Now in its fourth edition, the first part of this book is devoted to the basic material of complex analysis, while the second covers many special topics, such as the Riemann Mapping Theorem, the gamma function, and analytic continuation. Power series methods are used more systematically than is found in other texts, and the resulting proofs often shed more light on the results than the standard proofs. While the first part is suitable for an introductory course at undergraduate level, the additional topics covered in the second part give the instructor of a gradute course a great deal of flexibility in structuring a more advanced course.
Author(s): Serge Lang
Series: Graduate Texts in Mathematics, 103
Edition: 4
Publisher: Springer
Year: 1999
Language: English
Commentary: dcisneros
Pages: 503
City: New York
Front Cover
Title Page
© Page
Foreword
Prerequisites
Contents
PART ONE Basic Theory
CHAPTER I Complex Numbers and Functions
CHAPTER II Power Series
CHAPTER III Cauchy's Theorem, First Part
CHAPTER IV Winding Numbers and Cauchy's Theorem
CHAPTER V Applications of Cauchy's Integral Formula
CHAPTER VI Calculus of Residues
CHAPTER VII Conformal Mappings
CHAPTER VIII Harmonic Functions
PART TWO Geometric Function Theory
CHAPTER IX Schwarz Reflection
CHAPTER X The Riemann Mapping Theorem
CHAPTER XI Analytic Continuation Along Curves
PART THREE Various Analytic Topics
CHAPTER XII Applications of the Maximum Modulus Principle and Jensen's Formula
CHAPTER XIII Entire and Meromorphic Functions
CHAPTER XIV Elliptic Functions
CHAPTER XV The Gamma and Zeta Functions
CHAPTER XVI The Prime Number Theorem
Appendix
Bibliography
Index
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