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I want to do a step by step computation for obtaining the coefficents of the sine fourier series expansion of f(x)=x over the interval [-L,L]. The steps are as follows:

1-write the fourier expansion as: Sum(A[n]*sin(n*pi*x/L),n=1..N)
2-multiply the series by: sin(m*pi*x/L)
3-integrate the series over the interval [-L,L]
3-using the orthogonality properties of the set {sin(n*pi*x/L} compute the A[n].

I can't do these steps since I have problem with the series manipulations in maple!
Can any one suggest a way from begining to the end?

Thanks. :)
Below shows what I did in Maple 17.

Help Please! :)
As it is seen in the picture, I can not integrate the power series. In contrast, the differentiation works!
what is wrong?

I have a table of data arranged in the following columns: Year, Jan, Feb, Mar,..,Dec in Excel or csv

I would like to import this data into a time series in Maple so I can plot the result.

What is the simplest way of doing this?



I need you to help me in writting procedure with input "r" ( order of derivative) and some coefficients seq(alpha[i],i=1..N).  My code work very well, need only put all the element in procedure with output The Taylor series obtained in last line of my code and the order of error.  I want the procedure return the coefficients beta used in the series and the order of Error  and the coefficients beta[i]

May thinks.


I will not modify my previous question: only I add this remark. I tried to write these lines of procedure.

I need only to add( if the procedure is true) these lines in my procedure.  These lines gives the degree of error computed in the code, but when I put these lines in the codes, there is an error. Thanks for your help.

Degree := degree(Error,stepsize);
    if (showorder) then:
       print(cat(`This stencil is of order `,Degree));
    if (showerror) then:
       print(cat(`This leading order term in the error is `,Error));
    convert(D[r$n](f)(vars) = stencil,diff);




Hi all.

Assume that we have partitioned [0,a], into N equidistant subintervals and in each subinterval we have M sets of poly nomials of the following form:

where Tm(t)=tm( namely Taylor Series) and tf is a(final point)
for Example with N=4, M=3 we have:

now we want to approximate a function, asy f(t), in this interval with following form:

How can we do this with maple????

how can we find the ci's?????

Thanks a lot

Mahmood   Dadkhah

Ph.D Candidate

Applied Mathematics Department


Maybe someone can give me a nice answer without Maple.

I am given a fourier series:
ln|cosx|=Co - sum( (-1)^k/k * cos2kx,k=1..infinity)
and am asked what this tells me about the chevychev series for ln(u).




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.





Maybe a good question.

Write  f(x)=ln(abs(cos(x)))   with infinite serie cosine(2*n*x).

Thank for your remark.




I have this expression on image below and I would like to do multi taylor in these variables. The maple says that the expansion is not possible to do. Does somebody know where the problem could be ? Thank you very much for help.


Taylor series:



how maple calculate exp(x) with e.g. 100000 decimal numbers

a divsion of the series x^k/k! with e.g. 1/25000!/25001 lasts longer than the exp(1.xx) calculation


is there a faster way to calculate exp(x) than with the x^k/k! series











Dear All;

Happy, to discuss with you these lines, and thank you to help me.

My goal is:


ode := D(y)(x) = f(x,y(x));
In this expression, is assumed to be a known function of the independant variable
 and the function that we are trying to solve for
.  The simplest numerical stencils to solve this equation will give us an approximation to
 at some point
                                  x = X + h
 given some knowledge of
                                    x = X
.  All of these stencils are based on the Taylor series approximation for
                                    x = X
 to linear order:
eq1 := y(x) = series(y(x),x=X,3);
eq2 := h = x - X;
eq3 := subs(isolate(eq2,x),eq1);
Now, we can remove the first derivative of y
 by making use of the differential equation:
eq4 := subs(x=X,ode);
eq5 := subs(eq4,eq3);

Now we must compute the same for y(x-h)  and then make.  How can I do this please

Simple question...

February 27 2014 sarra 170

Dear All,

I have a simple question I try to find the Fourrier Series of:


with maple or without maple.




Dear all;

Special thanks for all the member who help me in Maple.

My last question is:

Write a maple procedure that solves for y(1) in the initial value problem y'(x)=f(y), y(0)=1

using a Numerical stencil based on the n^{th] order taylor series expansion of y.

The procedure arguments include an arbitrary function f, an integrer n, representing the accuracy of the taylor series expansion, and N representing the number of steps between x=0 and x=1.




Is there a simple way, given a functional equation satisfied by a formal power series, to obtain the explicit form (the Taylor expansion) of this formal power series? For example, my input is "f(x)=1+x*f2(x)", and I want to have as the output: "1+x+2x2+5x3+O(x4)".

Many thanks!

I'm attempting to plot several solutions of this differential equation (I have uploaded my worksheet). I have used this series of commands before without issue, but for some reason I keep getting the error message: "Error, (in plot) incorrect first argument" ect.. Does anyone have any insight into what might be going wrong? Thank you.


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