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16
votes
4answers
2k views

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 ...
10
votes
5answers
885 views

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? ...
19
votes
4answers
3k 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 ...
18
votes
2answers
870 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?
19
votes
5answers
806 views

Fitting points to tilted, off-center ellipse

I have 24 x-y points that are supposed to form an ellipse. ...
8
votes
2answers
770 views

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 ...
-4
votes
1answer
448 views

Plotting a piecewise parametric curve [duplicate]

I have no idea how to plot the following piecewise parametric curve in Mathematica; ...
4
votes
1answer
560 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: ...
7
votes
5answers
1k views

Filling between parametric plots

I am new with Mathematica, but am trying to fill an area between two parametric plots ...
1
vote
3answers
206 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 ...
1
vote
1answer
158 views

Can ParametricNDsolve be used for coupled PDEs with 5 parameters?

I have a system of coupled PDEs with five parameters that I only know ranges for rather than explicit values, and I was wondering if I could define a parametric equation with ParametricNDSolve and ...
1
vote
1answer
179 views

Using ParametricNDSolveValue with initial conditions of another ParametricNDSolveValue

I have a system of parameter-dependent ODEs, which I can solve using ParametricNDSolveValue. Now, I have another ODE, which has as initial condition the solution of ...
0
votes
0answers
85 views

Parameter sensitivities of ParametricNDSolveValue involving numerical function

This is a followup of my former question from here. Consider the code ...