Numerical Methods and Complex Variables is a comprehensive textbook that offers a unified exploration of two fundamental areas of applied mathematics numerical methods and complex analysis. Designed for students, educators, and professionals in mathematics, engineering, and the physical sciences, this book presents both theoretical foundations and practical applications with clarity and precision. The numerical methods section covers essential topics such as root-finding techniques, interpolation, numerical integration, solutions to differential equations, and matrix computations, with a strong focus on algorithm development and computational implementation using tools like MATLAB and Python. The complex variables section introduces readers to the elegant world of complex functions, analytic properties, conformal mappings, complex integration, power series, and residue calculus, supported by visual illustrations and engineering-oriented examples. Each chapter is structured to build conceptual understanding through detailed explanations, real-world problems, and step-by-step solutions. This book is ideal as a primary text for undergraduate and postgraduate courses or as a practical reference for researchers and professionals seeking to apply numerical and analytical techniques in scientific computing, signal processing, fluid dynamics, and other engineering domains.

About the Authors’

Dr. Anjani Kumar Shukla is a dedicated academician with over eight years of teaching experience. He currently serves as an Assistant Professor in the Department of Mathematics at the School of Computer Sciences and Engineering, Lovely Professional University, Jalandhar, Punjab, India. Renowned for his commitment to academic excellence, hard work, and passion for teaching, Dr. Shukla has been instrumental in fostering the intellectual growth of his students. His research interests primarily lie in Relativistic Cosmology, Data Analysis, and Convolutional Neural Networks (CNN), particularly in the field of Observational Cosmology. In addition to his teaching responsibilities, Dr. Shukla is actively involved in research, curriculum development, and student mentoring.

Dr. Saroj Yadav is a dedicated academician with over two years of teaching experience. She currently serves as an Assistant Professor in the Department of Applied Science and Humanities, at the School of Engineering and Sciences, MIT Art, Design & Technology University, Pune, Maharashtra. Renowned for her commitment to academic excellence, hard work, and passion for teaching, she has been instrumental in fostering the intellectual development of her students.Her research interests primarily focus on approximation theory and neural networks, particularly in the area of compressive sensing. In addition to her teaching responsibilities, Dr. Yadav is actively engaged in research, curriculum development, and mentoring students.

Ms. I. Sagaya Rebecca is an Assistant Professor of Mathematics at Velammal Institute of Technology. She holds a B.Sc in Soka Ikeda College .M.Sc., and M.Phil in Mathematics in Loyala College, Chennai and is currently pursuing her Ph.D. in Mathematics at Hindustan Institute of Technology and Science. With a strong academic foundation and a deep passion for teaching, she is committed to making mathematics engaging and understandable for all learners. Her interests include mathematical research, curriculum innovation, and mentoring aspiring scholars. She is recognized for her dedication to academic excellence and lifelong learning.

Mrs. K. Kavitha is presently working as a Assistant Professor in Velammal institute of technology, panchetti. She is having 18 years of experience in teaching. She has to her credit several publications in standard international journals.

Numerical Methods and Complex Variables

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