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### Difficult parametric function

I've got this strange parametric function and I want to implement it on Mathematica. I know that I could use Excel and calculate it, but my database is quite large and I want to do some reproducible ...
212 views

### How can I plot a 3-variables function to identify the neutral surface and a region

I wanted to plot a 3-D solid region, in which my function f(x,y,z)= x (1/(1 + 0.06))^3 + y (1/(1 + 0.06))^2 + (2 z^2)/15 (Sin[10 Degree])^2 -z/3 Cos[10 Degree] ...
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### Plot parametric solutions using Manipulate [duplicate]

I want to plot the parametric diagram of {y[t],z[t]}, in which I manipulate a parameter, ω, from $[1, 10 \pi]$. Here is what I have attempted, but I can't get a ...
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### Plot a parametric equation in cylindrical coordinates

I'm looking for a way to plot this parametric equation on cylindrical coordinates. r = e^t theta = t+1 z = e^2t Any help would be appreciated
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### Filling between ParametricPlot and Plot

There are some similar questions: (1) (2) have been ask, but I think this is a different one. If we have a ParametricPlot and a ...
63 views

### Finding roots of a function with a varying parameter

So I'm brand new to Mathematica, and basically what I want to do is find the roots of a function at varying time intervals. The function I'm using is: ...
598 views

### ParametricPlot3D with three variables

ParametricPlot3D can be used with one or two variables to plot paths and surfaces in 3-D such as ...
938 views

### Parametric plot from two NDsolve solutions

I have two independent ODE systems. A = NDsolve[..., {x, y}, {t, 0, 10}]; B = NDsolve[..., {a, b}, {t, 0, 10}]; I can draw a ...
155 views

### Plotting knot torus

I'd like to plot together a torus and a knot on it, that is, closed curve wrapping around the torus, $m$ times around a circle and $n$ times around the other circle. It will be used to explain ...
668 views

### Eliminating the Parameter: Transform parametric equation to Cartesian equation and draw arrows along parametric growth

Hey guys I really could use some help on this calc 3 problem. I'm stuck on how to write the code for this problem: a) Eliminate the parameter to find a Cartesian equation for a parametric curve. b) ...