Problems and Solutions for Undergraduate Complex Analysis II

by Kit-Wing Yu

This book Problems and Solutions for Undergraduate Complex Analysis II is the continuum of the first book Problems and Solutions for Undergraduate Complex Analysis I. Its aim is the same as its first We want to assist undergraduate students or first-year students who study mathematics in learning their first rigorous complex analysis course. The wide variety of problems, which are of varying difficulty, include the following Residue Theorem and its ConsequencesApplications of the Residue Theorem to Integrals and SumsSequences and Series of Analytic FunctionsConformal Mappings and the Riemann Mapping TheoremIntroduction to Harmonic FunctionsEntire Functions as Infinite ProductsZeros of Entire FunctionsFurthermore, the main features of this book are listed as book contains 227 problems which cover the topics mentioned above. The solutions are detailed and complete in the sense that every step and every theorem that I applied will be presented.Each chapter starts with a brief and concise note of introducing the notations, terminologies, basic mathematical concepts or important/famous/frequently used theorems (without proofs) relevant to the topic.Three levels of difficulty have been assigned to problems so that you can sharpen your mathematics step-by-step.There are 44 illustrations for explaining the mathematical concepts or ideas used behind the questions or theorems.Different colors are used in appropriate places so as to highlight or explain problems, examples, remarks, main points/formulas involved, or show the steps of manipulation in some complicated proofs. (ebook only)Appendix A contains important theorems that appeared in the book Problems and Solutions for Undergraduate Complex Analysis I. This provides a quick and easy guide to the reader.

Kindle Edition

Published May 2, 2022