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Complex Analysis
ISBN-13:
9780387747156
Veröffentl:
2007
Seiten:
220
Autor:
Jane P. Gilman
Serie:
245, Graduate Texts in Mathematics
eBook Typ:
PDF
eBook Format:
EPUB
Kopierschutz:
1 - PDF Watermark
Sprache:
Englisch
Beschreibung:
This book is intended for a graduate course on complex analysis, also known as function theory. The main focus is the theory of complex-valued functions of a single complex variable. This theory is a prerequisite for the study of many current and rapidly developing areas of mathematics including the theory of several and infinitely many complex variables, the theory of groups, hyperbolic geometry and three-manifolds, and number theory. Complex analysis has connections and applications to many other subjects in mathematics and to other sciences. It is an area where the classic and the modern techniques meet and benefit from each other. This material should be part of the education of every practicing mathematician, and it will also be of interest to computer scientists, physicists, and engineers.
The Fundamental Theorem in Complex Function Theory.- Foundations.- Power Series.- The Cauchy Theory-A Fundamental Theorem.- The Cauchy Theory-Key Consequences.- Cauchy Theory: Local Behavior and Singularities of Holomorphic Functions.- Sequences and Series of Holomorphic Functions.- Conformal Equivalence.- Harmonic Functions.- Zeros of Holomorphic Functions.
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