• ISBN13: 9788126911868
• Binding: Paperback
• Subject: Mathematics and Statistics
• Publisher: Atlantic Publishers & Distributors (P) Ltd
• Publisher Imprint: Atlantic
• Publication Date: February 11, 2025
• Pages: 201
• Original Price: INR 350.0
• Language: English
• Edition: N/A
• Item Weight: 390 grams
• BISAC Subject(s): N/A

Explore the Fascinating World of Complex Analysis

Complex Analysis: An Introduction is a thoughtfully crafted resource for undergraduate Mathematics and Engineering students and postgraduate learners in Physics and Statistics. It bridges foundational concepts with advanced topics, offering a seamless learning experience. Starting with the basics of complex numbers and elementary functions, the book delves into complex integration, series representations, conformal mappings and analytic continuation. Key theorems like the Monodromy, Riemann Mapping and Picard's Theorems are presented with simplified yet rigorous proofs. What sets this book apart is its active learning approach, featuring examples, exercises and graphical insights to enhance understanding. Whether you're a beginner or preparing for advanced studies, this book is your guide to exploring the elegance and depth of complex analysis.

Dr Mohammad Ibrahim is an Assistant Professor in the Department of Mathematics at the South Campus, University of Kashmir, Anantnag. With 17 years of experience in teaching complex analysis to postgraduate and PhD students, he is deeply committed to advancing mathematical education. Dr Ibrahim has contributed over 30 research publications to renowned international mathematics journals. He is a two-time qualifier of the JRF (NET) and was honoured as a gold medallist in the Department of Mathematics at the University of Kashmir. His extensive academic and research experience makes him a respected figure in the field of mathematics.

• Preface ............................................................. iii
• Acknowledgements ............................................ v
• 1. Introduction to Complex Numbers .................. 1
• 2. Geometry of the Complex Plane.................... 10
• 3. Analytic Functions ................. .....................25
• 4. Cauchy-Riemann Equations ........................ 41
• 5. Sequence, Series, and Power Serie.................... 48
• 6. Curves and Complex Line Integral ......................... 59
• 7. Cauchy’s Integral Theorem (Simple and General Forms) ...... 66
• 8. Cauchy’s Integral Formula and its Applications ............... 78
• 9. Series Expansion and Singularities of Complex Functions ... 90
• 10. Local Properties of Analytic Functions ............... 105
• 11. Calculus of Residues ................................. 115
• 12. Meromorphic Functions and Rouche’s Theorem ............. 126
• 13. Conformal Mappings .......................... 133
• 14. Analytic Continuation ................. 145
• 15. Weierstrass Factorization Theorem ................... 156
• 16. Riemann Mapping Theorem ............... 165
• 17. Picard’s Theorem and Schottky’s Theorem ................ 183
• Index .................................... 191