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complex closed contour integral

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salah zetreni
salah zetreni 2015-3-12
评论： Torsten 2022-4-10
plz explain to me how can I use matlab programe for solution of complex contour integral :
example : find ∮((z+1)dz)/(z^3-2z^2 ) around z-2=1 where 1 is Radius of the circle ?
when I solution it Manually the result was equal:-π*i

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Torsten
Torsten 2015-3-12
fun=@(z)(z+1)/(z^3-2*z^2);
g=@(theta)2+cos(theta)+1i*sin(theta);
gprime=@(theta)-sin(theta)+1i*cos(theta);
q1 = integral(@(t) fun(g(t)).*gprime(t),0,2*pi)
Best wishes
Torsten.
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salah zetreni
salah zetreni 2015-3-13
for the same problem he asked me to find a value of integration around z-1-2J=2 by using matlab ... plz see my answer and help me on detect the error :
fun=@(z)(z+1)/(z.^3-2*z.^2);
g=@(theta)1+2*i+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)
when I do run ,the matlab show me :
Warning: Maximum function count exceeded; singularity likely.
In quad at 106
q1 =
-0.0256 + 0.0013i

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Torsten
Torsten 2015-3-13
What about
fun=@(z)(z+1)./(z.^3-2*z.^2);
g=@(theta)(1+2*cos(theta))+1i*(2+2*sin(theta));
gprime=@(theta)-2*sin(theta)+1i*2*cos(theta);
q1=quad(@(t) fun(g(t)).*gprime(t),0,2*pi)
Best wishes
Torsten.
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Torsten
Torsten 2022-4-10
What graph ? The result is the value of the contour integral - thus a single number.

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