Complex Analysis

The textbook is a continuation of the study of Calculus but as the study of functions of complex variables. The first goal in writing this book is to present the theory of analytic functions in a more accessible way in the early stages of his/her complex analysis study.The second aim of this book is to give the students wide applications of complex variable techniques as complex analysis is a powerful tool in applied mathematics.The third aim of this book is to provide a comparative study between real variables and complex variables of various topics. Basically those areas where real and complex calculus differ have been discussed to give the clarity about the concept.I have also provided lots of examples and have tried very hard to supply all pertinent detail of their solution. The corresponding exercise sets are divided in order to make the study easier.A multifaceted book written to keep the interest of B.Sc (Hons) Mathematics (Part III) M.Sc.(Mathematics-Part I) students of University of Delhi. This book is also useful for those who want to appear in their National eligibility Test for Lecturership in Mathematics.Contents1. Complex Number and The Complex Plane 2. Functions of Complex Variable 3. Analytic Functions 4. Elementary Functions 5. Complex Integration 6. Cauchys Integral Formulas and their Consequences 7. Analytic Functions in a Disc 8. Simply Connected Region 9. Isolated Singularities 10. The Calculus of Residues 11. Contour Integration and Summation of Series 12. Conformal Mapings 13. Schwarzs Lemma-An Automorphism of Disc Appendix Bibliography Index