A Complete Solution Guide to Complex Analysis

This is a complete solution guide to all exercises in Bak and Newman's Complex Analysis . The features of this book are as follows: It covers all the 300 exercises with detailed and complete solutions. There are 34 illustrations for explaining the mathematical concepts or ideas used behind the questions or theorems. Different colors are used in order to highlight or explain problems, lemmas, remarks, main points/formulas involved, or show the steps of manipulation in some complicated proofs. (ebook only) Necessary lemmas with proofs are provided. Useful or relevant references are provided to some questions for interested readers. Untitled 2 Preface 6 List of Figures 8 The Complex Numbers 13 Functions of the Complex Variable z 35 Analytic Functions 49 Line Integrals and Entire Functions 59 Properties of Entire Functions 67 Properties of Analytic Functions 79 Further Properties of Analytic Functions 95 Simply Connected Domains 113 Isolated Singularities of an Analytic Function 121 The Residue Theorem 133 Applications of the Residue Theorem to the Evaluation ... 151 Further Contour Integral Techniques 175 Introduction to Conformal Mapping 185 The Riemann Mapping Theorem 199 Maximum-Modulus Theorems for Unbounded Domains 209 Harmonic Functions 213 Different Forms of Analytic Functions 223 Analytic Continuation; The Gamma and Zeta Functions 233 Applications to Other Areas of Mathematics 239 Index 249 Bibliography 251