A thorough introduction to the theory of complex functions emphasizing the beauty, power, and counterintuitive nature of the subject
Written with a reader-friendly approach, Complex Analysis: A Modern First Course in Function Theory features a self-contained, concise development of the fundamental principles of complex analysis. After laying groundwork on complex numbers and the calculus and geometric mapping properties of functions of a complex variable, the author uses power series as a unifying theme to define and study the many rich and occasionally surprising properties of analytic functions, including the Cauchy theory and residue theorem. The book concludes with a treatment of harmonic functions and an epilogue on the Riemann mapping theorem.
Thoroughly classroom tested at multiple universities, Complex Analysis: A Modern First Course in Function Theory features: * Plentiful exercises, both computational and theoretical, of varying levels of difficulty, including several that could be used for student projects * Numerous figures to illustrate geometric concepts and constructions used in proofs * Remarks at the conclusion of each section that place the main concepts in context, compare and contrast results with the calculus of real functions, and provide historical notes * Appendices on the basics of sets and functions and a handful of useful results from advanced calculus Appropriate for students majoring in pure or applied mathematics as well as physics or engineering, Complex Analysis: A Modern First Course in Function Theory is an ideal textbook for a one-semester course in complex analysis for those with a strong foundation in multivariable calculus. The logically complete book also serves as a key reference for mathematicians, physicists, and engineers and is an excellent source for anyone interested in independently learning or reviewing the beautiful subject of complex analysis.
This book concisely addresses the classical results of the field, emphasizes the beauty, power, and counterintuitive nature of the subject, and moves the notion of power series front and center, giving readers a primary tool to deal with problems from modern function theory. * Uniquely defines analyticity in terms of power series (as opposed to differentiability), making power series a central concept and tool to solve problems * Features many "counterintuitive" concepts as a learning tool, such as addressing Liouville's Theorem, the factorization of analytic function, the Open Mapping Theorem, and the Maximum Principle in quick succession early on in the book in an attempt to prepare readers for the development of the Cauchy integral theory * Classroom tested for 10+ years by the author at the University of Scranton as well as colleagues at Rose-Hulman Institute of Technology and Adams State College * Presents sequences and series early on, distinguishes complex analysis from real analysis and calculus, and emphasizes geometry when analyzing complex functions * Contains appendices for basic notation of sets and functions as well as necessary topics from advanced calculus, such as Leibnitz's Rule and Fubini's Theorem * An Instructor's Manual containing all solutions is available via request to the Publisher.
Written with a reader-friendly approach and provides a wide range of exercises and numerous figures throughout, allowing readers to gain intuition for solving problems.
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Buchbeschreibung WILEY ACADEMIC Jun 2015, 2015. Buch. Buchzustand: Neu. 250x150x15 mm. Neuware - A thorough introduction to the theory of complex functions emphasizing the beauty, power, and counterintuitive nature of the subject 280 pp. Englisch. Artikel-Nr. 9781118705223