# Question:Fourier series and partial sums of numerical valued functions

## Question:Fourier series and partial sums of numerical valued functions

Maple 13

How to change this general form to solve :

How to calculate with Maple Fourier coefficients on some numerical valued functions and how to calculate and plot the 3 partial sums :

Function B : on the interval [-phi, phi]

f(x)= NUMERICAL (x – phi/2) + NUMERICAL (x+phi/2)

Function C : on the interval [-phi, phi]

f(x) =  NUMERICAL (x+phi/2)

Fourier series

Calculate and plot serial part sums for Fourier series given by function g1 and g2

on the interval for g1: [- ,0] and for g2 : [0, ].

Fouriercoefficients:

> c:=(n,g1,g2)->(2*Pi)^(-1)*int(g1*exp(-I*n*x), x=-Pi..0)+(2*Pi)^(-1)*int(g2*exp(-I*n*x), x=0..Pi);

Partsums :

> s:=(n,g1,g2,x)->sum(c(k,g1,g2)*exp(I*k*x)+c(-k,g1,g2)*exp(-I*k*x),k=1..n)+c(0,g1,g2);

Plot of function :

> with(plots):PL:=(g1,g2)->plot(piecewise(x<0, g1, x>0,g2),x=-Pi..Pi, thickness=2, color=red, discont=true);

Plot of function and part sums and function and the n'de part sums :

> PLL:=(g1,g2,n)->display(PL(g1,g2),plot(s(n,g1,g2,x), x=-Pi..Pi, color=black, thickness=2), title=s[n], titlefont=[TIMES,BOLD,18]);

How to change this general form to solve :

How to calculate with Maple Fourier coefficients on some numerical valued functions and how to calculate and plot the 3 partial sums :

Concrete solutions is needed

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