how to calculate complex integration along a closed curve.

Let I = \frac{1}{2pi i} \int_{gamma} f(z)dz. I have to find the numerical value of I with help of matlab. What is is the procedure (command )to evaluate I.

[darova]

What is f(z)?

[Jibrail Ali]

f(z) is complex values function with a domain containg the curve \gamma. I am talking about general function and general closed curve.

Answer 1

[Torsten]

I = 1/(2*pi*1I) * integral_{t=0}^{t=T} f(z(t))*z'(t) dt

where z(t) is a parametrization of gamma.

The last integral can numerically be evaluated using MATLAB's "integral" function.

For an example, see

https://de.mathworks.com/help/matlab/math/complex-line-integrals.html