Complex Analysis: Use of Cauchy

In summary, the conversation discusses problem 2 on page 39 of the problems/solutions linked in the given link. The question is about how equation "(31)" of the solution was obtained, specifically the second term of the right-hand side. The person asking the question initially did not understand where the second term came from, but later figured it out.
  • #1
nateHI
146
4
http://www.math.hawaii.edu/~williamdemeo/Analysis-href.pdf

Please look at problem 2 on page 39 of the problems/solutions linked above.

I know I'm going to kick myself when someone explains this to me but how was equation "(31)" of the solution obtained? The first term of the RHS of (31) is clear but I'm not sure where the 2nd term came from.
 
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  • #2
nateHI said:
http://www.math.hawaii.edu/~williamdemeo/Analysis-href.pdf

Please look at problem 2 on page 39 of the problems/solutions linked above.

I know I'm going to kick myself when someone explains this to me but how was equation "(31)" of the solution obtained? The first term of the RHS of (31) is clear but I'm not sure where the 2nd term came from.

Nevermind I figured it out.
 

FAQ: Complex Analysis: Use of Cauchy

What is Cauchy's theorem in complex analysis?

Cauchy's theorem states that if a function is analytic in a simply connected domain D, then the line integral of that function around any closed path in D is equal to zero. In other words, the integral of an analytic function over a closed path depends only on the endpoints of the path, not the path itself.

How is Cauchy's theorem used in complex analysis?

Cauchy's theorem is an important tool in complex analysis that allows us to evaluate complex integrals and solve problems involving analytic functions. It is used to prove many fundamental theorems in complex analysis, such as Cauchy's integral formula and the Cauchy-Riemann equations.

What is the significance of Cauchy's integral formula?

Cauchy's integral formula is a powerful result in complex analysis that states that the value of a function at any point inside a closed contour can be calculated by integrating the function over the contour. This formula is essential in calculating complex integrals and solving problems in complex analysis.

What is the Cauchy integral theorem?

The Cauchy integral theorem is another important result in complex analysis that states that if two closed contours have the same endpoints, and a function is analytic inside and on the two contours, then the line integrals of the function over the two contours are equal. This theorem is closely related to Cauchy's integral formula and is used to prove it.

What are some applications of Cauchy's theorem in complex analysis?

Cauchy's theorem has many applications in complex analysis, including solving problems involving analytic functions, evaluating complex integrals, and proving other important theorems. It also has applications in other fields such as physics, engineering, and economics, where complex functions are used to model real-world phenomena.

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