%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   Math 275: This is program 
%   matlab_problems_examples.m to for Matlab project
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

clear all

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   Section 13.1 # 30
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

t=0.1:1e-3:5;

x=t.^2; y=log(t); z=t;

figure(1); clf(1)
set(gca,'FontSize',12); set(gca,'box','on')

plot3(x,y,z)
xlabel('x')
ylabel('y')
zlabel('z')
title('Section 13.1 # 30: graph of curve x=t^2, y=log(t), z=t')
grid on

print -depsc2 problem_13_1_30.eps  

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   Section 13.1 # 33
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

t=-10:1e-3:10;

figure(2); clf(2)
set(gca,'FontSize',12); set(gca,'box','on')

x=(1+cos(16*t)).*cos(t); 
y=(1+cos(16*t)).*sin(t); 
z=(1+cos(16*t));

subplot(2,2,1)

plot3(x,y,z,'Linewidth',1)
xlabel('x')
ylabel('y')
zlabel('z')
title('Section 13.1 # 33: curve')
grid on

t=-10:1e-1:10;

subplot(2,2,2)
x=t; y=t;
[X,Y]=meshgrid(x,y);
f=inline('sqrt(x.^2+y.^2)','x','y');
mesh(X,Y,f(X,Y))
%xlim([-2 2])
%ylim([-2 2])
%zlim([0 2])
title('Cone z=sqrt(x^2+y^2)')

print -depsc2 problem_13_1_33.eps  

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   Section 13.1 # 40
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
figure(3); clf(3)
set(gca,'FontSize',12); set(gca,'box','on')

subplot(2,2,1)
x=-2:1e-2:2;
z=0:1e-2:3;
f=inline('x.^2','x','z');
[X3,Z3]=meshgrid(x,z);
mesh(X3,f(X3,Z3),Z3)
hold on

subplot(2,2,2)
mesh(X3,f(X3,Z3),Z3)
hold on

subplot(2,2,1)

x=-2:1e-2:2;
y=-sqrt(2):1e-2:sqrt(2);
f=inline('sqrt(4-x.^2/4-y.^2)','x','y');
[X2,Y2]=meshgrid(x,y);
mesh(X2,Y2,f(X2,Y2))

xlabel('x')
ylabel('y')
zlabel('z')
title('Section 13.1: # 40')

x=-1:1e-2:1;
y=x.^2;
z=sqrt(4-x.^4-x.^2/4);
plot3(x,y,z,'rd','Linewidth',5)

subplot(2,2,2)
plot3(x,y,z,'r','Linewidth',4)

print -depsc2 problem_13_1_40.eps  

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   Section 13.2 # 27
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
figure(4); clf(4)
set(gca,'FontSize',12); set(gca,'box','on')

t=-3:1e-2:3;

x1=t; y1=exp(-t); z1=2*t-t.^2;
x2=t; y2=1-t; z2=2*t;

plot3(x1,y1,z1,'b','Linewidth',2)
hold on
plot3(x2,y2,z2,'r','Linewidth',2)
grid on

legend('curve','tangent line')
title('Section 13.2: # 27: curve and its tangent line')

print -depsc2 problem_13_2_27.eps  

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   Section 13.3 # 35
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

figure(5); clf(5)
set(gca,'FontSize',12); set(gca,'box','on')

x=-5:1e-2:5;
y=x.^(-2);
kappa=6*x.^(-4)./((1+4*x.^(-6)).^(3/2));

plot(x,y,'b','Linewidth',2)
hold on
plot(x,kappa,'r','Linewidth',2)
ylim([0 3])
legend('y(x)','\kappa(x)')
title('Section 13.3: # 35')

print -depsc2 problem_13_3_35.eps

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   Section 14.1 # 51, 52
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

figure(6); clf(6)
set(gca,'FontSize',12); set(gca,'box','on')

x=-2:1e-2:2;
y=x;
[X,Y]=meshgrid(x,y);
f=inline('exp(-x.^2)+exp(-2*y.^2)','x','y');
g=inline('(1-3*x.^2+y.^2).*exp(1-x.^2-y.^2)','x','y');

subplot(2,2,1)
mesh(X,Y,f(X,Y))
xlabel('x')
ylabel('y')
zlabel('z')
title('Section 14.1 # 51: surface plot')

subplot(2,2,2)
contour(X,Y,f(X,Y))
xlabel('x')
ylabel('y')
zlabel('z')
title('Section 14.1 # 51: contour plot')

subplot(2,2,3)
mesh(X,Y,g(X,Y))
xlabel('x')
ylabel('y')
zlabel('z')
title('Section 14.1 # 52: surface plot')

subplot(2,2,4)
contour(X,Y,g(X,Y))
xlabel('x')
ylabel('y')
zlabel('z')
title('Section 14.1 # 52: contour plot')

print -depsc2 problem_14_1_51_52.eps

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   Section 15.1 # 70
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

figure(7); clf(7)
set(gca,'FontSize',12); set(gca,'box','on')

x=-1:1e-2:1;
y=x;
[X,Y]=meshgrid(x,y);
f=inline('(x.*y)./(x.^2+y.^2)','x','y');

subplot(2,2,1)
mesh(X,Y,f(X,Y))
xlabel('x')
ylabel('y')
zlabel('z')
title('Section 14.1: # 70: close to the origin')

subplot(2,2,2)
x=-50:1e-1:50;
y=x;
[X,Y]=meshgrid(x,y);
mesh(X,Y,f(X,Y))
xlabel('x')
ylabel('y')
zlabel('z')
title('Section 14.1: # 70: away from the origin')

print -depsc2 problem_14_1_70.eps

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   Section 14.4 # 8
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

figure(8); clf(8)
set(gca,'FontSize',12); set(gca,'box','on')

x=-1:1e-2:1;
y=x;
[X,Y]=meshgrid(x,y);
f=inline('atan(x.*y.^2)','x','y');      % surface

subplot(2,2,1)
mesh(X,Y,f(X,Y))
hold on
g=inline('pi/4+(x-1)/2+y-1','x','y');   % tangent plane
mesh(X,Y,g(X,Y))
xlabel('x')
ylabel('y')
zlabel('z')
title('Section 14.4: # 8')

x2=0.9:1e-3:1.1;
y2=x2;
[X2,Y2]=meshgrid(x2,y2);

subplot(2,2,2)
mesh(X2,Y2,f(X2,Y2))
hold on
mesh(X2,Y2,g(X2,Y2))

xlabel('x')
ylabel('y')
zlabel('z')
title('Section 14.4: # 8: zoom in')
xlim([0.9 1.1])
ylim([0.9 1.1])

print -depsc2 problem_14_4_8.eps