An Introduction to Complex Analysis for Engineers - M. Adler
These notes are intended to be of use to Third year Electrical and Elec-tronic Engineers at the UniversityofWestern Australia coming to grips with
Complex Function Theory.
There are many text b o oks for just this purp ose, and I have insu cient time
to write a text b o ok, so this is not a substitute for, say, Matthews and How-ell's Complex Analysis for Mathematics and Engineering,[1], but p erhaps a
complement to it. At the same time, knowing how reluctant students are to
use a textb o ok (except as a talisman to ward o evil) I have tried to make
these notes su cient, in that a student who reads them, understands them,
and do es the exercises in them, will be able to use the concepts and tech-niques in later years. It will also get the student comfortably through the
examination. The shortness of the course, 20 lectures, for covering Complex
Analysis, either presupp oses genius ( 90% p erspiration) on the part of the
students or material skipp ed. These notes are intended to ll in some of the
gaps that will inevitably o ccur in lectures. It is a source of some disapp oint-ment to me that I can cover so little of what is a b eautiful sub ject, rich in
applications and connections with other areas of mathematics. This is, then,
a sort of sampler, and only touches the elements.
Styles of Mathematical presentation change over the years, and what was
deemed acceptable rigour by Euler and Gauss fails to keep mo dern purists
content. McLachlan, [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 intended for a di erent audience from the purists who damned him. My
exp erience leads me to feel that the need for rigour has b een develop ed to
the p oint where the intuitive and geometric has b een stunted. Both have a
part in mathematics, which grows out of the con
ict between them. But it
seems to me more imp ortant to p enetrate to the ideas in a sloppy, scru y
but serviceable way, than to reduce a sub ject to predicate calculus and omit
the whole reason for studying it. There is no known means of p ersuading a
hardheaded engineer that a sub ject merits his time and energy when it has
b een turned into an elab orate game. He, or increasingly she, wants to see two
elements at an early stage: pro cedures for solving problems which make a
di erence and concepts which organise the pro cedures into something intelli-gible. Carried to excess this leads to avoidance of abstraction and consequent loss of power later; there is a good reason for the purist's desire for rigour.
But it asks to o much of a third year student to fo cus on the underlying logic
and omit the geometry.
I have delib erately erred in the opp osite direction. It is easy enough for the
student with a taste for rigour to clarify the ideas by consulting other b o oks,
and to wind up as a logician if that is his choice. But it is hard to nd in
the literature any explicit commitment to getting the student to draw lots
of pictures. It used to be taken for granted that a student would do that
sort of thing, but now that the scho ol syllabus has had Euclid expunged, the
undergraduates cannot b e exp ected to see drawing pictures or visualising sur-faces as a natural prelude to calculation. There isascho ol of thought which
considers geometric visualisation as immoral; and another which sanctions it
only if done in private (and wash your hands b efore and afterwards). Tomy
mind this imp oses sterility, and constitutes an attempt by the bureaucrat to
strangle the artist. 1 While I do not want to imp ose my informal images on
anybody, if no mention is made of informal, intuitive ideas, many students
never realise that there are any. All the good mathematicians I knowhavea
rich supply of informal mo dels which they use to think ab out mathematics,
and it were as well to show students how this may b e done. Since this seems
to be the resp ect in which most of the text b o oks are weakest, I have p erhaps
gone to o far in the other direction, but then, I do not o er this as a text
book. More of an antidote to some of the others.
- pages: 178 pages
- Publisher:Michael D. Alder (June 3, 1997)
- Language: English
These notes are intended to be of use to Third year Electrical and Elec-tronic Engineers at the UniversityofWestern Australia coming to grips with
Complex Function Theory.
There are many text b o oks for just this purp ose, and I have insu cient time
to write a text b o ok, so this is not a substitute for, say, Matthews and How-ell's Complex Analysis for Mathematics and Engineering,[1], but p erhaps a
complement to it. At the same time, knowing how reluctant students are to
use a textb o ok (except as a talisman to ward o evil) I have tried to make
these notes su cient, in that a student who reads them, understands them,
and do es the exercises in them, will be able to use the concepts and tech-niques in later years. It will also get the student comfortably through the
examination. The shortness of the course, 20 lectures, for covering Complex
Analysis, either presupp oses genius ( 90% p erspiration) on the part of the
students or material skipp ed. These notes are intended to ll in some of the
gaps that will inevitably o ccur in lectures. It is a source of some disapp oint-ment to me that I can cover so little of what is a b eautiful sub ject, rich in
applications and connections with other areas of mathematics. This is, then,
a sort of sampler, and only touches the elements.
Styles of Mathematical presentation change over the years, and what was
deemed acceptable rigour by Euler and Gauss fails to keep mo dern purists
content. McLachlan, [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 intended for a di erent audience from the purists who damned him. My
exp erience leads me to feel that the need for rigour has b een develop ed to
the p oint where the intuitive and geometric has b een stunted. Both have a
part in mathematics, which grows out of the con
ict between them. But it
seems to me more imp ortant to p enetrate to the ideas in a sloppy, scru y
but serviceable way, than to reduce a sub ject to predicate calculus and omit
the whole reason for studying it. There is no known means of p ersuading a
hardheaded engineer that a sub ject merits his time and energy when it has
b een turned into an elab orate game. He, or increasingly she, wants to see two
elements at an early stage: pro cedures for solving problems which make a
di erence and concepts which organise the pro cedures into something intelli-gible. Carried to excess this leads to avoidance of abstraction and consequent loss of power later; there is a good reason for the purist's desire for rigour.
But it asks to o much of a third year student to fo cus on the underlying logic
and omit the geometry.
I have delib erately erred in the opp osite direction. It is easy enough for the
student with a taste for rigour to clarify the ideas by consulting other b o oks,
and to wind up as a logician if that is his choice. But it is hard to nd in
the literature any explicit commitment to getting the student to draw lots
of pictures. It used to be taken for granted that a student would do that
sort of thing, but now that the scho ol syllabus has had Euclid expunged, the
undergraduates cannot b e exp ected to see drawing pictures or visualising sur-faces as a natural prelude to calculation. There isascho ol of thought which
considers geometric visualisation as immoral; and another which sanctions it
only if done in private (and wash your hands b efore and afterwards). Tomy
mind this imp oses sterility, and constitutes an attempt by the bureaucrat to
strangle the artist. 1 While I do not want to imp ose my informal images on
anybody, if no mention is made of informal, intuitive ideas, many students
never realise that there are any. All the good mathematicians I knowhavea
rich supply of informal mo dels which they use to think ab out mathematics,
and it were as well to show students how this may b e done. Since this seems
to be the resp ect in which most of the text b o oks are weakest, I have p erhaps
gone to o far in the other direction, but then, I do not o er this as a text
book. More of an antidote to some of the others.
