Hi MaplePrimes team,

Is there a generalized way to fill an extremely CONCAVE closed 3d parametric plane curve in Maple with spacecurve command (NO implicitplot3d), preferably without doing any multi-decomposition or creating a particular skeleton, or algorithm/programming?

Here my example:

#Circle of reference
R0 := 1:
C0 := t-> < cos(t), sin(t), 0 >:

#Variable radius
R := t-> R0*(1 + 1/2*sin(t)):

#Variable phase
Dt := t-> Pi/2*sin(2*t):

#CONCAVE Curve
C := t-> R(t)*C0(t - Dt(t)):
'C(t)' = C(t);

#Range
t1, t2 := 0, 2*Pi:

#Plot
GC := spacecurve(C(t), t = t1..t2, color = "Red", thickness = 3
, linestyle = solid
, scaling = constrained, axes = frame, orientation = [50,40,0]):
GC;

We know how to do it easily for any convex 3d plane curve (circle, ellipse, regular polygon, etc ...).

We also know how to do it for 2d curve with the Maple’s plot option filled = true but obviously not in 3d.

Thank you for your time.

Best.

Guy.

Hello, I am new with Maple. I am using because I am taking a course in my college where I need it. I have the following problem: How it can be seen in image, code is not been adecuatelly executed, because I need numerical values at output. I think this problem is because a configuration issue, but I am not sure.

How can I restore default configuration in order to try a solution for this issue?

Equil-points.mw

I have defined a function II1norm of one variable. The variable has units "microns". It plots perfecting using a range defined in microns, but gives an error when I try to find the root using NextZero. If I just leave off the "microns" in the second argument, NextRoot just reports "FAIL". If I rewite the worksheet without units, then the NextZero executes fine. Why? How to I use units when finding roots?

I need to calculate the eigenvalues and eigenvectors of a big marix with enough Digits. When i apply the command Eigenvectors(K,M) for this purpose, it takes approximately 40 min to be calculated by maple. Where only 1/4 of cores of my CPU is used in this computation.

How is it possible to use all of my CPU cores to calculate the eigenvalues and eigenvectors of a big matrix faster?

change the txt to m for the following files.

K.txt

M.txt

As always, it's just about drawings.
The parametric equation of a circle has 3 variables and two equations. In 3-dimensional space, a circle is a spiral, but we only need one projection of this spiral into 2-dimensional space, and we also know how  the rest 2 it's projections on flat space look.
If we look at the equation of the sphere in parametric form, we will see that these are 3 equations and 5 variables:
x1 = sin(x4)*cos(x5); 
x2 = sin(x4)*sin(x5); 
x3 = cos(x4);
And so I wanted to see how the remaining 9 projections of the sphere onto 3-dimensional space look. It is very easy to do this with Maple.
SPHERE.mw

This is so useful to see geometrical mapping diagram to visualize Complex analysis

Something that also can be made for Maple 

Mapping Diagram for Cauchy Integral Formula – GeoGebra

Using GeoGebra for visualizing complex variable. (google.com)

I highly encourage everyone interested in complex variable to read Tristan Needham „Visual Complex Analysis” and try to solve problems with or without aid of GeoGebra. I hope that in this workshop we will manage to get a feeling of complex functions and as a final point understand how complex integration works. It is a common misconception that complex integration can't be visualized, and using Tristan Needham's ideas we will try to explore this idea. It's a pity that we don't have a lot of time, thus we will skip a lot of important information and construct only some graphs. 

There is so much experimenting with Geogebra software and doing too this in Maple ?

  How do you transform vector expression (*) into [M,A] – 3[M,B] = 7[M,C] using Maple command?

  Thank you for your help !

Hello there, 

Would you allow me to ask one question?

Is there any way to get a saturated water vapor pressure value with a temperature outside of the range?

The range here means [273.06 K, 647.096 K]. The pressure value certainly exists (T<273.06 K), but the API only comes up with an error. 

Here is the Maple worksheet where I got into this issue:

Download Q20220111.mw

Hello!

I'm new user in Maple and I have two question:

1. I have modeled transfer function in z term(without DynamicSystems). How quicky can I reearange it to difference equation to find coefficients?

2. I discretize transfer function of s to z using ToDiscrete(DynamicSystems) how here I can reearange this form to difference equation? 

I am studying the help pages for declare() statement in the PDEtool package. 
It can be used also for calculus(prime notation) for 1 variable and two variables (subscript notation) as i understand it now.

There is no input possible in Maple by using a prime notation and indexed functions notation?

Maybe with a alias ? ..remember that I can be chanced I (default) into the i for complex numbers 

Hello there, 

Would you allow me to ask these two questions?

1) is there any way to collect the expression 'eq14_2' w.r.t. DeltaP? The question is labeled as 'Q1' in the worksheet. 

2) Why does the 'DeltaP' term survive at the RHS of the expression 'eq14_2_3'? In other words, is it possible to cancel out the same term, 'DeltaP', in numerator and denominator?

Download Q20220110.mw

I am trying to plot the solution of the following complex-valued initial value problem (IVP), obtained numerically with dsolve:

odesys := {dy(x)/dx + I*y(x) = 0, y(0) = 1};

sol := dsolve(odesys,numeric,range=0..1);

In the Maple help page dsolve/numeric, they say that dsolve can solve complex-valued IVPs. When I try the code above, it seems to work (I don't get an error). But I can't find how to plot the real and imaginary parts of y(x). Indeed, odeplot(sol) yields an empty graph, and odeplot(Re(sol)) yields an error.

Does someone know how to do this? Thanks in advance for your help.

restart:

alias(f=f(t)):
alias(g=g(t)):

diff([f, g], t):  #ok

a := [alias()]:
diff(a, t);
      [0, 0]

More generally, how can we differentiate a list of aliases without naming them explicitely?

Thanks in advance