I have this very simple intergral

((Int(sin(m*Pi*y/a), y = 0 .. b))

I want to solve it when m is even then when it is odd. Of course, a and b are real positive. Then I will do the same with the other side of the integral.

Int(sin(n*Pi*y/a)*sin(m*Pi*y/a), y = 0 .. b)

Thank you in advance.

Mario

document:Laplace_Problem.mw

I know that this is a stupid question but I cannot find how to do the dyadic product of two matrix. Those matrix could be two tensor matrix and I need to do this multiplication:

Thank you in advance for your help.

Mario

In solving the brachistochrone for a fine string of length L under the pull of g passing through the point (0,0) and (a,b) using the euler-lagange method,I stumble on this non-linear relation:

C*sinh(mu*g*a/C)=L

which I need to solve for C.

Maple give me the famous RootOf:

RootOf(A*exp(_Z)^2 - 2*_Z*L*exp(_Z) - A)

where A = mu*g*a

Can it be solve for C or am I force to use numeric method?

Thank you in advance for your help.

Mario

After loading the Physics package, I have define the langragian L this way:

L:=sqrt((1+(y')^2)/y)

After some algebra, I get the following integral:

((1+(y'(x))^2)^(-1)*1/y(x) = C

At that stage, I would like to isolate the term y'(x) and do the change of variable. But since I am under the Physics package, I try to isolate it with no succes and worst if I try to change the variable first. A little help would be appreciate.

Thank you in advance

Mario

Maple 2022 under Windows

Hello everybody

In a course on numerical calculation in seismology (with jupyter notebook but I tried to adapt them in Maple), we use the Lagrangian interpolation:

First, have done the calculation and get the right answer. But I had to do it manually in Maple (see document below for the question and my solution. The question is describe more explicitly. What I want to do is to make Maple do it automatically and taking into account that there is the restriction i<>j. Then when the lagrangian is calculated, it will be easy to calculate u bar.

Thank you in advance for your help.

Mario

Lagrange_interpolation.mw