closed contour complex integral

hello.. please help me ∮(sinπz^2+cosπz^2)/((z-1)(z-2)) dz around z=2

answer this integral by using matlab ?

My attempt at the bottom but it was wrong .. please help me to detection the error ..thank u

fun=@(z)(sin(pi*z.^2)+cos(pi*z.^2))/((z-1)*(z-2));

>> g=@(theta)2*cos(theta)+1i*2*sin(theta);

>> gprime=@(theta)-2*sin(theta)+1i*2*cos(theta);

>> q1=quad(@(t) fun(g(t)).*gprime(t),0,2*pi)

??? Error using ==> mtimes

Inner matrix dimensions must agree.

[salah zetreni]

what did he mean by mtimes???? plz help me

Answer 1

[Mike Hosea]

MTIMES is matrix multiplication. The functional notation is mtimes(A,B), but the operator notation for matrix multiplication is A*B. So A*B assumes A and B have consistent matrix dimensions, i.e. size(A,2) must be the same as size(B,1), unless either is a scalar. You used .^ instead of ^, which is good. That's presumably because you meant element-wise powers of array inputs, but you did not always use .* instead of *, nor did you always use ./ instead of /. Go back and fix all of those operators.

The QUAD function (which is obsolete, BTW--use INTEGRAL or QUADGK instead), makes evaluations of your function in "batches", so your function must accept an array and return an array. It is not enough that it works only when you pass in a scalar. In other words f([1,2]) must work and return the same result as [f(1),f(2)].