t = linspace(0,2*pi,100);  % Parameter "t"

r = 1;         % Radius of circle
x0 = 2;        % X-center
y0 = 3;        % Y-center

x = x0 + r*cos(t);
y = y0 + r*sin(t);

plot(x,y, 'r','LineWidth',2)

axis equal
grid on

x = linspace(-2,2,1e3);

fx = sin(x);  % Curve 1
gx = x.^2;    % Curve 2

% Find intersections
x1 = fzero('sin(x)-x.^2',1);
y1 = sin(x1);
x2 = fzero('sin(x)-x.^2',0);
y2 = sin(x2);

% Plot
plot(x, fx, x, gx, 'g--','LineWidth',2)
hold on
plot([x1,x2], [y1,y2], 'ro','MarkerSize',10,'LineWidth',2)
grid on

x = linspace(0,10,1000);
y1 = sin(5*x);

yyaxis left
plot(x,y1,'color',[0 0.5 0])

xlabel('x','fontsize', 20);
ylabel('y_1','fontsize',20);

y2 = 100*exp(-x/10).*sin(x);
yyaxis right
plot(x,y2, 'LineWidth',2)

ylabel('y_2','fontsize',20);

A = [5, 3,-2;
     3,-2, 5;
     2, 6, 7];
 b = [11;30;53];

 X1 = A^-1*b % method 1

 X2 = A \ b  % method 2

 
fx = @(x) x.^3- exp(-x/2).*sin(2*x);


x1 = fzero(fx, 0)
x2 = fzero(fx,-1)
x3 = fzero(fx, 1)

xn = randn(1,1e4); % Normal  Distribution
x  = rand(1,1e4);  % Uniform Distribution

subplot(211); 
histogram(xn, 30); 
title('Normal','color','r');

subplot(212); 
histogram(x, 30);  
title('Uniform','color',[0,0.5,0]);

syms y(x) x

D2y = diff(y,2);   % y''
Dy  = diff(y);     % y'

eq = D2y + y + x == 0; % ODE

cond = [y(0) == 1, Dy(5)==-2];

Y = dsolve(eq, cond);

fplot(Y,[0,5],'r','LineWidth',3);

[x, y] = meshgrid(-2:.2:2);
z = x.*exp(-x.^2-y.^2);

subplot(211); 
surf(x, y, z); view([-20, 30])
title('3D view')

subplot(212); 
contour(x, y, z, 20);
title('Contour view')
colorbar

[x, y] = meshgrid(-3:.2:1, -1.5:.2:3);
z = y.^2 - x.^2 + x;

contour(x, y, z, 10)

[u, v] = gradient(z, 0.1);
hold on
quiver(x,y, u, v)

xspan = 0:.1:5;
y0 = 3;

[xx,yy] = ode45(@ODE_eq, xspan, y0);

plot(xx, yy, 'm','LineWidth',3)


function Dy = ODE_eq(x,y)
    Dy(1) = -sin(y.*x);
end