Compute the following multiple integral exactly and/or with 10 correct significant digits

Int(  exp( - add(x[i],i=1..10)^3),  seq(x[i]=0..1, i=1..10) );

  The problem is suggested by a previous post.

Hello everyone !

I have a problem when I want to calculate the following multiple integration numerically:

>evalf(Int(exp(sum(x[i],i=1..6)^2),[seq(x[i]=-1..1,i=1..6)]));
  value(%);

It doesn't work. But when I replace sum(x[i],i=1..6)^2 with sum(x[i],i=1..6), it works. Is there any feasible solution to my problem ?

Thank you for reading !

Dear Friends

In differential expressions(See Maple file) how to find coefficiets of dependent variable "u(x,t)" and "v(x,t)" and of their differentials ? There is command "dcoeffs(function)", but that work for single dependent variable only but in our case there are two dependent variables in consideration. There are other options like "indets", "specindex" but those do not work.

Download Coefficients_in_differential_expression.mw

Hello

I have an SEIR model.

Equation 5 is for disease death but I would like to plot the cumulative numbers of disease death which will be the integral of Equation 5. I added the integral inside odeplot but it is not working. Any idea  about  how to compute the integral ?

Maple code is attached

Thank you

code.mw

Found a strange behaviour in Mapke 2015 of the sqrt-function after loading the GRTensor package:

the square-root of a non-square integer, e.g. sqrt(5), does not terminate. 5^(1/2) instead works fine.

Can be reproduced with Maple 18, but not with Maple 11.

I consider this a serious bug, as it makes any expressions containing such roots useless.

As it worked with Maple 11 I am inclined to see it as your fault.

Some Maple 18 short (and I believe elegant) code for doing gravitational simulations with N bodies in space:

N_body_problem.mw

Initial velocities have been tweaked to keep the system stable for the duration of the animation.

Please feel free to fiddle with its parameters, velocities and positions and/or N itself, to produce more interesting animations or re-use the code therein (You can safely ignore the (c), it's there just for archiving purposes).

The following are animations from three runs with N=4, N=3 and N=2, no other parameters changed.

Let's say I've got somehow a result of the product:

as series expression and I want to factor out the series of

in order to get

How can I do that with Maple?

In PDEtools, suppose to I wish assign zero value to certain first order partial derivative such that higher order derivatives automatically vanish in subsequent excutions, how I can do that?

Download Assiging_Derivative.mw

I tried to load my document containing some notes, but then I got the message "There were problems during the loading process, Your worksheet may become incomplete", and as the message said my worksheet were incomplete. Is there a way to restore the document? I have tried following this and added the line it suggested:

http://www.maplesoft.com/support/help/Maple/view.aspx?path=worksheetmaybeincomplete

But it didn't work.

I have attached the file.

Noter.mw

There has been a spate of Questions posted in the past week about computing eigenvalues. Invariably, the Questioners have computed some eigenvalues by applying fsolve to a characteristic polynomial obtained from a floating-point matrix via LinearAlgebra:-Determinant. They are then surprised when various tests show that these eigenvalues are not correct. In the following worksheet, I show that the eigenvalues computed by the fsolve@Determinant method (when applied to a floating-point matrix) are 100% garbage for dense matrices larger than about Digits x Digits. The reason for this is that computing the determinant introduces too much round-off error into the coefficients of the characteristic polynomial. The best way to compute the eigenvalues is to use LinearAlgebra:-Eigenvalues or LinearAlgebra:-Eigenvectors. Furthermore, very accurate results can be obtained without increasing Digits.

Download Eigenvalues.mw

I never expected that the reflected light direction of sun from moon in the sky would be so dificult to imagine ...

at the following article mentioned :

we derive an equation for the magnitude of the moon tilt illusion that can be applied to all congurations of sun and moon in the sky.

THE MOON TILT ILLUSION

since the calculations contains many steps and high level mathematical formula , there is no way rather to recourse to maple (powerful math assistant )

I hope there was adaptations between a lots of functions and predefined schema of maple and this problem so that the calculations and visualization facilitated several times ?

your effort will be a graet present for all the people of the world that look to the moon crescent everytime !

hi.i trust that attached equation has more answer but fsolve only gain some of them!!! how i can gain another that i know value of them?

another root  that i known, are : 0.165237712988657e-1    and     .103583272213766    and    .290071279318035

thanks 

root.mw

Hi!

I am comptuing the eigenvalues and the characteristic polynomial of a 8 by 8 symmetric matrix, say M. Thus, we define the matrix M, and compute its charast. plynm. by

and its eigenvalues with the command

Well, Maple returns the charast. polynm. an dthe eigenvalues. But, if we compute p(E[k]), for k=1,...,8, thats is, the values of the polynomial p(x) in the eingenvalues, Maple not turns cero!!! I'm really confused ... anyone know what could be happening?

Maple attached file with this example. Thank very much for your help!!

Download exam_eigenvalues.mw

hi .how i can calculate eigenvector associated with the eigenvalue of the matrix.for example according attached file below

what are  eigenvector associated with the eigenvalue of matrix q which  determined as (2646.408147, 3142.030259, 6621.757707) respectively??

thanks...

eign.mw 

I would like to learn to use Maple to develop applications of math, physics, astronomy ecc.. . The problem is that I do not know where to start. Could you help me ? Thank you.

Blustar