MaplePrimes Questions

Please describe the step-by-step application of the rules of differentiation which produce this derivative:

diff(a(x)^b(x), x) =        

a(x)^b(x)*((diff(b(x), x))*ln(a(x))+b(x)*(diff(a(x), x))/a(x));

why pdsolve does not work?

Q and alpha are constant. I want to find f(x,y).

Thanks
 

"restart: w(x,y) :=Q*sin^(2)(Pi*x)*sin^(2)(Pi*y)"

proc (x, y) options operator, arrow, function_assign; Q*sin(Pi*x)^2*sin(Pi*y)^2 end proc

(1)

PDE := diff(f(x, y), x, x, x, x)+2*(diff(f(x, y), x, x, y, y))/alpha^2+(diff(f(x, y), y, y, y, y))/alpha^4+((diff(w(x, y), y, y))*(diff(w(x, y), x, x))-(diff(w(x, y), x, y))^2)/alpha^2

diff(diff(diff(diff(f(x, y), x), x), x), x)+2*(diff(diff(diff(diff(f(x, y), x), x), y), y))/alpha^2+(diff(diff(diff(diff(f(x, y), y), y), y), y))/alpha^4+((2*Q*sin(Pi*x)^2*Pi^2*cos(Pi*y)^2-2*Q*sin(Pi*x)^2*sin(Pi*y)^2*Pi^2)*(2*Q*Pi^2*cos(Pi*x)^2*sin(Pi*y)^2-2*Q*sin(Pi*x)^2*sin(Pi*y)^2*Pi^2)-16*Q^2*sin(Pi*x)^2*sin(Pi*y)^2*Pi^4*cos(Pi*x)^2*cos(Pi*y)^2)/alpha^2

(2)

pdsolve(PDE)

``


 

Download PLATE.mw

I currently have a list 2 elements long filled with lists 6 elements long similar to the following:

A := [[0, 1, 2, 3, 4, 5], list[0, 2, 4, 6, 8, 10]]

I would like to output 'A' (my list of lists) to a text file to look like the following:

0   0

1   2

2   4

3   6

4   8

5   10

 

Currently my code looks like this

L := [ ];
M := [ ];
for i from 0 to 5 do L := [op(L), 2*i]; M := [op(M), i] end do;
A := [M, L];
writedata(test, A, float);

 

Which provides me with almost what I need, but written horizontally instead of vertically:

0    1    2    3    4    5
0    2    4    6    8    10

 

How do I alter the code so that I can read my values vertically?

How do I solve for nonlinear differential equation with boundary value problem? Is it possible to solve nonlinear ODE by using Laplace Transform with Maple? If possible, can give me an example of solving nonlinear ODE using Maple. Thank you.

0.733333e^-1

0.733333e^-3

0.733333e^-5

0.733333e^-7

 

no matter what e is , expect to output the same 0.733333

 

I am trying to plot y:=x^2+x-12 as a curve and as a series of point. It is just not working. Suggestions, please.

Digitalize.mw
 

restart

f := proc (x) options operator, arrow; x^2+x-12 end proc

n := 10

h := 5``

printf("\n    i        x       f (dec.form)    f (sci. notat.)\n"); printf("  ---------------------------------------------------\n"); for i from 0 to n do X[i] := i*h; Y[i] := f(X[i]); printf(" %5d  %9.4f  %13.9f  %17.10e\n", i, X[i], Y[i], Y[i]) end do


    i        x       f (dec.form)    f (sci. notat.)
  ---------------------------------------------------
     0     0.0000  -12.000000000  -1.2000000000e+01
     1     5.0000   18.000000000   1.8000000000e+01
     2    10.0000   98.000000000   9.8000000000e+01
     3    15.0000  228.000000000   2.2800000000e+02
     4    20.0000  408.000000000   4.0800000000e+02
     5    25.0000  638.000000000   6.3800000000e+02
     6    30.0000  918.000000000   9.1800000000e+02
     7    35.0000  1248.000000000   1.2480000000e+03
     8    40.0000  1628.000000000   1.6280000000e+03
     9    45.0000  2058.000000000   2.0580000000e+03
    10    50.0000  2538.000000000   2.5380000000e+03

 

``

plot1 := plot([X[k], Y[k]], k = 0 .. n, style = point, symbol = soliddiamond, symbolsize = 24, color = blue)

plot2 := plot(f(x), x = 0 .. 50)

with(plots)

display([plot1, plot2])

 

``


 

Download Digitalize.mw

 

 

restart;

with(IntegrationTools):

# A very simple double integral

J:=Int(Int(x^2, x = 0 .. y), y = 0 .. 1);

Int(Int(x^2, x = 0 .. y), y = 0 .. 1)

(1)

value(J);

1/12

(2)

# Try a simple change of variables

Change(J, x=t*y, [t]);   # Why this form?

Intat(Intat(_a^2, _a = _b)-Intat(_a^2, _a = 0), _b = 1)-Intat(Intat(_a^2, _a = _b)-Intat(_a^2, _a = 0), _b = 0)

(3)

value(%);

1/12

(4)

# Now the same for 2*J

Change(2*J, x=t*y, [t]);  # OK, but why?

2*(Int(y^3*(Int(t^2, t = 0 .. 1)), y = 0 .. 1))

(5)

value(%);

1/6

(6)

 


Download IntegrationTools-Change.mw

Am trying to analyse a set of strings.   Can anyone help?

We have 10 x10 matrix into which we need to add connection score.
ExY := [WPKCPYWFYWCXHY, WPKCTEYFHCFEEE, HYCYTFHYYWWKCE, HYHHTFHKFEYHEH, HKXWYHFECTFFTF, HKWEHPPECWWHTC, HKXWYTPXHFHWYP, HKFEXCTFECXFKP, HKFEYPPEEEPHYW, HYTHCCFEWPPEXX, HKXKXCKFCHTEWK, HYEKPPCKFTWXXW];
Here is the code to create the connection matrix 
A__c = A__a+A__d;
.
Blist:=[W,P,K,C,Y,F,X,H,T,E]:# basis letters
nWords:=numelems(ExY):Wletters:=length(ExY[1]):Bletters:=numelems(Blist):A:=Matrix(Bletters,Bletters):# set up dimensions
for iW from 1 to nWords do  # loop through words
  for iL from 1 to Wletters-1 do # loop through letters of each word
     fromLett:=C(iW,iL); # see char extraction from ExY list above 
     toLett:=C(iW,iL+1); # ditto
     BfromLett:=Search(fromLett,Blist);# column id   <<<<<< the search is returning 0, it works if one uses "A" rather than say fromLett=A 
     BtoLett:=Search(toLett,Blist);# row id   <<<<<  ditto here
     A(BfromLett,BtoLett):=A(BfromLett,BtoLett)+ 1; # add statistic to the A-matrix
  end do; # end letter loop
end do; # end word loop
Error, index out of bounds
The search function is failing: 
Blist; Wletters; Bletters; nWords; fromLett; toLett; BfromLett; BtoLett; A; iW; iL;
                 [W, P, K, C, Y, F, X, H, T, E]
                               14
                               10
                               12
                              "W"
                              "P"
                               0
                               0

                 [0  0  0  0  0  0  0  0  0  0]
                 [                            ]
                 [0  0  0  0  0  0  0  0  0  0]
                 [                            ]
                 [0  0  0  0  0  0  0  0  0  0]
                 [                            ]
                 [0  0  0  0  0  0  0  0  0  0]
                 [                            ]
                 [0  0  0  0  0  0  0  0  0  0]
                 [                            ]
                 [0  0  0  0  0  0  0  0  0  0]
                 [                            ]
                 [0  0  0  0  0  0  0  0  0  0]
                 [                            ]
                 [0  0  0  0  0  0  0  0  0  0]
                 [                            ]
                 [0  0  0  0  0  0  0  0  0  0]
                 [                            ]
                 [0  0  0  0  0  0  0  0  0  0]
 

Hello

I found this paper. 

http://benson-labs.com/uploads/stuff/POW15.pdf

I'm not sure if the population after 1 year is correct.

I wanted to get the formula from rsolve. But i have incorrorectly formulated the sum by day and the total.

Rattus_recursion.mw

 

Whilst trying to debug another problem on this site, this one

https://www.mapleprimes.com/questions/225688-How-To-Compute-Inverse-Of-A-Matrix-For

I came across a Maple bug(?) which was so serious, I thought either

  1. I'm being more than usually dim
  2. it needs it's own entry here, so that others can check

Problem can be summarized as:

When using 2D input, can the '.' character be used for simple matrix multiplication???? Because it isn't working for me!

Entering the '.' character places a bold, midline dot between the two arguments, but executing the result gives "Error unable to parse". Converting to 1-D input, no issues - everything works as expected.I should also point out that

  1. I never normally use 2D-input for my own work
  2. the attached worksheet executes correctly in Maple 2017.3, X86 64 WINDOWS, Sep 13 2017, Build ID 1262472.

If this is reproducible then wtf!

restart; with(LinearAlgebra); kernelopts(version)

`Maple 2018.1, X86 64 WINDOWS, Jun 8 2018, Build ID 1321769`

(1)

A := RandomMatrix(2, 2); B := RandomMatrix(2, 2)

Matrix(2, 2, {(1, 1) = 44, (1, 2) = -31, (2, 1) = 92, (2, 2) = 67})

 

Matrix(%id = 18446744074378134462)

(2)

A.B

Error, unable to parse

"A*B;"

 

LinearAlgebra:-Multiply(A, B)

Matrix(%id = 18446744074378136502)

(3)

A:= RandomMatrix(2, 2);
B:= RandomMatrix(2, 2);
A.B

Matrix(2, 2, {(1, 1) = -32, (1, 2) = -4, (2, 1) = -74, (2, 2) = 27})

 

Matrix(2, 2, {(1, 1) = -93, (1, 2) = -72, (2, 1) = -76, (2, 2) = -2})

 

Matrix(%id = 18446744074378132406)

(4)

 

Download matMulProb.mw

I'm start making an homepage about mathematic and wondt to link a workpage writen in Maple 16 into WP, thanks to whose ho have any idea :)

 

Hello,

I have a set of nonlinear equations (transcendental) containing variables and one free parameter. I want to solve this system for variables while varying parameter's value. I have tried with fsolve and solve commands keeping fixed the parameter value, but they are not solving yet. Is there any way to solve this system for a range of parameter's value.
The systmem is like this, x,y,z are the variables and 'a' is the parameter:
f1(x,y,z,a)=0,
f2(x,y,z,a)=0,
f3(x,y,z,a)=0.

Many thanks in advance.

Hi,

I submit you this strange result:
for somenumerical  values of a, b, c  (a, b, c real and b > a), Maple 2018 is not able to compute the mean of
c*U where U is a Uniform random variable with support [a, b].


 

restart:

with(Statistics):

interface(version);

`Standard Worksheet Interface, Maple 2018.0, Windows 7, March 10 2018 Build ID 1298750`

(1)

z := .4070716688*RandomVariable(Uniform(0.12-0.02*0.12, 0.12+0.02*0.12));
Mean(z);

.4070716688*_R

 

Error, (in Statistics:-Mean) the expression does not have a taylor expansion at t = 0

 

z := .4070716688*RandomVariable(Uniform(a, b));
Mean(z);
subs({a=0.12-0.02*0.12, b=0.12+0.02*0.12}, %);

.4070716688*_R0

 

.2035358344*a+.2035358344*b

 

0.4884860026e-1

(2)

 


 

Download Mean.mw


PLEASE: Maple still fails if I replace  a = 0.12 -0.02*0.12 by its value 0.1174
                                                                       and b = 0.12+0.02*0.12 by its value 0.1224
                   

This is incomprehensible and could hide a more profound problem.

Good day everyone,

I am trying to write HAM code for coupled ODE but getting errors like "table(...)" or

 

"Error, (in dsolve) found the independent variables {eta} also present in the names of the functions of the system {(diff(diff(diff((table( [( 0 ) = proc (eta) options operator, arrow, function_assign; eta*exp(-eta)-F[w] end proc ] ))(eta), eta), eta), eta))(f[1](eta)), (diff(diff((table( [( 0 ) = proc (eta) options operator, arrow, function_assign; exp(-eta) end proc ] ))(eta), eta), eta))(theta[1](eta)), (diff((table( [( 0 ) = proc (eta) options operator, arrow, function_assign; eta*exp(-eta)-F[w] end proc ] ))(eta), eta))(f[1](eta)), ((table( [( 0 ) = proc (eta) options operator, arrow, function_assign; exp(-eta) end proc ] ))(eta))(theta[1](eta))}"

 

Anyone with useful informations should please help.

Thank you.

Below is the attached of the file

untitled22222.m

Does Maple have a way to upload a screenshot of a worksheet or a savefile of a worksheet to MaplePrimes?

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