Example 1: To run, save the following code in a file called chap10:

function chap10 

% Problem 10.3.8
% This function computes and graphs the partial sums of 
% the Fourier series for f(x) on the interval [-1/2, 1/2]
% f(x) = 1/2 + x on [-1/2, 0]; f(x) = 1/2 - x on [0, 1/2]

	x = linspace(-0.5,0.5,100);    

	for i=1:100
		if x(i) <= 0 
			y(i) = 0.5 + x(i);
		%elseif x(i) <= 0 
			%y(i) = -1;
		else
			y(i) = 0.5 - x(i);
		end
	end

	for i=1:100
		S1(i) = 0.25;
		S2(i) = S1(i) +2/(pi)^2*cos(2*pi*x(i));
		S3(i) = S2(i) +2/((3*pi)^2)*cos(6*pi*x(i));   
	end

	plot(x,y,x,S1,'-',x,S2,'--',x,S3,'-.')
	legend('f(x)', 'S1', 'S2', 'S3')
	grid on

% end function


Example 2: To run, save the following code in a file called chap10_2:

function chap10_2 

% Problem 10.7.1
% This function computes and graphs the partial sums of 
% the Fourier series for f(x) on the interval [-pi, pi]
% f(x) = -1 on [-pi, 0]; f(x) = 1 on [0, pi]

	x = linspace(-pi,pi,100);    

	for i=1:100
		if x(i) <= 0 
			y(i) = -1;	 
		else
			% x(i) <= 0
			y(i) = 1;
		end
	end

	for i=1:100
		S1(i) = 4/pi*sin(x(i));
		S2(i) = S1(i) + 4/(3*pi)*sin(3*x(i));
		S3(i) = S2(i) + 4/(5*pi)*sin(5*x(i));   
	end

	plot(x,y,x,S1,'-',x,S2,'--',x,S3,'-.')
	legend('f(x)', 'S1', 'S2', 'S3')
	grid on

% end function