schzan

130 Reputation

5 Badges

9 years, 349 days

MaplePrimes Activity


These are questions asked by schzan

Dear Friends,

I am having trouble in defining a linear differential operator. This is how Maple defines a linear differential operator

"A differential operator L in C(x)[Dx] is an expression a_0*Dx^0+ ... +a_n*Dx^n where a_0, ... , a_n are elements of C(x). So it is a polynomial in Dx with rational functions as coefficients."

Here's the link http://www.maplesoft.com/support/help/maple/view.aspx?path=diffop

where Dx^n implies n-th derivative with respect to x.

Now I want to know how can I apply this operator to a given function. Here is a failed example:

>L :=Dx^2+Dx;
Dx^2 + Dx
>simplify(L(x));
Dx(x)^2 + Dx(x)

I was expecting to get 1 if the given opertor is applied to x. I would really appreciate if someone can help me with this. 

Many thanks.

 

I am performing the int operation on an experssion but it does not consider constants to be constants. For example, maple is considering this constant namely, f'(-1) or eval(diff(f(x), x), x=-1) as a function and henceforth does not give the desired output. Please tell me how to make eval(diff(f(x), x), x=-1) as a constant function or to say, how to convert any given function in to a constant function.

Thank you for your time and help!

Hello everyone,

 

I am working on a program in Maple and got stuck in exchanging limits for integrals. For example, if I have an expression of following type.

Eq:=4*Int(f(x), x=0..1/3)+Int(x*f(x), x=0..2/3);

I want to convert it in to an expression of form

4*Int(f(x),x=0..x)-4*Int(y,x=1/3..x)+ Int(x*f(x), x=0..x)- Int(x*f(x), x=2/3..x)


In short, I want to split both the integral at x but flip in limits in the second integral. I tried as follows which did not work

applyrule(Int(f::anything,y=c::numeric..d::numeric)=Int(f,y=c..x)-Int(f,y=c..x), Eq)

Please, help me!

Thank you for your time.

Sorry for the bad format, maple input is not working.

In particular,from an expression, something like

 Int(x*f(x), x = 0 .. 1)+ Int(x, x = 0 .. 1/3)+3* Int(x*f(x), x = 0 .. 2/3)

I want to extract 

x*f(x)+x+3*x*f(x)

That is all the integrands occuring in the expression. GetIntegrand helps to find the integrand but only for one integral, how do I do it for an expression like above.

 

I tried to apply following approach

subs(sin(c::anything)=c, sin(x)+f);


and the output was

f

I was expecting to get only 'x+f' for output.

EDIT 1: 

Thank you so much for your help. You guys answered exactly what I asked for. I needed this to do something different but I should have been more careful. I realized, I could not get that part now. This is what I actually need to do, if

A:=-(5/8)*x*(Int(f(x), x = 0 .. x))+(5/24)*(Int(f(x), x = 1/3 .. x))-(1/4)*x*(Int(x*f(x), x = 1/3 .. x));

then I wish to get a function, g(xi),


g(xi)= -(5/8)x*f(xi) ;   if 0<= xi <= x
                                                  (5/24)*f(xi)-(1/4)*x*xi*f(xi) ; if 1/3<= xi<= x

Notice, all the terms after integral should use variable 'xi' and terms occurring before integral remains as it is.

1 2 3 4 Page 4 of 4