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Complex Analysis: Book Series P-8/24
This book is designed to help aspirants preparing for the CSIR NET (JRF) in Mathematical Sciences, with a specific focus on Complex Analysis. Complex analysis, an essential branch of mathematics, plays a critical role in various fields such as algebra, geometry, and mathematical physics. The book provides comprehensive coverage of the syllabus and aims to deepen the student's understanding of complex numbers and their applications.
The content is structured to progress from fundamental concepts to advanced topics. Chapter 1 covers the basics of complex numbers, including their operations, representation, and power series. Chapter 2 discusses transcendental functions in the complex domain, focusing on exponential, trigonometric, and hyperbolic functions. Chapter 3 introduces analytic functions, Cauchy-Riemann equations, and harmonic functions. Chapter 4 deals with contour integrals, Cauchy’s Theorem, and applications like Liouville’s Theorem and the Maximum Modulus Principle. Finally, Chapter 5 explores advanced topics, including the Schwarz Lemma, Taylor and Laurent series, residue calculus, and conformal mappings.
The book offers a clear, systematic approach with detailed explanations, diagrams, and examples, making complex concepts easier to understand. Exercises at the end of each chapter help reinforce learning and are tailored to the CSIR NET exam pattern, preparing students for both objective and subjective questions. This book is a valuable resource for students seeking to excel in both the exam and future mathematical research.
The content is structured to progress from fundamental concepts to advanced topics. Chapter 1 covers the basics of complex numbers, including their operations, representation, and power series. Chapter 2 discusses transcendental functions in the complex domain, focusing on exponential, trigonometric, and hyperbolic functions. Chapter 3 introduces analytic functions, Cauchy-Riemann equations, and harmonic functions. Chapter 4 deals with contour integrals, Cauchy’s Theorem, and applications like Liouville’s Theorem and the Maximum Modulus Principle. Finally, Chapter 5 explores advanced topics, including the Schwarz Lemma, Taylor and Laurent series, residue calculus, and conformal mappings.
The book offers a clear, systematic approach with detailed explanations, diagrams, and examples, making complex concepts easier to understand. Exercises at the end of each chapter help reinforce learning and are tailored to the CSIR NET exam pattern, preparing students for both objective and subjective questions. This book is a valuable resource for students seeking to excel in both the exam and future mathematical research.
182 pages, Hardcover
Published April 28, 2025
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