SET 28 | 10 Solved Problems on Contour Integrals, Branch Cut, Branch Point etc| Complex Analysis

#Complex_Analysis #SET_28 #PhysicsHub
It consists of problems from “COMPLEX ANALYSIS” Section on the following topics:
Cauchy Riemann condition, Contour Integrals, Branch Point and Branch Cut etc.
Complex analysis is the study of complex numbers together with their derivatives, manipulation, and other properties. Complex analysis is an extremely powerful tool with an unexpectedly large number of practical applications to the solution of physical problems. Contour integration, for example, provides a method of computing difficult integrals by investigating the singularities of the function in regions of the complex plane near and between the limits of integration.
The key result in complex analysis is the Cauchy integral theorem, which is the reason that single-variable complex analysis has so many nice results. A single example of the unexpected power of complex analysis is Picard's great theorem, which states that an analytic function assumes every complex number, with possibly one exception, infinitely often in any neighborhood of an essential singularity!
A fundamental result of complex analysis is the Cauchy-Riemann equations, which give the conditions a function must satisfy in order for a complex generalization of the derivative, the so-called complex derivative, to exist. When the complex derivative is defined "everywhere," the function is said to be analytic.

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[physicshub]

Little correction in Q.3 : the contour is |z+1|=2

[physicshub]

Like the video if you want more such SET videos in future.

[physicshub]

It consists of problems from “COMPLEX ANALYSIS” Section on the following topics:
Cauchy Riemann condition, Contour Integrals, Branch Point and Branch Cut etc.
Complex analysis is the study of complex numbers together with their derivatives, manipulation, and other properties. Complex analysis is an extremely powerful tool with an unexpectedly large number of practical applications to the solution of physical problems. Contour integration, for example, provides a method of computing difficult integrals by investigating the singularities of the function in regions of the complex plane near and between the limits of integration.

[pardeeppanghal]

in 3rd sinhyper will have only odd power of z sir

[pragatidixit]

Where are set 1 and set 2 I didn't find them on your channel

[sudipmandal]

Sir, the figure corresponding to the question 3 is not correct as mod(z-1)=2 then it's origin must be at z=1

[PrankrishnaBorgohain]

I have one confusion. Q3, if z =0 is a pole, it is inside the circle. Why didn't we consider it to find the residue? Where am I wrong? I am puzzled. Pls help