%K1
figure(1);
x=[1:0.1:10];
y=[1:0.1:10];
[X,Y]=meshgrid(x,y);
K1= X.^3./(X.^3.-cos(Y)./3);
surf(X,Y,K1);
hold on,
    xlabel('x');
    ylabel('y');
    zlabel('K(x,y)');
title('K1(x,y)');

%K2
figure(2);
[X,Y]=meshgrid(x,y);
K2= (cos(Y)./3)./(X.^3.+(cos(Y)./3));

surf(X,Y,K2);
hold on,
    xlabel('x');
    ylabel('y');
    zlabel('K(x,y)');
title('K2(x,y)');

%K3
figure(3);
[X,Y]=meshgrid(x,y);
K3= (cos(Y)./3)./(X.^3.+(cos(Y)./3));
surf(X,Y,K3);
hold on,
    xlabel('x');
    ylabel('y');
    zlabel('K(x,y)');
title('K3(x,y)');

%K4
figure(4);
[X,Y]=meshgrid(x,y);
surf(X,Y,K4);
hold on,
    xlabel('x');
    ylabel('y');
    zlabel('K(x,y)');
title('K4(x,y)');

%K5
figure(5);
[X,Y]=meshgrid(x,y);
K5= (sin(Y)./2)./(Y-(sin(Y)./2));
surf(X,Y,K5);
hold on,
    xlabel('x');
    ylabel('y');
    zlabel('K(x,y)');
title('K5(x,y)');

%K6
figure(6);
[X,Y] = meshgrid(1:10,1:10);
K6= 1*ones(length(Y),length(X));
surf(X,Y,K6)
hold on,
    xlabel('x');
    ylabel('y');
    zlabel('K(x,y)');
title('K6(x,y)');

%K7
figure(7);
[X,Y] = meshgrid(1:10,1:10);
K7= -1*ones(length(Y),length(X));
surf(X,Y,K7)
hold on,
    xlabel('x');
    ylabel('y');
    zlabel('K(x,y)');
title('K7(x,y)');

%K8
figure(8);
[X,Y] = meshgrid(1:10,1:10);
K8= 1*ones(length(Y),length(X));
surf(X,Y,K8)
hold on,
    xlabel('x');
    ylabel('y');
    zlabel('K(x,y)');
title('K8(x,y)');

%Tx
figure(9);
[X,Y]=meshgrid(x,y);
Tx= 3.*X.^3./(X.^3.+cos(Y)./3);
surf(X,Y,Tx);
hold on,
    xlabel('x');
    ylabel('y');
    zlabel('T(x,y)');
title('Tx(x,y)');

%Ty
figure(10);
[X,Y]=meshgrid(x,y);
Ty= (Y./(X.^3 + (cos(Y))./3) .* ((3.*X.^3 - 2).*cos(Y) - 6.*X.^3 + sin(Y).^2 - 2.*Y.*sin(Y)+ cos(Y).^2)./(6.*(Y - sin(Y)./2)));
surf(X,Y,Ty);
hold on,
    xlabel('x');
    ylabel('y');
    zlabel('T(x,y)');
title('Ty(x,y)');

%============================================ZADANIE 2============================================

rows=100;
columns=100;
matrix=zeros(100,100);
eps = 10.^(-13);

for x = 1: 0.1: 10
    for y = 1: 0.1: 10
        matrix(x,y)= abs(Tx) + abs(Ty) + abs(K1) + abs(K2) + abs(K3) + abs(K4)+ abs(K5) + abs(K6)+ abs(K7)+ abs(K8);
        %matrix(x,y)= abs(3.*x.^3./(x.^3 + ( cos(y)./3))) + abs(y./(x.^3 + (cos(y))./3) .* ((3.*x.^3 - 2).*cos(y) - 6.*x.^3 + sin(y).^2 - 2.*y.*sin(y)+ cos(y).^2)./(6.*(y - sin(y)./2))) + abs(x.^3./(x.^3 + ( cos(y)./3))) + 2.*abs((cos(y)./3)./(x.^3 + cos(y)./3)) + 2.*abs((sin(y)./2)./(y - sin(y)./2)) + abs(1)+ abs(- 1) + abs(1);
        matrix(x,y)= matrix(x,y)*eps;
    end
end

disp(matrix)
disp('max value:')
disp(max(matrix(:)))