An Introduction To Complex Analysis For Engineers.pdf

An In tro duction plex Analysis for
Engineers
Mic hael D. Alder
June 3, 1997
1
Preface
These notes are in tended to be of use to Third y ear Electrical and Elec-
tronic Engineers at the Univ ersit yofW estern ing to grips with
Complex F unction Theory .
There are man y text b o oks for just this purp ose, and I ha v e insucien t time
to write a text b o ok, so this is not a substitute for, sa y , Matthews and Ho w-
ell'plex A nalysis for Mathematics and Engine ering ,[1 ], but p erhaps a
complemen t to it. A t the same time, kno wing ho w reluctan t studen ts are to
use a textb o ok (except as a talisman to w ard o evil) I ha v e tried to mak e
these notes sucien t, in that a studen t who reads them, understands them,
and do es the exercises in them, will be able to use the concepts and tec h-
niques in later y ears. It will also get the studen fortably through the
examination. The shortness of the course, 20 lectures, for co v plex
Analysis, either presupp oses genius ( 90% p erspiration) on the part of the
studen ts or material skipp ed. These notes are in tended to ll in some of the
gaps that will inevitably ur in lectures. It is a source of some disapp oin t-
men t to me that I can co v er so little of what is a b eautiful sub ject, ric h in
applications and connections with other areas of mathematics. This is, then,
a sort of sampler, and only touc hes the elemen ts.
St yles of Mathematical presen tation c hange o v er the y ears, and what w as
deemed acceptable rigour b y Euler and Gauss fails to k eep mo dern purists
con ten t. McLac hlan, [2], clearly smarted under the criticisms of his presen-
tation, and he go es to some trouble to explain in later editions that the b o ok
is in tended for a dieren t audience from the purists who damned him. My
exp erience leads me to feel that the need for rigour has b een dev elop ed to
the p oin t where the in tuitiv e and geometric has b een stun ted. Both ha v e a
part in mathema