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This comprehensive textbook explores the theory and applications of complex functions in mathematics. Beginning with the foundations of complex numbers (z = x + iy), the book develops the geometric interpretation of the complex plane where these numbers reside. The core chapters examine mappings of complex numbers, covering linear transformations, Möbius transformations, and conformal mappings, with special emphasis on the Riemann mapping theorem that allows conformally mapping any simply connected domain onto the unit disk.The text progresses to analytic functions, characterized by the...

This comprehensive text explores the fascinating interplay between complex function theory and integral transforms, providing both theoretical foundations and practical applications. Beginning with the fundamental principles of complex analysis-including analytic functions, contour integration, and residue theory-the book builds a rigorous framework for understanding how complex-valued functions behave in ways that extend and enrich real analysis.The text then transitions to integral transforms, demonstrating how the Laplace, Fourier, and other transforms serve as powerful tools for solving...

This comprehensive 337-page textbook provides a systematic exploration of electromagnetic theory, beginning with fundamental concepts of magnetic fields and their interactions with current-carrying conductors, including the Lorentz force, Ampere's law, and Faraday's law of electromagnetic induction. The text progresses through three main chapters that build upon each other: the first chapter (pages 1-56) establishes the foundations of magnetic phenomena through topics such as magnetic dipole moments, the Hall effect, and energy storage in magnetic systems including coils and toroids; the...

Probability is a fundamental branch of mathematics that deals with the study of randomness, uncertainty, and chance. It provides a mathematical framework for analyzing and quantifying the likelihood of different events occurring. The book would typically cover: 1. Basic probability concepts, definition of probability, sample spaces and events, probability axioms and rules;2. Probability calculations, combinatorics, permutations and combinations, calculation of probabilities of complex events;3. Probability distributions, discrete and continuous probability distributions, normal distribution,...

This comprehensive textbook provides a practical approach to understanding fundamental physics principles, focusing on electricity, magnetism, and wave phenomena. The book bridges theoretical concepts with real-world applications through extensively worked examples and problem-solving strategies. Perfect for undergraduate physics students, engineering students, and professionals seeking to strengthen their understanding of electromagnetic principles. This book stands out with its systematic approach to learning physics, including comprehensive chapters on electrical potential energy,...