meaning of the complex residue


by skook
Tags: complex, residue
skook
skook is offline
#1
Oct23-09, 09:22 AM
P: 15
Just spent the last few months working on an undergrad course in complex analysis and have a couple of things that aren't clear to me yet. One of them is the meanings of the residue of a complex function. I understand how to find it from the Laurent series and using a couple of other rules and I understand how it works with the residue theorem. But I still feel like there is a deeper interpretation out there waiting for me.......perhaps it's something geometrical?

Grateful for any enlightened comment.
:-)
Phys.Org News Partner Science news on Phys.org
SensaBubble: It's a bubble, but not as we know it (w/ video)
The hemihelix: Scientists discover a new shape using rubber bands (w/ video)
Microbes provide insights into evolution of human language
lurflurf
lurflurf is offline
#2
Oct23-09, 02:47 PM
HW Helper
P: 2,168
There are several equivalent ways to think about it. One is as the 1/(z-a) term of the laurent expansion. Another is the inner product of f with 1/(z-a). One could also think of it as the amount of (order 1) infinity at the point a.
skook
skook is offline
#3
Oct24-09, 02:52 PM
P: 15
Thanks for that........the nearest I can get is that it could be 1/(2*pi) of a Dirac delta function with a pi/2 twist.
:-)


Register to reply

Related Discussions
Physical Meaning of Complex Numbers General Math 14
Complex Integration / Residue Problems Calculus & Beyond Homework 6
Meaning of a complex polarizability? Advanced Physics Homework 5
Complex residue integral Calculus & Beyond Homework 1
what exactly is a residue - what are its applications[complex analysis] Calculus 2