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 T_{m}(t)=t^{m}( namely Taylor Series) and t_{f} 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 c_{i}'s?????

Thanks a lotMahmood Dadkhah

Ph.D Candidate

Applied Mathematics Department

Hi,

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).

Thanks

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.

Hello,

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.

Equation:

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

thanks

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 x and the function that we are trying to solve for y(x). The simplest numerical stencils to solve this equation will give us an approximation to y at some point x = X + h given some knowledge of y at x = X. All of these stencils are based on the Taylor series approximation for y(x) about 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

Dear All,

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

f(x)=x*e^{I*x}

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*f^{2}(x)", and I want to have as the output: "1+x+2x^{2}+5x^{3}+O(x^{4})".

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.

Download ass_1_#9.mw

ass_1_#9.mw

Hi, i need help. I'm currently working with Taylor and Maclaurin series in Maple. I can easily compute the sum by typing in fx :

taylor( (e^{x},x=0, 5) , and then I get the first 5 numbers of the series. But I would like Maple to write the series as a sum from n =0 to infinity fx. I can't figure out how to do it. Can it be done? Thanks for helping.

M5 :=series((1+1/(2*a^2)+(1/2)*b^2-1/(2*a))^a, a=0,3);

there is a variable b too

Can anyone help me to transform a system of ODE into a power series solution. The system of ODE is as follows:

diff(f(eta), eta, eta, eta)+(diff(f(eta), eta, eta))*f(eta)+1 - (diff(f(eta), eta))^2=0

f(eta)*(diff(theta(eta), eta))+(1/Pr)*diff(theta(eta), eta, eta)=0

where Pr is the prendtl no.

I have following expression:

y1:=t->1/(4*cosh(t)^2)

I:=int(y1(t)^2,t=-T/2..T/2)

Now I tried:

MultiSeries:-asympt(I,T,5)

for which I only get the highest order.

Can I increase the order in any way?

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