This book has plenty of figures, plenty
of examples, copious commentary, and even in-text exercises for the students.
But, since it is not a formal textbook, it does not have exercise sets. It does
not have a Glossary or a Table of Notation. Topics covered includes: The
Complex Plane, Complex Line Integrals, Applications of the Cauchy Theory,
Isolated Singularities and Laurent Series, The Argument Principle, The Geometric
Theory of Holomorphic Functions, Harmonic Functions, Infinite Series and
Products, Analytic Continuation .
The book is intended as a text, appropriate for use by advanced
undergraduates or graduate students who have taken a course in introductory real
analysis, or as it is often called, advanced calculus. No background in complex
variables is assumed, thus making the text suitable for those encountering the
subject for the first time. The Elementary Theory, General Cauchy Theorem ,
Applications of the Cauchy Theory, Families of Analytic Functions, Factorization
of Analytic Functions and The Prime Number Theorem.
This note covers the following topics: Complex Numbers, Eulerís
Formula, Roots and multi-valued arithmetic, Functions from C to C, Continuity
and Limits, Analytic and entire functions, Harmonic Conjugates, Moreraís
Theorem, Taylorís Theorem, Laurent Series and Residues.