Problems and Solutions for Undergraduate
Complex Analysis I Kit-Wing Yu
Kit-Wing Yu-Problems and Solutions for Undergraduate Complex Analysis I_Kit-Wing Yu


Preface The book Problems and Solutions for Undergraduate Compler Analysis I, provides a compre-
hensive problem book for those students and instructors who need to know essential theories and techniques of complex analysis at the undergraduate level.
"The only way to learn mathematics is to do mathematics."-Paul Halmos. My learning and teaching experience has convinced me that this assertion is definitely true. In fact, I believe that "doing mathematics"means a lot to everyone who studies or teaches mathematics. It is not only a way of writing a solution to a mathematical problem, but also a mean of reflect-
ing mathematics deeply, exercising mathematical techniques expertly, exchanging mathematical thoughts with others effectively and searching new mathematical ideas unexpectedly. Thus I hope everyone who is reading this book can experience and acquire the above benefits eventually.
The wide variety of problems, which are of varying difficulty, includes the following topics: Complex Numbers, Geometry of Complex Numbers, nth Roots of a Complex Number, Complex Functions and the Analyticity, Power Series, Elementary Theory of Complex Integration, Prop-
erties of Analytic and Entire Functions, Further Properties of Analytic Functions and IsolatedSingularities of Analytic Functions. Furthermore, the main features of this book are listed as follows: The book contains 226 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, terminolo-
gies, basic mathematical concepts or important/famous/frequently used theorems (without proofs) relevant to the topic.
Three levels of difficulty have been assigned to problems: