Check the file: Questions.pdf

**Subject Mathematics Advanced Math**

Check the file: Questions.pdf

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function solutions()

clear all

close all

disp('--------------Problem 1-----------------')

problem1=true;

if (problem1)

N=100;T=2;

t=linspace(-3*T/2,3*T/2,3*N);

plot(t,[-1/2+(t(1:N)+T).^2,-1/2+t(N+1:2*N).^2,-1/2+(t(2*N+1:3*N)-T).^2],'b');

xlabel('t')

ylabel('y=f(t)')

hold on

coeff_for_pi4=rat(7/60/8-1/36/8)

syms x

c(1)=1/2*int(x^2-1/2,x,-1,1);

c(2)=1/2*int(exp(-i*pi*x)*(x^2-1/2),x,-1,1);

c(3)=1/2*int(exp(-i*2*pi*x)*(x^2-1/2),x,-1,1);

Nmin=ceil((5/100*7/60*3*pi^4/8)^(-1/3))

S2=c(1)+2*c(2)*cos(pi*t)+2*c(3)*cos(2*pi*t);

plot(t,S2,'r')

legend('function f','Fourier approximation with 2 terms')

hold off

error=x^2-1/2-(c(1)+2*c(2)*cos(pi*x)+2*c(3)*cos(2*pi*x));

errorenergy=int(error^2,x,-1,1);...

clear all

close all

disp('--------------Problem 1-----------------')

problem1=true;

if (problem1)

N=100;T=2;

t=linspace(-3*T/2,3*T/2,3*N);

plot(t,[-1/2+(t(1:N)+T).^2,-1/2+t(N+1:2*N).^2,-1/2+(t(2*N+1:3*N)-T).^2],'b');

xlabel('t')

ylabel('y=f(t)')

hold on

coeff_for_pi4=rat(7/60/8-1/36/8)

syms x

c(1)=1/2*int(x^2-1/2,x,-1,1);

c(2)=1/2*int(exp(-i*pi*x)*(x^2-1/2),x,-1,1);

c(3)=1/2*int(exp(-i*2*pi*x)*(x^2-1/2),x,-1,1);

Nmin=ceil((5/100*7/60*3*pi^4/8)^(-1/3))

S2=c(1)+2*c(2)*cos(pi*t)+2*c(3)*cos(2*pi*t);

plot(t,S2,'r')

legend('function f','Fourier approximation with 2 terms')

hold off

error=x^2-1/2-(c(1)+2*c(2)*cos(pi*x)+2*c(3)*cos(2*pi*x));

errorenergy=int(error^2,x,-1,1);...

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