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 1 Preface 5 List of Figures 7 The Complex Numbers 12 Functions of the Complex Variable z 34 Analytic Functions 48 Line Integrals and Entire Functions 58 Properties of Entire Functions 66 Properties of Analytic Functions 78 Further Properties of Analytic Functions 94 Simply Connected Domains 112 Isolated Singularities of an Analytic Function 120 The Residue Theorem 132 Applications of the Residue Theorem to the Evaluation ... 150 Further Contour Integral Techniques 174 Introduction to Conformal Mapping 184 The Riemann Mapping Theorem 198 Maximum-Modulus Theorems for Unbounded Domains 208 Harmonic Functions 212 Different Forms of Analytic Functions 222 Analytic Continuation; The Gamma and Zeta Functions 232 Applications to Other Areas of Mathematics 238 Index 248 Bibliography 250