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how to calculate complex integration along a closed curve.

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Jibrail Ali
Jibrail Ali on 8 Aug 2019
Commented: Jibrail Ali on 8 Aug 2019
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.

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Jibrail Ali
Jibrail Ali on 8 Aug 2019
f(z) is complex values function with a domain containg the curve \gamma. I am talking about general function and general closed curve.

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Accepted Answer

Torsten
Torsten on 8 Aug 2019
Edited: Torsten on 8 Aug 2019
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

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