Unanswered Questions

This page lists MaplePrimes questions that have not yet received an answer

I am using Maple worksheets in a class. I have a student who finds it difficult to spend much time at the keyboard because of a joint disorder. I am looking for alternate input methods such as Dragon or the Dictate Facility on MacBooks which might help her out. Any suggestions would be appreciated. 

Thanks,

-Maury

intergration

f:=Intat(1.0000000000000000000*(1.7969454312181156991*_f^1.2+1.80)^1.2/sqrt(-1.4974545260150964159*(8.9847271560905784954*_f^3+14.640368911168931285*_f^2+30.220202497712627297)^1.2), _f = 0);

 

I tried to use  value(f);  eval(f); simplify(f); expand(f), but non provide an answer, but return an integral unevaluated.

 

Is there a command to produce a  numerical result ?

THE FOLLOWING CODE 

restart;

A:=Matrix([[ a , b ], [ c , d ]]);

a:=1; b:=0; c:=0; d:=1;

A; 

produces differents results under MAPLE 16  linux i386 and under MAPLE 16  linux amd64

in the first case the last evalution has the following printed output:

Matrix([[a,b],[c,d]])

on the second machine the printed output is

Matrix([[1,0],[0,1]])

Does anybody has an explication; I thought that the "coorect behaviour was the first one since tables use last-name evalutation. But now I am puzzled.

 

how to decompose a matrix into time invariant and time variant 

is it possible to make time invariant and time variant template and then decompose into it

 

i mean decomposition can be 

 time invariant matrix + time variant matrix

or

 time invariant matrix * time variant matrix

 dsolve([Diff(f, t) = f, Diff(f,t) + g = h], f);

 dsolve([Diff(f, t) = f, Diff(f,t)*g = h], f);

where h is orthogonal matrix, f,g,h are matrix

would like to find g and f from h

 

can dsolve solve differential equation of matrix ? how?

 

dsolve([Diff(f(t), t) = f(t), Diff(f(t),t) + g(t) = h1(x)*h2(x), int(h1(x)*h2(x),x=-1..1) = 0], [f(t),g(t),h1(x),h2(x)]);


dsolve([Diff(f(t), t) = f(t), Diff(f(t),t)*g(t) = h1(x)*h2(x), int(h1(x)*h2(x),x=-1..1) = 0], [f(t),g(t),h1(x),h2(x)]);

 

assume x^2 + 1 is from interpolation of polynomial

pdsolve([Diff(f(t), t) = f(t), Diff(f(t),t) + g(t) = h1(x,t)*h2(x,t), h1(x,t)*h2(x,t)= x^2+1], [f(t),g(t),h1(x,t),h2(x,t)]);
pdsolve([Diff(f(t), t) = f(t), Diff(f(t),t)*g(t) = h1(x,t)*h2(x,t), h1(x,t)*h2(x,t) = x^2+1], [f(t),g(t),h1(x,t),h2(x,t)]);

these system can not be solved

 

hope no real number any more after decomposition and only have iinteger in I time invariant function

I am trying to get a solution to the heat equation with multiple boundary conditions.

Most of them work but I am having trouble with two things: a Robin boundary condition and initial conditions.

First, here are my equations that work:

returns a solution (actually two including u(x,y,z,t)=0).

 

However, when I try to add:

or

 

I no longer get a solution.

 

Any guidance would be appreciated.

 

Regards.

 

I have uploaded a worksheet with the equations...

Download heat_equation_pde.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


 

 

 

 

I received an unexpected error message when trying to minimize a function: evaluating

returns the error message

Error, (in @) too many levels of recursion

Why am I getting this message?  It's hard for me to see how minimizing a function involves recursion, unless Maple is trying to iteratively approximate a solution.

How to open batch maple output as mws in Maple Player?  I was used to doing this daily at work before retirement in my university office on a campus computer.  There was an "open" command in a file menu of some sort that I could click on, I seem to remember.   Am just fresh afte downloading Maple Player on my iMac and have it installed.  The file from my batch Maple output is form a run of batch Maple on the office machine that I can logon to remotely from home, as I did in this case.  I get rough looking graphic output (using the alphabet style graphics methods).  It would be good to have a more detailed and fine grained graphics to answer some basic questions that I am analyzing.  Thanks . . !!

Hello;
        i am wording on fluid dynamics, in which i can up a system of nonlinear partial differential equation with i am suppose to solve using implicit keller box method. i need an asistance on how to implement this in maple.

 

error module is maple.dll_unloaded

 

i have already called stopmaple(kv);

in

testfunction(string hello){....stopmaple(kv));

 

testfunction(1);

testfunction(2);

when call testfunction again , it got error

Hello everybody,

 

This one is an easy one but I cannot find the answers.  Suppose that I clik on the template for evaluating a function.  But mine have two (or more) variables (f=f(x,y)).  I have the x=a as one placeholder.  But I need to have an another inplut placeholder for y=b.  Can somenone tell me how to do it under Windows and under Linux.

 

Thank you in advance for your help.

 

--------------------------------------
Mario Lemelin
Maple 17 Ubuntu 13.10 - 64 bits
Maple 17 Win 7 - 64 bits messagerie : mario.lemelin@cgocable.ca téléphone :  (819) 376-0987
 u_{tt} = c^2 u_{xx}, \,
 u(t,0)=0, \quad u(t,L)=0,

as well as the initial conditions

 u(0,x)=f(x), \quad u_t(0,x)=g(x).

 

Trace  on computing the distinct-degree decomposition of the squarefree polynomial
f=x^17+2x^15+4x^13+x^12+2x^11+2x^10+3x^9+4x^4+3x^3+2x^2+4x belong to F_5[x].tell from the output only how many irreducible factors of degree i the polynomial f has, for all i.

 

Mapleprimes_Integral.mw

I have a question regarding following problem:

assume(a > 0, a < 1, t > 0, Z0 > 0, z > 0)

f1 := proc (z) options operator, arrow; 1/z end proc

proc (z) options operator, arrow; 1/z end proc

(1)

I_1 := int(f1(z)*ln((a*z+1)/(1+z/a)), z = 0 .. Z0); 1; MultiSeries:-asympt(%, Z0, 3)

2*ln(Z0)*ln(a)+(a^2-1)/(a*Z0)-(1/4)*(a^4-1)/(a^2*Z0^2)+O(1/Z0^3)

(2)

Using the representation which should hold for all a>0 and z>0

int(z*exp(t)*(a^2-1)/((exp(t)+a*z)*(exp(t)*a+z)), t = 0 .. infinity); 1; combine(%)

ln((a*z+1)*a/(z+a))

(3)

I'm calculating the result the other way around

int(z*exp(t)*(a^2-1)*f1(z)/((exp(t)+a*z)*(exp(t)*a+z)), z = 0 .. Z0); 1; I_2 := int(%, t = 0 .. infinity); 1; MultiSeries:-asympt(%, Z0, 3)

2*ln(Z0)*ln(a)+(a^2-1)/(a*Z0)-(1/4)*(a^4-1)/(a^2*Z0^2)+O(1/Z0^3)

(4)

plot(eval([I_1, I_2], a = 1/2), Z0 = 0 .. 10)

 

So the results are the same.

But if I calculate this with another function

f2 := proc (z) options operator, arrow; 1/(z*(z+a)) end proc

proc (z) options operator, arrow; 1/(z*(z+a)) end proc

(5)

I_3 := int(f2(z)*ln((a*z+1)/(1+z/a)), z = 0 .. Z0); 1; MultiSeries:-asympt(%, Z0, 3)

-dilog(a^2)/a-2*ln(a)/Z0+(1/2)*(2*ln(a)*a^2+a^2-1)/(a*Z0^2)+O(1/Z0^3)

(6)

int(z*exp(t)*(a^2-1)*f2(z)/((exp(t)+z*a)*(exp(t)*a+z)), z = 0 .. Z0); 1; I_4 := IntegrationTools:-Change(int(%, t = 0 .. infinity), t = ln(z)); 1; MultiSeries:-asympt(%, Z0, 3); 1; simplify(convert(convert(MultiSeries:-series(I_4, Z0, 1), polynom), polynom))

ln(a)*(ln(Z0)+ln(a))/a

(7)

I get another result :-/ The Integral doesn't even vanish in the limit Z0 -> 0

Though if I take the limit prior:

int(z*exp(t)*(a^2-1)*f2(z)/((exp(t)+z*a)*(exp(t)*a+z)), z = 0 .. infinity);

-dilog(a^2)/a

(8)

the result is correct. What is the problem here?



Download Mapleprimes_Integral.mw

 

I converted this comment into a question since it was unrelated to the question in which it was put.
That way also other MaplePrimes users can have a shot at this new question.
Preben Alsholm
 

Dear Preben Alsholm 

Hi;

Hope you to be healthy and have nice times,

I have another problem and if it doesn't consuming your valuable times, please guide me.

I have some Basis function,say W1(t),W2(t),W3(t),W4(t) which are orthonormal and i want to write a program that can approximate the integral of W(t)=[W1(t),W2(t),W3(t),W4(t)] again by Wi's, in other word
int(W(t')dt',t'=0..t)≈PW(t), where P is knows as integral operational matrix. the following is my attempt and unfortunately has no real solution!!!!

 

restart:
>              # Definition of 3th B-Spline
>
> piecewise(x>=0 and x<=1,1,0):
> h[1]:=unapply(%,x):
>
>             # Definition of 3th B-Spline
>
> h[2]:=simplify(int(h[1](x-t),t=0..1)):
> hh:=unapply(%,x):
>
>              #Definition of 3th B-Spline

int(hh(x-t),t=0..1): 
> simplify(%):
> N:=unapply(%,x):
>
> J:=1:     # Number of base function is 2^J+2
> phi:=linalg[matrix](2^J+2,1):
> for i from -2 to 2^J-1
> do
> N(2^J*x-i)*h[1](x): #for deleting out side of[0,1]
> simplify(%):
> phi[i+3,1]:=unapply(%,x):
> od:
>
> w[1]:=phi[1,1](x):
> w[1]/sqrt(int(w[1]^2,x=0..1)):
> W[1]:=unapply(%,x):     
>
> for i from 2 to 2^J+2
> do
> kk:=0:
> for j1 from 1 to i-1
> do
> aa[j1]:=int(phi[i,1](x)*w[j1],x=0..1):
> bb[j1]:=int(w[j1]^2,x=0..1):
> kk:=kk+aa[j1]/bb[j1]*w[j1]:
> od:
> w[i]:=simplify(phi[i,1](x)-kk):
> w[i]/sqrt(int(w[i]^2,x=0..1)):
> W[i]:=unapply(%,x):                 #Orthonormality process
>
>
> for j from 1 to 2^J+2 do
> for io from 1 to 2^J+2 do
> f[j]:=int(W[j](s),s=0..x);
> c[io][j]:=int(f[j](x)*W[io](x),x=0..1);
> od;
> od;

 

 

Best Wishes

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