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Hi,

I open a discussion about convolution and Fourier coefficients in Fourier series.

 

I have a function defined by f(x)=0 if x in [-Pi,0[ and 1 if x in [0,Pi[, of course f 2*Pi periodic function.

My goal is compare the Fourier coefficients of f*f ( * convolution ) and The Fourier Coefficient of f.

 

Thanks for your help.

 

 

 

the question

 

I already finished part a, my question is how do i define the function g with the variable k being any real value so that maple will find <f,g> = 0 (using the inner product defined)?

 

Hi all;

Hope all of you  be in good health

I want to construct a special function b_{nm}(t) like:

with piecewise command i did it but the result is incorrect.

any one can help me to do it?

Best wishes

 

Mahmood   Dadkhah

Ph.D Candidate

Applied Mathematics Department

Hi,

I open a new subject about Fredholm Integral equation. My code work correctly.

But, I need some modification to get a nice display of the matrix found using
MatA,Vectb := GenerateMatrix(convert(sys3,list),Sol_phi);

such as Sol_phi is my solution that I want to find.

I introduced two function alpha1 and alpha2 in the code  see Equation (9) can I write all the coeficient of my matrix using the two function alpha[1] and alpha[2], it's better to see and read the matrix form.

 

Fred.mw

Hello,

I have to simplify a piecewise function and Maple gets a more complicated solution than needed.




I don't know how to handle this kind of problems with Maple?
I don't understand why Maple doesn't see this?
Am I doing something wrong?

Thanks in advance for your help / advice.


# the code of my example
restart:
Mf(x):=piecewise(x<=L/2,1/2*x*F,x>1/2*L,1/2*x*F-F*(x-1/2*L));
# Make a dimensionless function:
# -    Mf(x):= Mf(xi)*F*L
# -    variable ξ  ( xi:=x/L )
eq[1]:=Mf(xi)*F*L=Mf(x);
Mf(xi):=solve(eq[1],Mf(xi));
Mf(xi):=subs(x=xi*L,Mf(xi));
# F is the Force and L is the Length of the beam:
Mf(xi):=simplify(Mf(xi)) assuming F>0,L>0;
print("When I simplify this function by hand it will be");
Mf(xi):=piecewise(xi<=1/2,1/2*xi,xi>1/2,-1/2*xi+1/2);




Hi all,

I will use the following dummy example.

with function,f

f:=(xid,yid)->sum(x[i],i=1..xid)*sum(y[i],i=1..yid);

 

and a complicated term, myterm


myterm:=(f(3,4)+f(2,2))*f(1,1):
myterm:=expand(myterm);

 

'if' i have some previous knowledge, or know a bit of the term, i can find the structure by doing this


repar:=[f(1,1),f(2,2),f(3,4)];  # Or with more f(xid,yid) terms

tmp:=seq(repar[i]=ff[i],i=1..3);
simplify(myterm,{tmp});          # This is fine, gives me what i want

 

But, can we go further, and more 'obvious'

 

Given the fucntion f, same as before, and the same 'myterm'

can I have this
restart:
iwant:=(f(3,4)+f(2,2))*f(1,1);  # as a result, straightforward

so I dont have to go back to 'repar' and find that the terms exactly are.

 

Thanks,

 

Hi say I have the vector V1.

V1:=Vector([a,b,c,d,e,f,g]):

and function myfun.

 

how do i use it as the input to the function my fun, by taking away each element in turn?
myfun(V1[2..]);              # 1st element removed
myfun(V1[[1,3..]]);         # 2nd element removed
myfun(V1[[1,2,4..]]);      # 3rd element removed

and so go

is there a more efficient way?

 

Many thanks,

This has been buggin me all day, but if i define a variable with an expresion say "a:=3 x+5" and i then want to assign this expression to a function like so "f:=x->a". if i then call f(7), maple return with "3 x+5" so just returning the value of a without substituting x with 7.

Is there any way in which i can define a function this way?

I am new user of Maple. I have an expression like f(x,y)/g(x,y) and I want to have Maple name f(x,y) as something simple like "h" so that later equations write h/g(x,y) instead of the complete f(x,y)/g(x,y), and also to be able to simplify other equations in terms of h.

For example, a=(x+1)(y-5)^2/(x+y-3). Can I get Maple to let h=(x+1)(y-5)^2, so that I get h/(x+y-3) when I ask for a?

Sorry if this question is basic (and my math terminology incorrect), but I have been trying for a while.

Hi all

In matlab software we have a command namely fmincon which minimizes any linear/nonlinear algebric equations subject to linear/nonlinear constraints.

Now my question is that: what is the same command in maple?or how can we minimize linear/nonlinear function subject to linear/nonlinear constraints in maple?

thanks a lot

Mahmood   Dadkhah

Ph.D Candidate

Applied Mathematics Department

Hi all,
I need to find mina(w) then a=-1,0,1 and

w := piecewise((x-a)/t <= -10, 202*a-200*x-(202001/101)*t, (x-a)/t <= -910/101, 3*a-x-(1011/101)*t, (x-a)/t <= 910/101, 2*a-t, (x-a)/t <= 10, a+x-(1011/101)*t, 10 < (x-a)/t, -198*a+200*x-(202001/101)*t)

Also need to plot it, i think it should look like this 

Thanks

 

 

 

Hello fellow maple fans :)

 

I have tried to plot this continuous Piecewise function

plot(piecewise(0 <= t and t < 2, 2-t, 2 <= t and t <= 3, 2*t-4))

On the interval [0,6]

When i try it plot it it won't show the entre internal, is there a way to tell maple that the funktion should continuous until [0,6]

Please see this http://snag.gy/NPrjG.jpg if you are not sure what i mean in the end it should look like this http://snag.gy/ScgtF.jpg

Greetings David Thanks in advance :)

 

hi all.
i have a system of ODE's including 9 set of coupled OED's . 

i have  converted second deravaties to dd2 , in other words : diff(a[i](t),t,t)=dd2[i](t) . i =1..9 :

and i have set these 9 equations in form of vibrational equations such :  (M.V22)[i]+(K(t).V(t))[i]+P(t)[i] = eq[i] , where M is coefficient Matrix of second  derivatives , V22 is Vector of second derivaties , for example V22[1] = diff(a[1](t),t,t) , and  P(t) is the numeric part of equations ( they are pure number and do not contain any symbolic function ) and K(t).V(t) is the remaining part of equations such that : (K(t).V(t))[i] = eq[i] - (M.V22)[i] - P(t)[i]  , and V(t) are vector of a[i](t)'s which V(t)[1] = a[1](t) ,

i have used step by step time integration method (of an ebook which i have attachted that part of ebook here), when i set time step of solving process to h=0.01 , i can solve this system up to time one second or more, but when i choose h=0.001 or smaller, the answer diverges after 350 steps . i do not know whether the problem is in my ODS system, or maple can not handle this ?the answer about the time t=0.3 are the same in both steps, but after that, the one with stpe time h=0.001 diverges. my friend has solved this in mathematica without any problem, could any body help me ?! it is urgent for me to solve this problem,thnx everybody.


ebook.pdf  step_=_0.001.mw  step_=_0.01.mw 

I've been poking around with convolutions on Maple, and some weird behavior came up---if I let it compute the convolution of a piecewise function, then take the convolution of that, it comes out differently than if I enter a function from scratch as the middle step---file attached (PiecewiseProblem.mw).  I'm not really a Maple pro, so am I'm doing something crazy here?

Thanks!

I have two equations that are valid under the substitution sin <-> cos, so a simple way to generate the second equation is to replace all occurrences of sin with cos. But Maple gets the wrong answer when I do this, because of its built-in simplification. Here is an example. Z1 and Y1 shows the problem; Z2 and Y2 shows that my attempt to overcome the problem doesn't work.  Z3 doesn't work either, proving that the problem is internally generated by Maple because Maple insists on ordering variables in its own way, no matter how I write them.

________simplified example from Maple 15

restart;
Z1:=sin(-a*x+b);
Z2:='sin(-a*x+b)';
Z3:=sin(b-a*x);



                         -sin(a x - b)
                         sin(-a x + b)
                         -sin(a x - b)
Y1:=subs(sin=cos,Z1);
Y2:=subs(sin=cos,Z2);


                         -cos(a x - b)
                         -cos(a x - b)
 correct answer should be cos(-a*x+b) but the calculated results are off by a minus sign.

Ans1:=evalf(subs(a=1,b=2,x=3,[Y1,Y2,cos(-a*x+b)]));
          [-0.5403023059, -0.5403023059, 0.5403023059]

Question: How do I override Maple's desire to stick the "-" sign outside the sin function?

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