MaplePrimes Questions

Goodday sirs, 

            How can I get over these error message123.mw
 

restart

 

 

(int((1/6)*(eta-s)^3*(S*(s*f[i](s)+3*(diff(diff(f[i](s), s), s))+(diff(f[i](s), s))*(diff(diff(f[i](s), s), s))-f[i]*(diff(diff(diff(f[i](s), s), s), s)))+M^2*(diff(diff(f[i](s), s), s))), s = 0 .. eta))/(1+1/y)

(1)

G := (int((eta-s)^3*(S*(s*f[i](s)+3*(diff(f[i](s), `$`(s, 2)))+(diff(f[i](s), s))*(diff(f[i](s), `$`(s, 2)))-f[i]*(diff(f[i](s), `$`(s, 3))))+M^2*(diff(f[i](s), `$`(s, 2))))/factorial(3), s = 0 .. eta))/(1+1/y)

 

f[0] := (1/6)*s+(1/6)*s^3:

for i from 0 to n do f[i+1] := (1/6*(-eta^3+eta))*subs(eta = 1, diff(G, `$`(eta, 2)))-eta*subs(eta = G)+G; f[i+1] := subs(eta = s, f[i+1]) end do

Error, final value in for loop must be numeric or character

 

``


Anyone with useful informations please.

Thanking you in anticipation for a favurabke response

Download 123.mw

 

pde := [diff(u(x, y), x, x)+diff(u(x, y), y, y) = 2*Pi*(2*Pi*y^2-2*Pi*y-1)*exp(Pi*y*(1-y))*sin(Pi*x), u(0, y) = sin(Pi*y), u(1, y) = exp(Pi)*sin(Pi*y), u(x, 2) = exp(-2*Pi)*sin(Pi*x), u(x, 0) = u(x, 1)]pdsolve(pde)

pdsolve(pde)

it does not return any solution and answer, kindly help.

Hi, 

I have a vector field that has positive constants. I don't want to set perminant values for the constants becuase future calculations will be wrong. 

Instead, how can I set a sample set of values for these constants? Thanks

Hi guys. I tried to find Killing Vectors for Taub-NUT metrics but the maple gives an error.  Can someone explain what is wrong?

How can one calculate isogeny of elliptic curves over finite fields in maple ?

Can't seem to get Retrieve from DocumentTools to get any labels from any worksheet.  I just get an error saying unable to retrieve label reference.

with(DocumentTools):

Retrieve("c:/test/test/mw","L1") #sample test file named test.mw in directory test

Here's the same issue (unanswered) way back in 2015 https://www.mapleprimes.com/questions/203811-DocumentTools-Retrieve-Function-Returns

Maybe it's a Windows administrator issue?  Does it work for anyone else?

restart;

u1 := proc (x, y) options operator, arrow; 1-e^(a*x)*cos(2*Pi*y) end proc;
a := -.39323780;
evalf(int(int(u1(x, y)^2, y = -.5 .. 1.5), x = -.5 .. 1.5));
             1             /                  /          5 
  ------------------------ \0.000002034392421 \6.25000 10  
         (5898567/5000000)                                 
  ln(e) e                                                  

     (1966189/1250000)              6        (5898567/5000000)
    e                  + 1.966189 10  ln(e) e                 

                 5\\
     - 6.25000 10 //

I need help me , how can find this integral as simple number?

u1 := proc (x, y) options operator, arrow; 1-e^(a*x)*cos(2*`πy`) end proc;
u2 := proc (x, y) options operator, arrow; a*e^(a*x)*cos2*`πy` end proc;

norm(u2(x, y), 2)/norm(u1(x, y), 2);
Error, invalid input: norm expects its 1st argument, p, to be of type {Matrix, Vector, matrix, polynom, vector}, but received a*e^(a*x)*cos2*`πy`

Hi, I want to define A matrix (shown below) that has some definite products. These products have two arguments e.g. (k=1..N) and (k<>i) but product expects only one argument. What should I do?

I appreciate any help you can provide.

 

Hi,

How to import and manipulate different formulas of  Excel files in maple ?

See example in attachment

Thanks

Hi all

I wnat to produce following matrix P2r+1, 2r+1 in maple.

can any one help me please?

Error, (in dsolve/numeric/process_input) system must be entered as a set/list of expressions/equations
moadele_asli2.mw

solve does not show result!!

dtm.mw

can i have step by step procedure of the solution of the follwoing problem

 

sys[1] := [-(diff(u(x, t), t, t))-(diff(u(x, t), x, x))+u(x, t) = 2*exp(-t)*(x-(1/2)*x^2+(1/2)*t-1), u(x, 0) = x^2-2*x, u(x, 1) = u(x, 1/2)+((1/2)*x^2-x)*exp(-1)-((3/4)*x^2-(3/2)*x)*exp(-1/2), u(0, t) = 0, eval(diff(u(x, t), x), x = 1) = 0]

I am attempting to use the Gram-Schmidt process with Maple to show that the first six orthogonal polynomials which satisfy the following orthogonality condition:

$\int_0^1 (1-x)^{3/2} \phi_n(x) \phi_m(x) dx = h_{n} \delta_{nm}$   

can be expressed in the form:

\phi_0(x) = 1, \phi_1(x) = x − 2/7 , \phi_2(x) = x^2 − (8/11)x + 8/99 , \phi_3(x) = x^3 − (6/5)x^2 + (24/65)x − 16/715 , \phi_4(x) = x^4 − (32/19)x^3 + (288/323)x^2 − (256/1615)x + 128/20995 , \phi_5(x) = x^5 − (50/23)x^4 + (800/483)x^3 − (1600/3059)x^2 + (3200/52003)x − 256/156009.

At the same time I have to find the corresponding values for h_n, so for example, h_0 = 2/5 and h_1 = 8/441.  The polynomials which I obtain have to be combined with the Gaussian quadrature method to show that

$\int_0^1 (1-x)^{3/2} \phi_n(x) \phi_m(x) dx = h_{n} \delta_{nm} \approx \sum_{k=1}^4 c_k f(x_k)$

where x_k are the four roots of \phi_4(x)=0 such that x = [0.0524512, 0.256285, 0.548299, 0.827175]

and the 4 c_k coefficients are given by c = [0.121979, 0.168886, 0.0920439, 0.0170909].

I have learned about Gram-Schmidt orthogonalisation in a basic setting in linear algebra courses where a system of N linearly independent orthogonal vectors is constructed from a system of N linearly independent vectors, but unsure how to apply it to polynomials.  I am also vaguely familar with the idea of appoximating integrals with sets of orthogonal polynomials (Legendre, for example) but not exactly sure how this all works.

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