MaplePrimes Questions

i have try to solve these eq by maple 

and i got these errors 

 

new2fornet.maple

 

simplify(series(sin(g(x)),x=0,4));

 

sin(g(0)) + cos(g(0))*D(g)(0)*x + (-1/2*sin(g(0))*D(g)(0)^2 + 1/2*cos(g(0))*(D@@2)(g)(0))*x^2 + (1/6*(-D(g)(0)^3 + (D@@3)(g)(0))*cos(g(0)) - 1/2*sin(g(0))*(D@@2)(g)(0)*D(g)(0))*x^3 + :-O(1)*x^4

 

and I'd like to give the various values for g to evaluate the series. That is, I know g and it's derivatives at 0.

Maple 2019.2.

These two expressions are mathematically equivalent:

But simplify(expr1-expr2) does not give zero where simplify(convert(expr1,trig)-expr2) does.

Is this normal behavior or can be expected sometimes? As a user I would have expected Maple internally to figure all of this itself. Compare to Mathematica:

Is there a different command in Maple that will show mathematical equivalence of two expressions to try other than simplify?

Thanks
 

restart;

expr1:=(-exp(n*Pi*(2*b - y)/a) + exp(n*Pi*y/a))/((exp(2*n*Pi*b/a) - 1)):
expr2:= sinh(n*Pi/a*y)/tanh(n*Pi/a*b)-cosh(n*Pi/a*y):
simplify(expr1-expr2);

(-sinh(n*Pi*b/a)*exp(n*Pi*(2*b-y)/a)+(-sinh(n*Pi*y/a)*cosh(n*Pi*b/a)+cosh(n*Pi*y/a)*sinh(n*Pi*b/a))*exp(2*n*Pi*b/a)+(exp(n*Pi*y/a)-cosh(n*Pi*y/a))*sinh(n*Pi*b/a)+sinh(n*Pi*y/a)*cosh(n*Pi*b/a))/((exp(2*n*Pi*b/a)-1)*sinh(n*Pi*b/a))

simplify(convert(expr1,trig)-expr2);

0

 


 

Download q.mw

 

How to change default directory for Maple 2019?

Solving_ODE.mw

 

Here is an example.  How would I solve this non-homogeneous system of ODEs

Is there a guide for programming in maple?  I mean like using it like a normal programming language using the code editor (external one not the whole worksheet thing maple has by default) debugging writing functions and the lot.

Source of interest in this topic.  There is a problem with drawing a cylinder. I draw a cylinder using the arrow function as follows:

cylinder := seq(arrow(`<,>`((L[1][i]+L[4][i])*(1/2), (L[2][i]+L[5][i])*(1/2), (L[3][i]+L[6][i])*(1/2)), `<,>`(-(L[1][i]+L[4][i])*(1/2)+(L[7][i]+L[10][i])*(1/2), -(L[2][i]+L[5][i])*(1/2)+(L[8][i]+L[11][i])*(1/2), -(L[3][i]+L[6][i])*(1/2)+(L[9][i]+L[12][i])*(1/2)), width = 1, color = green, head_length = 0, head_width = 0, length = VectorNorm(`<,>`((L[1][i]+L[4][i])*(1/2)-(L[7][i]+L[10][i])*(1/2), (L[2][i]+L[5][i])*(1/2)-(L[8][i]+L[11][i])*(1/2), (L[3][i]+L[6][i])*(1/2)-(L[9][i]+L[12][i])*(1/2)), 2), transparency = 0.), i = 1 .. N+1):

(L [j], j = 1..12 - the coordinates of the red points on the cylinder).


But, as you can see, because of the faces, everything does not turn out very smoothly. Is there a way to display the cylinder smoothly, but so that without too much computing resources, ie no more resource than a "arrow"?

Hai

Help required to plot the graphs for system  difference schemes .

 I am attaching the codes and sample graphs and  maple query but still getting  error.

here is the codes 

restart;
restart; Digits := 1;
Pr:=0.01:E:=1:a:=0:N:=10:

`&Delta;t`:=0.01:`&Delta;y`:=0.01:

#Discritization scheme

for i from 1 by 1 while i<=N do;  
end:
for j from 0 by 1 while j<=N do;
end:

eq1[i, j] := (U[i, j+1]-U[i, j])/`&Delta;t` = (1/2)*Gr*(theta[i, j+1]+theta[i, j])+(1/2)*Gc*(C[i, j+1]+C[i, j])+(U[i-1, j+1]-2.*U[i, j+1]-2.*U[i, j]+U[i+1, j])/(2.*`&Delta;y`)^2-(1/2)*M*(U[i, j+1]+U[i, j]):

eq2[i, j] := (theta[i, j+1]-theta[i, j])/`&Delta;t` = (1/Pr)*(theta[i-1, j+1]-2*theta[i, j+1]+theta[i+1, j+1]+theta[i-1, j]-2*theta[i,j]+theta[i+1,j])/(2.*`&Delta;y`)^2-E*((1/`&Delta;y`)^2*(U[i+1, j]-U[i, j])^2):

eq3[i, j] := (C[i, j+1]-C[i, j])/`&Delta;t` = (1/Sc)*(C[i-1, j+1]-2*C[i, j+1]+C[i+1, j+1]+C[i-1, j]-2*C[i,j]+C[i+1,j])/(2*`&Delta;y`)^2-(K/2)*(C[i, j+1]-C[i, j]):
end do;  
Error, reserved word `end` unexpected
end do:
Error, reserved word `end` unexpected

# initial conditions
U[i, 0] := 0:
theta[i, 0]:= 0:
C[i, 0] := 0:
 

NULL;
U[0,j]:=exp(a*j*`&Delta;t`):
theta[0,j]:=(j*`&Delta;t`):
C[0,j]:=j*`&Delta;t`:

U[N,j]:=0:
theta[N,j]:=0:
C[N,j]:=0:

sys := ([seq])(seq(eq[i, j], j = 0 .. N), i = 1 .. N):
nops(sys);
vars:=indets(sys):
nn := Matrix(N+1, N+1,(i, j)-> U[i-1, j-1]):
##
p:=proc(kk) local U_res,A;
  U_res:=solve(eval(sys,k=kk),vars);
  A:=eval(nn,U_res);
  plots:-matrixplot(A)
end proc;

plots:-(U,[M],Y=0..4);

 

https://www.mapleprimes.com/questions/225117-How-To-Solve-This-Error-In-Maple

 

I have just upgraded my laptop from Windows 7 to Windows 10.  On starting up Maple 2018,  I receive the attached message on screen.  This is after previously loading the worksheet successfully.   Today,  I am not able to do so.  I need to permanently register my firewall to allow Maple to run; can anyone help?

Melvin

 

The routines for finding nonclassical symmetries of PDE, mentioned in the research articles are not currently available. The routines like GENDEFNC may have been changed to other one. Please tell how to find nonclassical symmetries of a PDE or a system of PDE. I am using Maple 2016.

I've found the Taylor series expansions for two functions.  The two expansions are identical until the third term.  When I subtract one expansion from the other, I expected that the identical terms would cancel and disappear.  But I can't get Maple to do this.  If I copy and paste the output into a Maple command, the "big Oh" terms are not treated correctly.  The correct answer would be (x^3)/6 + O(x^4).  Here's my work:
 

taylor(ln(1+x), x = 0, 4)

series(x-(1/2)*x^2+(1/3)*x^3+O(x^4),x,4)

(1)

taylor(ln(1+sin(x)),x=0,4)

series(x-(1/2)*x^2+(1/6)*x^3+O(x^4),x,4)

(2)

 

(series(x-(1/2)*x^2+(1/3)*x^3+O(x^4),x,4))-(series(x-(1/2)*x^2+(1/6)*x^3+O(x^4),x,4))

(series(x-(1/2)*x^2+(1/3)*x^3+O(x^4),x,4))-(series(x-(1/2)*x^2+(1/6)*x^3+O(x^4),x,4))

(3)

collect((3),x)

(series(x-(1/2)*x^2+(1/3)*x^3+O(x^4),x,4))-(series(x-(1/2)*x^2+(1/6)*x^3+O(x^4),x,4))

(4)

x-(1/2)*x^2+(1/3)*x^3+O(x^4)-x+(1/2)*x^2-(1/6)*x^3-O(x^4)

(1/6)*x^3

(5)

x-(1/2)*x^2+(1/3)*x^3+O(x^4)-x+(1/2)*x^2-(1/6)*x^3-O(x^4)

(1/6)*x^3

(6)

``

How can I get Maple to give me the right answer?  I tried various commands (collect, combine, simplify, etc.) but nothing worked.  Also, why do the font and color of my first two commands differ?  Thanks
 

Download Taylor_question.mw

Would you help me to figure out how to solve this error?

 

totalsalesx := 60.1 + tax + profit

tax := 0.3*profit

profit := 0.1*totalsalesx

then, 'Error, recursive assignment'

What I want to do is to calculate the 'totalsalesx' from the cost (60.1). 

;

= 2*1/10);
                               1
                               -
                               5
= -1;
                               -1

= 10;
                               10
= -25;
                              -25

C= 1;
                               1

= (1/12*sqrt6/sqrtbeta*lambda*mu);
                       1     (1/2)  (1/2)
                      --- I 6      2     
                       24                
= alpha/((10*sqrt-lambda*mu)*beta);
                             1  (1/2)
                           - - 5     
                             4       
A0]= (1/2*alpha/((10*sqrt-lambda*mu)*(1/12*beta*sqrt6/sqrtbeta*lambda*mu)));
                    1    (1/2)  (1/2)  (1/2)
                   -- I 5      6      2     
                    4                       
A1]= -(1/10*alpha/((1/12*beta*mu*sqrt6/sqrtbeta*lambda*mu));
                        1    (1/2)  (1/2)
                       -- I 6      2     
                        2                
A[2] := -(12*((112)*sqrt(6)/sqrt(beta*lambda*mu)))*lambda^2*alpha/(10*sqrt(-lambda*mu));
                    1     (1/2)  (1/2)  (1/2)
                   --- I 6      2      5     
                    20                       
H := ln(sqrt(lambda/(-mu))*tanh(sqrt(-lambda*mu)*(xi+C)));
              /1/2)     /1  (1/2         \\
              ln|- 5      tanh|- 5      ( 1)||
                \5            \5                //
xi := k*x-t*w;
                1     (1/2)  (1/2)     1    (1/2)
               --- I 6      2      x + t    
        2               4         
u[0] := A[0]+A[1]*exp(-H)+A[2]*exp(-H)*exp(-H);
  1    (1/2)  (1/2)  (1/2)
 -- I 5      6      2     
  4                       

                     1    (1/2)  (1/2)  (1/2)                
                     - I 6      2      5                     
                     2                                       
    - -------------------------------------------------------
         (1/2) / 1     (1/2)  (1/2)     1    (1/2)    \\
      tanh|- 5      |--- I 6      2      x + - t 5      + 1||
          \5        \ 24                     4             //

                      1    (1/2)  (1/2)  (1/2)                
                      - I 6      2      5                     
                      4                                       
    - --------------------------------------------------------
                                                             2
          (1/2) / 1     (1/2)  (1/2)     1    (1/2)    \\ 
      tanh|- 5      |--- I 6      2      x + - t 5      + 1|| 
               \ 24              4             // 


plot3d(Im(u[0]), x = -10 .. 10, t = -10 .. 10);

I have a .mapleinit file that amongst other things sets libname so my own packages are accessible and can be loaded using with(). Imagine my surprise when I found that a maple program that ran half an hour ago on Maple2019 bombed when it did not find its package. Closer investigation indicates that maybe .mapleinit is only searched for in currentdir()??

The updated Maple is `Maple 2019.2, APPLE UNIVERSAL OSX, Oct 30 2019, Build ID 1430966`

The old one is gone :-(. It was Maple2019.0. I should add that on this system, Maple is installed on an administrator account that is not my user account (luckily I have access to that). I am running macOS 10.14.6 Mojave.

I verified my older Maples still work as before.

Has anyone else seen this behaviour?

Mac Dude.

Edit: I need to be more specific here: When I double-click a worksheet (.mw file) then currentdir() will be set to the directory the .mw file is in. This has been long-standing Maple behaviour. But then currentdir() does not cover the home directory where .mapleinit sits. As a result, a blank sheet finds my .mapleinit whereas my files (that habitually I open with double-click or drag-drop) do no longer run the .mapleinit file.

 

Dear all 

I need to animate the following function in two dimensions

,u:=  (x, y) -->x^2+y^2+3

((gradplot(u(x, y), x = -10 .. 10, y = -2 .. 2, grid = [8, 8], thickness = 3, arrows = SLIM, color = u(x, y

thanks

Amr

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