Maple 17 Questions and Posts

These are Posts and Questions associated with the product, Maple 17

Code was computed on two different PC:
1) Win 8.1, Maple 17.02 x64
2) Win 8.1, Maple 18.01 x64

In brief:

n:=3: 
Grid:-Seq('f(i)', i = 1 .. n):

works well in Maple 17.02 but gives an error in Maple 18.01. Why?

However,

(j -> Grid:-Seq('f(i)', i = 1 .. j))(n):

works well for both Maple versions.

according to examples from Maple help page
http://www.maplesoft.com/support/help/Maple/view.aspx?path=Grid%2fSeq
we have to pass exactly 'f(i)' (not just f(i)) into Grid:-Seq(...). Why?

Why doesn't Digits:=30: work properly for Grid:-Seq(...)?

For details see attached file. Output was produced in Maple 17.02. In Maple 18.01 the output will differ.


restart; n := 3; f1 := proc (i) options operator, arrow; evalf(sqrt(i)) end proc; f2 := proc (i) options operator, arrow; evalf(sqrt(i+1)) end proc; f3 := proc (i) options operator, arrow; evalf(i*Pi) end proc; g1 := proc (f, n) local za, zb, zc, str; str := sprintf("g1(%a,n)", f); za := seq(f(i), i = 1 .. n); zb := Grid:-Seq(f(i), i = 1 .. n); zc := (proc (j) options operator, arrow; Grid:-Seq(f(i), i = 1 .. j) end proc)(n); print("------------------------------"); print(cat("(a):   ", str), za); print(cat("(b):   ", str), zb); print(cat("(c):   ", str), zc); print("------------------------------") end proc; g2 := proc (f, n) local za, zb, zc, str; str := sprintf("g2(%a,n)", f); za := seq('f(i)', i = 1 .. n); zb := Grid:-Seq('f(i)', i = 1 .. n); zc := (proc (j) options operator, arrow; Grid:-Seq('f(i)', i = 1 .. j) end proc)(n); print("------------------------------"); print(cat("(a):   ", str), za); print(cat("(b):   ", str), zb); print(cat("(c):   ", str), zc); print("------------------------------") end proc

3

(1)

g1(f1, n);

"------------------------------"

 

"(a):   g1(f1,n)", 1., 1.414213562, 1.732050808

 

"(b):   g1(f1,n)", 1, 2^(1/2), 3^(1/2)

 

"(c):   g1(f1,n)", 1, 2^(1/2), 3^(1/2)

 

"------------------------------"

 

"------------------------------"

 

"(a):   g1(f2,n)", 1.414213562, 1.732050808, 2.

 

"(b):   g1(f2,n)", 1.414213562, 1.732050808, 2.000000000

 

"(c):   g1(f2,n)", 1.414213562, 1.732050808, 2.000000000

 

"------------------------------"

 

"------------------------------"

 

"(a):   g1(f3,n)", 3.141592654, 6.283185308, 9.424777962

 

"(b):   g1(f3,n)", 3.141592654, 6.283185308, 9.424777962

 

"(c):   g1(f3,n)", 3.141592654, 6.283185308, 9.424777962

 

"------------------------------"

 

"+++++++++++++++++++++++++++++++++++++++++++"

 

"------------------------------"

 

"(a):   g2(f1,n)", 1., 1.414213562, 1.732050808

 

"(b):   g2(f1,n)", 1., 1.414213562, 1.732050808

 

"(c):   g2(f1,n)", 1., 1.414213562, 1.732050808

 

"------------------------------"

 

"------------------------------"

 

"(a):   g2(f2,n)", 1.414213562, 1.732050808, 2.

 

"(b):   g2(f2,n)", 1.414213562, 1.732050808, 2.

 

"(c):   g2(f2,n)", 1.414213562, 1.732050808, 2.

 

"------------------------------"

 

"------------------------------"

 

"(a):   g2(f3,n)", 3.141592654, 6.283185308, 9.424777962

 

"(b):   g2(f3,n)", 3.141592654, 6.283185308, 9.424777962

 

"(c):   g2(f3,n)", 3.141592654, 6.283185308, 9.424777962

 

"------------------------------"

(2)

Digits := 30;

30

 

"------------------------------"

 

"(a):   g1(f1,n)", 1., 1.41421356237309504880168872421, 1.73205080756887729352744634151

 

"(b):   g1(f1,n)", 1, 2^(1/2), 3^(1/2)

 

"(c):   g1(f1,n)", 1, 2^(1/2), 3^(1/2)

 

"------------------------------"

 

"------------------------------"

 

"(a):   g1(f2,n)", 1.41421356237309504880168872421, 1.73205080756887729352744634151, 2.

 

"(b):   g1(f2,n)", 1.414213562, 1.732050808, 2.000000000

 

"(c):   g1(f2,n)", 1.414213562, 1.732050808, 2.000000000

 

"------------------------------"

 

"------------------------------"

 

"(a):   g1(f3,n)", 3.14159265358979323846264338328, 6.28318530717958647692528676656, 9.42477796076937971538793014984

 

"(b):   g1(f3,n)", 3.14159265358979323846264338328, 6.283185308, 9.424777962

 

"(c):   g1(f3,n)", 3.14159265358979323846264338328, 6.283185308, 9.424777962

 

"------------------------------"

 

"+++++++++++++++++++++++++++++++++++++++++++"

 

"------------------------------"

 

"(a):   g2(f1,n)", 1., 1.41421356237309504880168872421, 1.73205080756887729352744634151

 

"(b):   g2(f1,n)", 1., 1.414213562, 1.732050808

 

"(c):   g2(f1,n)", 1., 1.414213562, 1.732050808

 

"------------------------------"

 

"------------------------------"

 

"(a):   g2(f2,n)", 1.41421356237309504880168872421, 1.73205080756887729352744634151, 2.

 

"(b):   g2(f2,n)", 1.414213562, 1.732050808, 2.

 

"(c):   g2(f2,n)", 1.414213562, 1.732050808, 2.

 

"------------------------------"

 

"------------------------------"

 

"(a):   g2(f3,n)", 3.14159265358979323846264338328, 6.28318530717958647692528676656, 9.42477796076937971538793014984

 

"(b):   g2(f3,n)", 3.141592654, 6.283185308, 9.424777962

 

"(c):   g2(f3,n)", 3.141592654, 6.283185308, 9.424777962

 

"------------------------------"

(3)

``

NULL


Download Grid[Seq].mw

I am not able to simplify my equation, any help would be appreciated ! I want the V[0]^2/r[0]  term to be eliminated

restart:with(Student[VectorCalculus]): 

R1:=rho(diff(u(r,theta,z,t)*(V[0])^2/r[0],t)+ u(r,theta,z,t)*V[0](diff(u(r,theta,z,t)*V[0]/r[0],r))+v(r,theta,z,t)*V[0]/(r*r[0])*diff(u(r,theta,z,t)*V[0],theta)+w(r,theta,z,t)*V[0]*diff(u(r,theta,z,t)*V[0]/r[0],z)-(v(r,theta,z,t)*V[0])^2/(r*r[0])) +diff(p(r,theta,z,t)*rho*V[0]^2/r[0],r); simplify(R1*r[0]/V[0]^2);

rho((diff(u(r, theta, z, t), t))*V[0]^2/r[0]+u(r, theta, z, t)*V[0]((diff(u(r, theta, z, t), r))*V[0]/r[0])+v(r, theta, z, t)*V[0]^2*(diff(u(r, theta, z, t), theta))/(r*r[0])+w(r, theta, z, t)*V[0]^2*(diff(u(r, theta, z, t), z))/r[0]-v(r, theta, z, t)^2*V[0]^2/(r*r[0]))+(diff(p(r, theta, z, t), r))*rho*V[0]^2/r[0]

 

((diff(p(r, theta, z, t), r))*rho*V[0]^2+rho((w(r, theta, z, t)*V[0]^2*(diff(u(r, theta, z, t), z))*r+(diff(u(r, theta, z, t), t))*V[0]^2*r+u(r, theta, z, t)*V[0]((diff(u(r, theta, z, t), r))*V[0]/r[0])*r*r[0]-v(r, theta, z, t)^2*V[0]^2+v(r, theta, z, t)*V[0]^2*(diff(u(r, theta, z, t), theta)))/(r*r[0]))*r[0])/V[0]^2

(1)

 

Download 1.mw

 

 

Good day, please how can one solve these BVPs using FINITE DIFFERENCE METHOD in maple. Here is the problem FDM.mw

I have a worksheet. I edit some variables' value. I then execute the whole worksheet to see how the graphs change. But the graphs generated by display command do not appear. All other calculations update fine. 

To overcome this. I save worksheet with my new variable values. Close the worksheet. Reopen it. Execute it. And now the graphs appear fine.

 

Hi

I'm using Maple 17 on Windows 8 (64-bit).

I have noticed that when I use the 'spacecurve' command and try to display it with the 'display' command, nothing shows up. I made sure that I used 'with(plots)' and 'with(plottools)', still nothing. However 'plot3d' works fine. I think it has something to do with the version of Java I'm using but I don't know what. Any help is welcome, thx

Specifications of my laptop:

Graphics: NVIDIA Geforce GT 740m

Processor: Intel(R) Core(TM) i7-3630QM (2.40GHz)

Ram: 6,00 GB

OS: Windows 8.1

I have a plot of a sinusoidal function(cos_phi) which changes with incrementing values of variable k. When this function goes above 1 or below -1 I would like to have the range of k for which it occurs outputed somehow. Would anybody know how to do this?

Hello,

• Is there a simple way to find the domain for the real solutions of f(x)?

• And is there a way to let maple get the part of f(x) with the sqrt?
   (not by typing it by hand as I dit below)

• Is there a way to write the summary of the found domains in one line?

Thanks for your help. 





restart:
# How to find the Domain for real solutions for x?
f(x):=(x-1+sqrt(x^2-3*x+2))/(x-1);
discont_for_x=discont(f(x),x);
# x<>+1 (because the de denom=0 is not allowed)
denom(f(x))=0;
x={solve(denom(f(x))=0,x)};
# x<=1 union  2<=x (because the part under the sqrt must be >=0 to give Real solutions)
sqrt(x^2-3*x+2);
0<=x^2-3*x+2;
x=solve(0<=x^2-3*x+2,x);




restart:

Eq1:=1/r*diff(r*diff(w(r),r),r)-(cos(z1))^2*(w(r)+1)-DP;

dsolve({Eq1});

bcs:=D(w)(0)=0,w(r2)=A1;

dsolve({Eq1,bcs},w(r)):

where z1, Dp, r2, A1 are constants.

 

how maple calculate exp(x) with e.g. 100000 decimal numbers

a divsion of the series x^k/k! with e.g. 1/25000!/25001 lasts longer than the exp(1.xx) calculation

 

is there a faster way to calculate exp(x) than with the x^k/k! series

 

thanks

 

 

 

 

 

 

 

 

(a) Design your own 3-stage explicit Runge-Kutta method with one-step error O(h4).

(b) Test your method by solving y= −y. Confirm that the global error in your numerical solution

is O(h3).

restart:

Eq1:=S*diff(f(x,t),x,t)+diff(f(x,t),x)^2-f(x,t)*diff(f(x,t),x$2)=diff(f(x,t),x$3);

BCs := {D[1](f)(0,t)=cos(t), f(0,t)=0,D[1](f)(L,t)=0};

ICs := {f(x,0)=0};

S:=10:L:=5:
smod3:= pdsolve(Eq1,ICs union BCs,numeric,range=0..L);

smod3:-plot(t=0,  color=red):

it seems to me that the problem is due to the mixed bcs. Any way around?

Cheers!

Good afternoon sir.

 

I am working on problems related to functions which require dynamic geometry program or

the Geometers sketch pad. I request to you to kindly suggest me with regard to the above cited query.

 

 

With thanks & Regards

 

M.Anand

Assistant Professor in Mathematics

SR International Institute of Technology,

Hyderabad, Andhra Pradesh, INDIA.

Dear Experts,

When I run this code in maple I am facing with "Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging".

restart:
 
 unprotect('gamma');
 lambda:=5*10^5:
 mu:=0.003:
 beta:=4*10^(-10):
 delta:=0.2:
 alpha:=0.043:
 sigma:=alpha+delta:
 k:=6.24:
 gamma:=0.65:
 A[1]:=1:
 A[2]:=1:

ics := x[1](0)=1.7*10^8, x[2](0)=0,x[3](0)=400,psi[1](50)=0,psi[2](50)=0,psi[3](50)=0:

ode1:=diff(x[1](t), t)=lambda-mu*x[1](t)-(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[1](t)*x[3](t)+delta*x[2](t),
 diff(x[2](t), t) =(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[1](t)*x[3](t)-sigma*x[2](t),
 diff(x[3](t), t) =(1+psi[3](t)*k*x[2](t)/A[2])*k*x[2](t)-gamma*x[3](t),
 diff(psi[1](t), t) =-1+1/A[1]*beta^2*x[1](t)*x[3](t)^2*(psi[1](t)-psi[2](t))^2-psi[1](t)*(-mu+beta^2*x[3](t)^2*(psi[1](t)-psi[2](t))/A[1]*x[1](t)-(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[3](t))-psi[2](t)*(-beta^2*x[3](t)^2*(psi[1](t)-psi[2](t))/A[1]*x[1](t)+(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[3](t)),
> diff(psi[2](t), t) =1/A[2]*psi[3](t)^2*k^2*x[2](t)-psi[1](t)*delta+psi[2](t)*sigma-psi[3](t)*(psi[3](t)*k^2/A[2]*x[2](t)+(1+psi[3](t)*k*x[2](t)/A[2])*k),
> diff(psi[3](t), t) = 1/A[1]*beta^2*x[1](t)^2*x[3](t)*(psi[1](t)-psi[2](t))^2-psi[1](t)*(beta^2*x[1](t)^2*(psi[1](t)-psi[2](t))/A[1]*x[3](t)-(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[1](t))-psi[2](t)*(-beta^2*x[1](t)^2*(psi[1](t)-psi[2](t))/A[1]*x[3](t)+(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[1](t))+psi[3](t)*gamma;

sol:=dsolve([ode1,ics],numeric, method = bvp[midrich]);

Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging

Please help me to solve this equation on Maple.




Hello,

I understand that the question is not really Maple related, but I still hope for some help.


See the worksheet below. I defined a pure sine wave and determined the complex Fourier coefficients for it which I used to plot the amplitude and power spectra. It is easy to see the relations in terms of amplitude and power between the time and frequency signal.

The Fourier Transform of the sine wave logically shows the Dirac distribution, but I can't see the relation in terms of amplitude and power to the original time signal. Taking the integral of the transformed signal (A) wil result in a step of Pi at w=-1 and again at w=1. What am I missing here?

Thanks

restart; with(inttrans); with(plots); with(DynamicSystems)

 

Define a signal:

 

T := 2*Pi;

2*Pi

 

sin(t)

(1)

 

Determine the waveform power:

 

F := (int(f^2, t))/T+C:

C := simplify(solve(subs(t = 0, F) = 0, C)):

eval((int(f^2, t = -(1/2)*T .. (1/2)*T))/T)

1/2

(2)

plot([f, f^2, F], t = -Pi .. Pi, gridlines = true)

 

 

Determine the complex Fourier series coefficients and plot the spectra:

 

q := proc (n) options operator, arrow; (int(f*exp(-(2*I)*n*Pi*t/T), t = -(1/2)*T .. (1/2)*T))/T end proc:

simplify(q(n))

I*sin(Pi*n)/(Pi*(n^2-1))

(3)

ComplexCoefficients := evalf(`<,>`(seq(q(n), n = -1 .. 1)))

ComplexCoefficients := Vector(3, {(1) = .5000000000*I, (2) = 0., (3) = -.5000000000*I})

(4)

B := evalf(`<,>`(seq(sqrt(Re(q(n))^2+Im(q(n))^2), n = -3 .. 3))):

 

C := evalf(`<,>`(seq(Re(q(n))^2+Im(q(n))^2, n = -3 .. 3))); -1; DiscretePlot(C, -3, 1, titlefont = ["ARIAL", "bold", 14], title = "Power Spectrum", color = "Red", gridlines = true, style = stem)

 

So, the signal power for f of 1/2 can be found directly within the power spectrum plot "(2*1/(4))."

 

I would expect to be able to directly see the amplitude and power relation to the time signal from the Fourier Transform of f but i can't.

 

A := fourier(f, t, w);

I*Pi*(Dirac(w+1)-Dirac(w-1))

(5)


Download 20140127MaplePrime.mw

 

 

Hi everyone

I am currently trying to make my own simple package including a few procedures. So far I have been able to write some "code" that actually works when I open the document and hit "enter". I would, however, like to save the package so it can be accessed during any Maple session using the command "with". I have unsuccesfully tried to comprehend the Maple help pages regarding this question but I definitely don't want to mess things up.

This is what I have written:

mat := module ()
description "useful procedures for mathematics, physics and chemistry";
export AtomicWeight;
option package;

   AtomicWeight := proc (x) description "returns the average atomic mass of the naturally ocurring element";
   Units:-AddSystem(NewSystem, Units:-GetSystem(SI), u);
   return evalf(ScientificConstants:-Element(x, atomicweight, system = NewSystem, units))
   end proc

end module;

What should I do to save it correctly?

Thank in advance,
Mads


 

 

 

 

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