Complex Variables & Numerical Methods BY Dr.Rashmi Mishra,Dr.G Bhaskar Reddy ,Dr.K.R.Kavitha,Dr.Chillara Soma Shekar

The subject of Complex Variables and Numerical Methods occupies a pivotal place in the curriculum of science, engineering, and applied mathematics. These disciplines form the mathematical backbone for analyzing and solving a wide variety of practical and theoretical problems, ranging from fluid dynamics, electromagnetism, and signal processing to numerical simulation and optimization in scientific computing.

This book, “Complex Variables and Numerical Methods,” is designed to provide students, researchers, and practitioners with a comprehensive and rigorous treatment of both classical theory and modern computational techniques. It covers essential topics in complex analysis, including complex functions, contour integration, series expansions, conformal mappings, and residue theory, alongside a detailed study of numerical methods for solving algebraic and differential equations, interpolation, numerical integration, and error analysis.

The book is a collective effort of multiple authors, each an expert in their respective fields, who have contributed to developing clear, concise explanations of fundamental concepts, supported by illustrative examples, practical applications, and problem sets designed to enhance understanding and foster analytical skills. The collaborative nature of this work ensures that each chapter benefits from specialized insight and pedagogical clarity.

This volume is intended to serve as both a textbook for advanced undergraduate and graduate courses and a reference book for researchers engaged in computational mathematics, engineering analysis, and applied sciences. The integration of theory with numerical methods equips readers with the tools necessary to tackle complex real-world problems by bridging analytical techniques with computational proficiency.

We gratefully acknowledge the support and dedication of all contributing authors, reviewers, and the publishing team who have worked diligently to bring this project to fruition. Our hope is that this book will prove to be an invaluable resource for students and professionals alike, inspiring a deeper appreciation of complex variables and numerical methods and their profound impact across scientific disciplines.