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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Complex analysis
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A First Course on Complex Functions (Paperback)
Loot Price: R1,364
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A First Course on Complex Functions (Paperback)
Series: Chapman and Hall Mathematics Series
Expected to ship within 18 - 22 working days
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This book contains a rigorous coverage of those topics (and only
those topics) that, in the author's judgement, are suitable for
inclusion in a first course on Complex Functions. Roughly speaking,
these can be summarized as being the things that can be done with
Cauchy's integral formula and the residue theorem. On the
theoretical side, this includes the basic core of the theory of
differentiable complex functions, a theory which is unsurpassed in
Mathematics for its cohesion, elegance and wealth of surprises. On
the practical side, it includes the computational applications of
the residue theorem. Some prominence is given to the latter,
because for the more sceptical student they provide the
justification for inventing the complex numbers. Analytic
continuation and Riemann surfaces form an essentially different
chapter of Complex Analysis. A proper treatment is far too
sophisticated for a first course, and they are therefore excluded.
The aim has been to produce the simplest possible rigorous
treatment of the topics discussed. For the programme outlined
above, it is quite sufficient to prove Cauchy'S integral theorem
for paths in star-shaped open sets, so this is done. No form of the
Jordan curve theorem is used anywhere in the book.
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