Maple 17 Questions and Posts

These are Posts and Questions associated with the product, Maple 17

Dear all

I can I obtain the sigma-algebra generated by a given set. 

sigma_algebra.mw

thanks

Dear all

Can I compute using maple some Riemann Stieltjes integrals 

RSI.mw

Thanks 

Dear all

I have a proc I would like to construct two vectors as output of  the proposed proc, the following code, contains  an example to illustrate this idea, 

output_pro.mw

thanks for any help 

Dear all

I have many points, and I would like to use pointplot to hold all plots in the same curve. 

plot_many_points.mw

thanks for any help 

dear all

I have a three lines of codes, used to create vectors, I would like to put these vectors in two columns and each columns has a title.

simple_code_table.mw

thank you

Dear all

I have the following code, 

for i to 6 do
for j to i do
F[i, j] :=  g(i+1)/g(j);
 end do;
end do;
How can display F as a full matrix  

Thak you for your help 

Dear all
I have an algorithm  to solve a first order odes, all steps of the algorithm ( as presented in the book are coded) but unfortunately something wrong. 
The algorithm and the code are attached in the following code. 
Thank you in advantage for your help. 

sol_odes.mw

Hello friends, I have the following problem:
I have two lists of vectors, L1 and L2. The lists have the same number of vectors, and all the vectors have the same length.
I need to check if there is a permutation that, when applied to all the elements of one list, will obtain all the elements of the other list. For example, consider the following lists :

L1:=[<0|0|0>,<2|1|2>,<1|2|1>];
L2:=[<1|1|2>,<2|2|1>,<0|0|0>];

In this example the vectors are of length 3. Therefore, there are 3!=6 possible permutations. Namely:

P1:=<<1,0,0>|<0,1,0>|<0,0,1>>;
P2:=<<0,1,0>|<0,0,1>|<1,0,0>>;
P3:=<<0,0,1>|<1,0,0>|<0,1,0>>;
P4:=<<0,0,1>|<0,1,0>|<1,0,0>>;
P5:=<<0,1,0>|<1,0,0>|<0,0,1>>;
P6:=<<1,0,0>|<0,0,1>|<0,1,0>>;

In this case there are two permutations that satisfy the condition above, namely:

P3:=<<0,0,1>|<1,0,0>|<0,1,0>>;
P6:=<<1,0,0>|<0,0,1>|<0,1,0>>;

Cause

for i in L1 do Multiply(i, P3) end do;
>[0 0 0]
  [2 2 1]
  [1 1 2]
 
The same result is obtained using the permutation P6.
I'm working with larger lists and longer vectors so I'm looking for a quick way to check this. Thanks for your valuable help.

Hi all,

I want to verify the sum of associated Laguerre polynomials as shown in the picture below. I have tried numerical, but I am struggling with the syntax.

Anyone know how to do that?

Dear all
My goal, is expand a given function using chebyshev polynomails. Everything is well written, but unfortynattely, the coeffients an, are not computed exactly, but the result return only integral form and there is evalaution of this integral.

How, can I expand my function f , using sum ( a_n chebyshev Tn), for x in [0,1] and we get explicitely the results. 

Question_integral_chebyshev.mw

Thank you for any help 

Dear all;

I have a data, I would like to save this data in a table with labeled columns and  each column contains the corresponding values.

cretae_tabl.mw

thank you for your help 

Dear all

I would like to compute the monomial polynomial in taylor series, I tried 
f:=cos(t);

fn:=n->subs(diff(f(x),x$n),x=0)/factorial(n);
but it is does not work 
anay help please

Dear all

I solve a first order nonlinear ode, using dsolve but there is no solution obtained.

problem_dsolve.mw
How, can I get the exact solution.

tahnk you for your help

Dear all

I compute the solution of first order nonlinear ode, supplied to initial condition.

The code is written, the exact solution is derived.

 plot the solution in a small interval like (0,1/5) I see that there is no difference between exact and semi-analytical soluton.

But, If I plot the solution in other interval like (0,1) or (0,2), It is noticed that the semi-analytical solution is different to the exact solution. 
Thansk you in advance for your help 

test3.mw

Hi

I got the error like this unable to convert to an explicit first-order system

please anyone can help me to solve this

I am attaching the worksheet

with(plots); restart

eq1 := (2*eta*gamma+1)*(diff(f(eta), `$`(eta, 3)))+2*gamma*(diff(f(eta), `$`(eta, 2)))+f(eta)*(diff(f(eta), `$`(eta, 2)))-(diff(f(eta), eta))^2-(Q+S)*(diff(f(eta), eta))+beta*(diff(F(eta), eta)-(diff(f(eta), eta))) = 0;

(2*eta*gamma+1)*(diff(diff(diff(f(eta), eta), eta), eta))+2*gamma*(diff(diff(f(eta), eta), eta))+f(eta)*(diff(diff(f(eta), eta), eta))-(diff(f(eta), eta))^2-(Q+S)*(diff(f(eta), eta))+beta*(diff(F(eta), eta)-(diff(f(eta), eta))) = 0

(1)

eq2 := (diff(F(eta), `$`(eta, 2)))*F(eta)-(diff(F(eta), eta))^2+beta*(diff(f(eta), eta)-(diff(F(eta), eta))) = 0;

(diff(diff(F(eta), eta), eta))*F(eta)-(diff(F(eta), eta))^2+beta*(diff(f(eta), eta)-(diff(F(eta), eta))) = 0

(2)

eq3 := (2*eta*gamma+1)*(1+Rd)*(diff(theta(eta), `$`(eta, 2)))+Pr*((diff(theta(eta), eta))*f(eta)-2*(diff(f(eta), eta))*theta(eta))+gamma*(diff(theta(eta), eta))+N*Pr*betat*((theta[p](eta), eta)-theta(eta))+N*Pr*Ec*betat*(diff(F(eta), eta)-(diff(f(eta), eta)))+Pr*delta*theta(eta) = 0;

(2*eta*gamma+1)*(1+Rd)*(diff(diff(theta(eta), eta), eta))+Pr*((diff(theta(eta), eta))*f(eta)-2*(diff(f(eta), eta))*theta(eta))+gamma*(diff(theta(eta), eta))+N*Pr*betat*((theta[p](eta), eta)-theta(eta))+N*Pr*Ec*betat*(diff(F(eta), eta)-(diff(f(eta), eta)))+Pr*delta*theta(eta) = 0

(3)

eq4 := 2*(diff(theta[p](eta), eta))*f(eta)-F(eta)*theta[p](eta)+betat*delta*(theta[p](eta)-theta(eta)) = 0;

2*(diff(theta[p](eta), eta))*f(eta)-F(eta)*theta[p](eta)+betat*delta*(theta[p](eta)-theta(eta)) = 0

(4)

bcs := f(0) = 0, (D(f))(0) = 1, (D(f))(5) = 0, (D(F))(5) = 0, F(5) = f(5), theta(0) = 1, theta(5) = 0, theta[p](5) = 0;

f(0) = 0, (D(f))(0) = 1, (D(f))(5) = 0, (D(F))(5) = 0, F(5) = f(5), theta(0) = 1, theta(5) = 0, theta[p](5) = 0

(5)

params := [Rd = .1, beta = .5, Q = .5, S = .5, gamma = .1, Pr = 6.2, N = .5, betat = .5, Ec = .1];

[Rd = .1, beta = .5, Q = .5, S = .5, gamma = .1, Pr = 6.2, N = .5, betat = .5, Ec = .1]

(6)

sol := dsolve(eval([eq1, eq2, eq3, eq4, bcs], params), numeric, output = array([0]), maxmesh = 5000, initmesh = 1000)

Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system

 

``

Download MapleOde.mw

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