x = [0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1];

x = 0 : 0.1 : 1;

for i = 1:11
    x(i) = 0.1 * (i-1);
end
x;

for i = 0:10
    x(i+1) = 0.1 * i;
end
x;

x = 0 : 0.01 : 1;

y = sin(2*pi*x);

figure(1);
plot(x,y);
title('function y = sin(2*\pi*x)');
xlabel('x (in radians)');
ylabel('y');

x = linspace(0, 1, 101);

xx = logspace(1, 2, 4);



figure(2)
x = linspace(0, 1, 200);
y1 = sin(2*pi*x);
y2 = cos(2*pi*x);
plot(x,y1,x,y2);





n = 200;
m = 4;
x = linspace(-2,2,n);
A = zeros(n,m);
for j = 1:m
    for k = 1:n
        A(k,j)=sin(j*x(k));
    end
end
figure(3);
hold on;
colr = 'bmgr';
for j = 1:m
    plot(x, A(:,j), colr(j));
end

figure(4);
vec = [2 3 5 7]';
y = A*vec;
plot(x,y,'b');

hold on;
yy = 2*sin(x) + 3*sin(2*x) + 5*sin(3*x) + 7*sin(4*x);
plot(x,y,'r');



x = [-1 0 2 3 5];
y = [ 1 2 4 8 6];
a = polyfit(x,y,length(x)-1);

xx = min(x)-1 : 0.1 : max(x)+1;
yy = polyval(a, xx);

figure(5);
plot(xx,yy);
hold on;
plot(x,y,'r*');