MaplePrimes Questions

Consider a standard initial/boundary value problem for the heat equation on the interval x ∈ [0,1]:

restart;
pde := diff(u(x,t),t) = diff(u(x,t),x,x);
ic := u(x,0) = f(x);
bc := u(0,t)=0,  u(1,t)=0;

Then
pdsolve({pde, ic, bc});
produces the expected Fourier series solution.

However, if we change the interval to x ∈ [-1,1], as in:
bc := u(-1,t)=0,  u(1,t)=0;
pdsolve({pde, ic, bc});

then Maple fails to return a solution.  Why?

Dear all

I need a help how can i solve for example the following PDEs with Initial condition and boundary condition given at x=-1, and x=1.

pde:=diff(u(t,x),t)=diff(u(t,x),x$2);

ics:=u(0,x)=sin(x);

Bcs:=diff(u(t,-1),x)=0;

Bcs:=diff(u(t,1),x)=0;

Many thanks

 

 

 

In using Isolate in RootFinding to compute roots of a real polynomial, the output contains, say, z= some number.  How to get rid of the "z =" so that I can declare that "some number" to be some variable?

I am writing a matrix to file where each matrix element is placed on a new line. An example of such code:

restart:
HH:=Matrix([[x**2,x**z,z**12],[2*x,5**y,6**1]]):
filenameHH:=fopen("test.txt",WRITE,TEXT):

nRow,nCol :=LinearAlgebra[Dimension](HH);
for i from 1 to nRow do
   for j from 1 to nCol do
      fprintf(filenameHH,"%a\n",HH[i,j]):
   od:
od:
fclose(filenameHH):

When this is printed to file, it will print as the power sign ^ regardless of the input it is given. This particular output file will be read in by another language, and due to this the power symbol "^" is not desired, but instead " ** ". By converting the matrix into a string format and applying string operations, this can be done; but is there a simpler way to do it?

-Yeti

Hello,

I am solving a simple system of algebraic equations in a "for" loop. I would like to write all the values of solutions to a matrix, but I only get the symbols. Here is my code:

A:=1:E:=0.1:L0:=<5,5,5,5>:m0g:=0.05:u:=<-5/4,-1/4,-3/4,-1/4>:v:=<-1/2,-3/2,1/2,1/2>:w:=<0,1,0,-1>:
Force:=Matrix(m,2);
for i from 1 to m do
 r1||i:=H||i*L0(i)/(A*E)+H||i/m0g*(arcsinh(V_A||i/H||i)+arcsinh((m0g*L0(i)-V_A||i)/H||i))-sqrt(u(i)^2+v(i)^2);
 r2||i:=V_A||i*L0(i)/(A*E)*(m0g*L0(i)/(2*V_A||i)-1)+H||i/m0g*(sqrt(1+((m0g*L0(i)-V_A||i)/H||i)^2)-sqrt(1+(V_A||i/H||i)^2))-abs(w(i));
 rozw||i:=fsolve({r1||i, r2||i}, {H||i,V_A||i},H||i=0..1);Force(i,1):=H||i;Force(i,2):=V_A||i;subs(rozw||i,Force(i,..));
end do:
evalf(Force);

Thanks in advance,

Iza

I need to create randomly several {1,2,3}-sequences of length 15. I execute:

> with(RandomTools):

> w:=Generate(list(posint(range = 3), 15)):
 

The problem is that when I close the program and then open and run it again, it always produces the same sequences. 

What should I do in order to make it work really randomly? That is, to start at a "random" sequence as well?

Thanks!

Can any one help me correct my doc wherein I want to record 5 minutes with microphone and play it for the same duration through my speaker with a click of button component. I find problem in file path specification.This document in my PC is  in E:\A_PhD2017\MAPLEPhDFiles\RequestCorrection_Microphone_Speaker_from_primetime.mw

Components added are only three: microphone0, Speaker0 and Button0

``

``

``

Edit*Data*Available*Action*contains*the*following*commands

rate := DocumentTools:-GetProperty("Microphone0", samplerate); 1; R := DocumentTools:-GetProperty("Microphone0", value)

Array(%id = 18446745571883247742)

(1)

Edit Click Action for Button contains the following commands.

R := DocumentTools:-GetProperty("Microphone0", value); 1; srate := DocumentTools:-GetProperty("Microphone0", samplerate); 1; DocumentTools:-SetProperty("Speaker0", samplerate, srate); 1; DocumentTools:-SetProperty("Speaker0", value, R)

16000

(2)

NULL

No errors displayed for both the above doc tools use``

Also nonstop continuous evaluation takes place! Where is the loop formation if at all there is any?

Thanks for answering

Ramakrishnan V


 

Download RequestCorrection_Microphone_Speaker_from_primetime.mwRequestCorrection_Microphone_Speaker_from_primetime.mw

PhDFiles\....mw

Hello,

I'm trying to write and simplify expressions involving partial derivatives of an arbitrary function, say f(x,y).

Specifically, I would like diff(f(t,y),t) to evaluate to D[1](f)(t,y), instead of 
diff(f(t,y),t)

And eval(diff(f(x,y),x),x=t) gives the same result. 

Interestingly, diff(f(2*t,y),t) does evaluate to 2*D[1](f)(2*t,y), as expected.

I could get some results by using a custom differentiation function
 

`diff/f` := proc(x,y,v) 
    if v = x then return D[1](f)(v,y):
    elif v = y then return D[2](f)(x,v):
    else return 0: # is there a fallback I can use without risking infinite recursion?
    fi:
end proc:

and it works for the simple case, but now diff(f(2*t,y),t) does not work.

All this makes me feel that there must be a way to get what I want by default, but I can't figure it out.

Is there? Thank you in advance!

Hi Mapleprimes people and robots,


My question is regarding a recursive sequence.  It can be defined non-recursively as - 


a(r) :=  0.8*3^r + 0.2*(-2)^r.

The first few terms are - 

1,2,8,20,68,188, and so on.

Here is my Maple Worksheet.
recursive_sequence_A133467.mw      recursive_sequence_A133467.pdf

I want some Maple code that will produce 30 terms of this sequence.  It is defined as

s[1]:=1:
s[2]:=2:

for n>2 we let s[n] = s[n-1] + 6*s[n-2].

Let me know if my question does not make sense.

Regards,
Matt

 

Hello,
I have a second problem which is related to converting horizontal axis to degrees ( or in terms of Pi :  0 - Pi/2 ).

Thank you for your helps

Bengu


restart;
s1 := (1/3*(4*(1.66+10^(-1))^2-x^2))^(3/2)/(x^2*(1+.66+10^(-1)))-sin(2*a);
s2 := (1/3*(4*(1.66+10^(-2))^2-x^2))^(3/2)/(x^2*(1+.66+10^(-2)))-sin(2*a);
s3 := (1/3*(4*(1.66+10^(-3))^2-x^2))^(3/2)/(x^2*(1+.66+10^(-3)))-sin(2*a);
k1 := series(s1, x);
                    (-2)                                 
       4.769067180 x     + (-0.5773502688 - 1. sin(2. a))

                           2    / 4\
          + 0.01164914507 x  + O\x /
k2 := series(s2, x);
                    (-2)                                 
       4.293792441 x     + (-0.5773502692 - 1. sin(2. a))

                           2    / 4\
          + 0.01293857500 x  + O\x /
k3 := series(s3, x);
                    (-2)                                 
       4.247636750 x     + (-0.5773502693 - 1. sin(2. a))

                           2    / 4\
          + 0.01307916821 x  + O\x /
p1 := convert(k1, polynom);
  4.769067180                                                2
  ----------- - 0.5773502688 - 1. sin(2. a) + 0.01164914507 x 
       2                                                      
      x                                                       
p2 := convert(k2, polynom);
  4.293792441                                                2
  ----------- - 0.5773502692 - 1. sin(2. a) + 0.01293857500 x 
       2                                                      
      x                                                       
p3 := convert(k3, polynom);
  4.247636750                                                2
  ----------- - 0.5773502693 - 1. sin(2. a) + 0.01307916821 x 
       2                                                      
      x                                                       
with(plots, implicitplot);
implicitplot([p1, p2, p3], a = 0 .. (1/2)*Pi, x = 0 .. 3, style = point, symbol = [box, cross, circle], labeldirections = [horizontal, vertical], labels = ["&theta; (radians)", "Switching  field (T)"], color = [blue, red, black], symbolsize = 13);


Hello,

How can I fit my equation with the experimental data given below? 

My equation is:  y = A*y^3+B*x ,  where x is the independent variable,  and y is the dependent variable. 
Also how can I determine A and B constants? 
Thanks

Bengu


restart;
Xvals := [.53993447, .5599647, .57995479, .59995566, .61996118, .63994512, .65994136, .6799731, .69996782, .71997949, .73997422, .75995044, .77994976, .7999707, .81995146, .83995244, .85996729, .87994951, .8999458];
Yvals := [-.79625455, -.75585259, -.67800183, -.47955884, -.25493698, -0.65747361e-1, .10114507, .26994542, .41484068, .50621122, .60363251, .65510417, .7251356, .75804148, .76002419, .8030069, .82774732, .8429559, .8692888];
with(Statistics);
points := ScatterPlot(Xvals, Yvals);
PLOT(CURVES(Matrix(19, 2, {(1, 1) = .53993447, (1, 2) = 

   -.79625455, (2, 1) = .5599647, (2, 2) = -.75585259, (3, 1) = 

   .57995479, (3, 2) = -.67800183, (4, 1) = .59995566, (4, 2) = 

   -.47955884, (5, 1) = .61996118, (5, 2) = -.25493698, (6, 1) 

   = .63994512, (6, 2) = -0.65747361e-1, (7, 1) = .65994136, 

   (7, 2) = .10114507, (8, 1) = .6799731, (8, 2) = .26994542, 

   (9, 1) = .69996782, (9, 2) = .41484068, (10, 1) = .71997949, 

   (10, 2) = .50621122, (11, 1) = .73997422, (11, 2) = 

   .60363251, (12, 1) = .75995044, (12, 2) = .65510417, (13, 1) 

   = .77994976, (13, 2) = .7251356, (14, 1) = .7999707, (14, 2) 

   = .75804148, (15, 1) = .81995146, (15, 2) = .76002419, (16, 

   1) = .83995244, (16, 2) = .8030069, (17, 1) = .85996729, 

   (17, 2) = .82774732, (18, 1) = .87994951, (18, 2) = 

   .8429559, (19, 1) = .8999458, (19, 2) = .8692888}, datatype 

   = float[8]), COLOUR(RGB, 0., 0.054901961, 0.47058824), 

  STYLE(POINT)), AXESLABELS("", ""), VIEW(DEFAULT, DEFAULT))
with(plots);
display(points);

Statistics:-Fit(a*y^3+b*x, Xvals, Yvals, y);
                              3                             
   HFloat(2.996866026020011) y  - HFloat(0.9272751314432008)
example("?");

  

 

I want to find the first positive solution of the system of trigonometric equations inside the loop.

The solutions are in the form of "d=number*_Z +number" but I need one exact solution to use it for next run of the loop.
 

restart;
L[0]:=0:
for i from 1 by 1 to 3 do
assume(0<d[i], d[i]<1):
assume(-0.01<a[i], a[i]<0):
L[i]:= L[i-1]+ d[i]:
sys[i]:={Re((-80*Pi*I*a[i]/((a[i]+1)^3))*exp(4*Pi*I*L[i])) = -0.4, Im((-80*Pi*I*a[i]/((a[i]+1)^3))*exp(4*Pi*I*L[i])) = 0.8}:
solve(sys[i], {a[i],d[i]}, useassumptions = true,AllSolutions=true):
end do;
 

These are the solutions:

d[1] = 0.03689590440 + 0.5000000000 _Z1

d[2] = -1.000000000 d[1] + 0.03689590440 + 0.5000000000 _Z2

d[3] = -1.000000000 d[1] - 1.000000000 d[2] + 0.03689590440 + 0.5000000000 _Z3

 

Hello all, 

 

This is my first time with Maple, I have been a student of Mathematica for 7 years. I purchased Maple to learn a new software and I have heard great things about it. I somehow dont feel the flexibility of Mathematica in Maple documentations. It seems to be a bit constrained and not very straight forward in some aspects. Please correct me if I am wrong and also point out to tutorials or documents that I should be looking at before nose diving into Maple.

worksheet example here: 

I have faced 2 simple problems which I think is a bug in some form, or I may be wrong. Please advise.

  1. How do I insert Equation 7 before Equation 6? The worksheet wont let me do it.
  2. Why are 'and' and 'in' bolded automatically in SECTION format?

I need a help on the error message below as when I enter it on my browser the answer is that there isn't any hel for this subject.

Error Message:

Error, (in DynamicSystems:-EquilibriumPoint) the independent variable in the equations does not match the 'continuoustimevar' (t) specified by the DynamicSystems[SystemOptions].

Thank you!

Hey friends

I want to solve this relation with respect to "M"analytically but maple answer me: "Warning, solutions may have been lost"

How I can solve this problem and get to an analytical solution. It must be noted -1<w<-1/3. we can fix "w" with any value inn this interval. It be accepted any solution for any fixed "w".

Thank you

Analytically_solution.mw

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