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Hello I am a Maple 15 user and I am using the command fsolve to solve for the intersection of two curves over a specified interval in x, namely from 0 to the lim defined in the Maple document. The specified interval contains asymptotes and when I specify the full interval only one of the three solutions is returned even if I can see that there are three distinct solutions by looking at the plot of RHS and LHS. Should I use another technique to find the solution or is my implementation of fsolve command wrong?

Thanks in advance


restart

with(ListTools):

n1 := 1:

n2 := 1.50:

n3 := 1.40:

lambda := 1.3:

k0 := 2*Pi/lambda:

d := 3:

x0 := k0*d:

arg1 := sqrt(x0^2*(n2^2-n1^2)):

arg2 := sqrt(x0^2*(n2^2-n3^2)):

lim := FindMinimalElement([arg1, arg2]):

sqr1 := sqrt(x0^2*(n2^2-n1^2)-x^2):

sqr2 := sqrt(x0^2*(n2^2-n3^2)-x^2):

LHS := tan(x):

RHS := (sqr1+sqr2)/(x*(1-sqr1*sqr2/x^2)):

plot([LHS, RHS], x = 0 .. lim, y = -6 .. 6)

 

fsolve(RHS = LHS, x = (1/2)*Pi .. 3*Pi*(1/2))

2.634254816

(1)

fsolve(RHS = LHS, x = 3*Pi*(1/2) .. 9*Pi*(1/4))

5.222527128

(2)

fsolve(RHS = LHS, x = 9*Pi*(1/4) .. lim)

7.598486053

(3)

``


Download HW4Q2.mw

Hi Maple friends.

Is there a Maple function to determine the intersection of two curves? For simple curves where the intersection is clear, I can plot them and use probeinfo to get the approximate intersection values.

But for more complex curves, where the scales are large, or the intersection point is not clear, it is difficult.

ie. intersection of y=x-3 and y=x^2-2*x-1

or intersection of y=x+1 and y=(x+1)/(x-1)

Thanks in advance.

Hi, guys and happy eastern to all! :)

I have a realy big problem. I have to do beziercurves in 3d plots.

I can´t plot it in 3d, something wrong with the plot (complex). Can anybody pls help me?! It´s very important to me, thanks! :)

I'm taking calculus and my professor introduced us to maple software. The professor asked us to plot the families of curves for this orthogonal equation:

dy/dx = (x^2) - (2y^2) - C = 0

This is what I had so far:

 

restart;

with(DEtools):

with(plots):

 

Function:=unapply(simplify(x^2-2y^2-C),(x,y)):

'Function'(x,y) = Function(x,y);

plotFunction:=C->implicitplot(eval(F(x,y),a=C),x=-5..5,y=5..5,scaling=constrained):

plot1:=display(seq(plotFunction(a),a=-5..5)):

display(plot1);

 

This is only display one family. How do I code for it plot the other families?

(The graph should look like curves converging from left, top and right sides toward to the origin of the axes)

Please help.

"Circular segment" is the unfortunate but standard term for the region between a chord and an arc of a circle sharing the same endpoints (see http://en.wikipedia.org/wiki/Circular_segment).  I say "unfortunate" because the phrase suggests a line segment when it actually means a planar region.

I would like to plot a shaded circular segment using Maple17.  I want the endpoints of the chord & arc to be anything I please, so the chord is not necessarily horizontal, or vertical, or the diameter of the circle, etc.

At the URL

http://www.mapleprimes.com/questions/139057-Segment-Of-A-Circle

there is an image containing a shaded circular segment, but I don't see what code produced the image.  The image there includes a horizontal chord, and I don't know if the code used to produce that image can be adapted for chords that are not horizontal.

If I have to, I can plot a shaded polygon with a huge number of sides that is indistinguishable from a circular segment.  I have plotted polygons before.  But it would obviously be preferable to plot a shaded circular segment.

If there a way to plot two curves of the form r = f(theta) and shade the region between them?  This would be better than the huge-polygon approach, but not as good as a simple command for plotting a shaded circular segment, if such a command exists.

Hi, I am trying to plot these two curves:

I tried:


with(plots);  A := Array(1..2)  A[1] :=plot (0.199563349672261+0.0178636902277546 x^1.14406289706794-0.0182070811144750 x^(1.13867380551454),x=50..2050,  color=red);  A[2]  := plot(0.298910542599302+0.0117459591500434 x^1.00390277106937-0.0137065176395662 x^0.970667551759677, x = 50..2050, color = blue);  display (A);

and I got:

Error, (in plot) unexpected option: .298910542599302+0.117459591500434e-1*x^1.00390277106937-0.137065176395662e-1*x^.970667551759677

so I tried

so I am not sure how I would graph these two functions...

eqt := y^5+y^4 + -0.5109*y^3 + -0.0595*y^2 + 0.0000-(-3.1086e-015*u^4 + u^3 + -0.5109*u^2 + -0.0595*u) = 0;

solve({eqt, y=m*t+c, u=n*t+d}, {y, u}, 'parametric');

 

solve({y^5+y^4 + -0.5109*y^3 + -0.0595*y^2 + 0.0000-(-3.1086e-015*u^4 + u^3 + -0.5109*u^2 + -0.0595*u) = 0, u=t}, [x,y]);

 

solve(eqt, [y(t), u(t)])

algcurves[parametrization](eqt, y, u, t);

 

all trials i failed

 

with(algcurves):

f := y^2 - x^3  - x^2 =0;

c := simplify(subs(x=x1/x0, subs(y=x2/x0, f)));

c := -x2^3+x1^3+x0*x1^2;

parametrization(c, x0, x1, x2, u, v);

 

how to make

x0 = a0*u + b0*v

x1 = a1*u + b1*v

x2 = a2*u + b2*v

 

OK, I want to plot 10-15 curves on the same coordinate system P. I generate and put the equations of said curves in an array with a procedure, but when plotting the array, I receive an array of plots, instead of the 10 curves on one coordinate system. Any ideas how can I do that?

 

The obvious solution, something like P:=plot (something) Q:=plot(other thing) display({P,Q}) obviously doesn't work for me.

For a math class, we have to create a roller coaster. Part of the coaster consists of two banked curves. I've tried looking it up but Maple isn't very clear on how to create the. So, how do you create banked curves in Maple?

Consider the planar region bounded by the curves y=x^2 + 4x + 6, x=1 and y=2. Rotate about the line x=3 

I'm trying to plot and fill the area between these two curves from x[0,450]

line1:=20-0.05*x

line2:=2+0.0002*x^2

 

I can do it separately but when I do them together, it gives me extra area that isn't shared between the two curves.

Also, whenever I try to plot them together I get the following error message:

Error, (in plot) unexpected option: 2+0.2e-3*x^2

 

Any help will be greatly appreciated!

I have an equation that is a function of two variables i.e Cp(beta,lambda). I have to plot several Cp curves on the same graph for a range of lambda=0..15 (x-axis). The 1st curve I want Cp@beta=0, 2nd curve Cp@beta=5, 3rdcurve Cp@beta=10 .... and so on

How can I do this without having to define a separate Cp equation for each beta value?

Hi all.

I want to make a graphical application for a webpage, showing curves with a certain number of points on X axis (about 10 or 15), and some sort of “handles” on curve values (for every curve,...

 

Hi!

 

I have seven curves (expressions) R:=f(x) for different value A.

1. How to Plot all curves on one 3D spece plot?
2. Hot to get (fit) surface equation R:=f(x,A) from all 2D curve?



 

surf_eq.mw 

 

wzel

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