Foundations Of Complex Analysis  (Paperback, S. Ponnusamy)

Enter MNS ANGr Preface to the Second Edition The main aim of this book is to persent the conepts and techni of comples funetion theory in a way that will give the reader maim tanoce in matering the fundamentale of the theory The book is desigoed to erve as a text for a fiest coure on the clansical theory complex functions or an a suppleent to otber standand texts, The selection and the sepuencing of the contents are the rel of the experieeces I had dering the coure of my stulies and teaching. As a real analysis However, in an effort to make the book accesible to a wider wwdience, I have tried a prerequisite the reader is expected to have adequate kwlelgr of the elementa I have included a mumber of examples motivating the ideas involved in moet of the theorems ad definitions Most of the exercises have been peovided with hints for their solutions. Some theorems have been given more than one proof to help the reader acquire a deeper understanding of the theory. The present edition has a large number of illuminating new examples, observations, LL A kre w onoda i da os ue s basad a a u on edo paouape amos uaao q e jeuoppe amo pere soa Within each chapter, all the numbered items (except figures) eg. Corollary, equation, Exam- ple, Lemma, Progposition, Remark, Theorem are mumbered consecutively they appear. For the sake of coovenience, the signsignals the end of the proofs of Theorem, Corollary, Lemma and Proposition whereas the sign indicates the end of Remark, Observation and Example. It is a great plensure for me to express my gratitude to Prof. M.S. Rangachari who has not only encouraged me to write the first edition of the book but also has read several drafts with care and patience. During my doctoral work at the Indian Institute of Technology Kanpur, I had opportunities to be a tutor to graduate and undergraduate students on this subject. In this context, I would like to thank my teacher Prof. O.P. Juneja who introduced me to the theory and has been a source of inspiration since then Many people have given me help, encouragement, and inspiration. I should take this oppor- tunity to mention just a few. I express my deep gratitude to Professors R. Balasubramanian, St. Ruscheweyh, CS. Seshadri, V. Singh, M. Vuorinen, and G.P. Youvaraj whose contimued encouragement has been invaluable for widening my research interest. Particularly, I am deeply indebted to Prof. M. Vuorinen for his continued support in bringing out this edition. In addition, a number of my research visits to work with him has helped me to learn a lot. It is my pleasant duty to thank Prof. G.P. Youvaraj who has been my best friend and to this work. He has proofread the final manuscript and his constructive criticisms has improved the presentation a lot. I take this opportunity to thank Prof. Roger W. Barnard for his support and friendship during my visit to Texas Tech University. I greatly appreciate his careful reading of the final version of the manuscript and making suggestiona, I welcome and appreciate any suggestions for improvements and comments regardling errors and misprints. I must also record my appreciation due to my daughter Abirami and son Ashwin for their understanding and love during the long period that I have taken to complete this secod edition of the book. Above all, my deepest gratitude goes to my wife Booma (alias Geetha) for her infinite patience, coptinued support, and loving encouragements in all walks