My Math Forum  

Go Back   My Math Forum > College Math Forum > Complex Analysis

Complex Analysis Complex Analysis Math Forum

LinkBack Thread Tools Display Modes
November 7th, 2012, 08:23 AM   #1
Joined: Sep 2012

Posts: 29
Thanks: 0

Positively oriented circle...


Find ?_c_1(0) of (e^z + cosz)z^-1 dz

I know it should be 4pi(i)
Juliayaho is offline  
November 7th, 2012, 08:25 AM   #2
Joined: Sep 2012

Posts: 29
Thanks: 0

Re: Positively oriented circle...

actually is Find ?_c_1(0) of (e(z) + cos(z))z^-1 dz
Juliayaho is offline  
December 4th, 2012, 08:14 AM   #3
Math Team
Joined: Sep 2007

Posts: 2,409
Thanks: 6

Re: Positively oriented circle...

The integral around a closed path (in this case a circle), is equal to times the sum of the residues at each pole of the integrand inside the circle. Here, everything is analytic except for that so the only pole is at z= 0 and that is a pole of order 1. I would expand as a Taylor's series around z= 0 and multiply each term by 1/z to get the Laurent series for the entire integrand. The residue is the coefficient of in the Laurent series.

Or you can do it directly. I presume that by "C_1(0)" is the unit circle with center at z= 0. A standard parameterization for the circle is so we can write the integral .
That looks difficult to me so I would use the "residue" method!
HallsofIvy is offline  
December 6th, 2012, 12:14 AM   #4
Math Team
Joined: Nov 2010
From: Greece, Thessaloniki

Posts: 1,990
Thanks: 133

Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus
Re: Positively oriented circle...

[color=#000000]I guess you mean,

ZardoZ is offline  

  My Math Forum > College Math Forum > Complex Analysis

circle, oriented, positively

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Similarity and possibly algebra oriented geometry question. jadry Geometry 13 November 4th, 2017 03:03 AM
Area enclosed by a semi-circle and a quarter circle yeoky Algebra 4 May 3rd, 2014 01:06 AM
Object-Oriented Formal Specification - Help please GamerGirl Applied Math 0 May 4th, 2011 01:58 AM
Object oriented and trees question Nivg Computer Science 0 May 3rd, 2010 05:21 PM
Foci oriented ellipse collision detection James_Kidder Computer Science 1 July 31st, 2007 04:21 PM

Copyright © 2019 My Math Forum. All rights reserved.