Check the file: Questions.pdf

**Subject Mathematics MATLAB for Mathematics**

Check the file: Questions.pdf

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%problem 1.

f1=@(x) cos(2*x(1))-cos(2*x(2))-0.4;

f2=@(x) 2*(x(2)-x(1))+sin(2*x(2))-sin(2*x(1))-1.2;

f=@(x) [f1(x);f2(x)];

%Jacobian

df=@(x) [-2*sin(2*x(1)) 2*sin(2*x(2)); (-2-2*cos(2*x(1))) (2+2*cos(2*x(2)))];

%start point

x=[1;0];

%tolerance

tol=1.e-12;

done=0;

iteration=0;

while done==0 && iteration < 10

iteration=iteration+1;

xnew=x-inv(df(x))*f(x); %newton step

if norm(xnew-x)<tol

done=1;

end

x=xnew;

end...

f1=@(x) cos(2*x(1))-cos(2*x(2))-0.4;

f2=@(x) 2*(x(2)-x(1))+sin(2*x(2))-sin(2*x(1))-1.2;

f=@(x) [f1(x);f2(x)];

%Jacobian

df=@(x) [-2*sin(2*x(1)) 2*sin(2*x(2)); (-2-2*cos(2*x(1))) (2+2*cos(2*x(2)))];

%start point

x=[1;0];

%tolerance

tol=1.e-12;

done=0;

iteration=0;

while done==0 && iteration < 10

iteration=iteration+1;

xnew=x-inv(df(x))*f(x); %newton step

if norm(xnew-x)<tol

done=1;

end

x=xnew;

end...

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