Complex Functions An Introduction To Complex Analysis
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Complex Functions An Introduction To Complex Analysis
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Author : Lexa N. Palmer
language : en
Publisher: Book Lovers HQ
Release Date : 2025-05-07
Complex Functions An Introduction To Complex Analysis written by Lexa N. Palmer and has been published by Book Lovers HQ this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-07 with Mathematics categories.
Discover the elegant and powerful world of complex analysis in this comprehensive introduction to one of mathematics' most beautiful subjects. "Complex Functions: An Introduction to Complex Analysis" bridges the gap between introductory calculus and advanced mathematical theory, revealing how the simple addition of the imaginary unit transforms mathematics into something extraordinary. Complex analysis stands as a cornerstone of modern mathematics, physics, and engineering, offering tools of remarkable power and elegance. Whether you're a mathematics student seeking deeper understanding, a physicist requiring analytical techniques, or an engineer solving practical problems, this book provides the foundation you need to master this essential field. Written with clarity and precision, this text balances theoretical rigor with intuitive explanations, making abstract concepts accessible without sacrificing mathematical depth. From the foundations of complex numbers to the frontiers of modern research, this book guides you through the fascinating landscape of complex functions with carefully crafted examples and applications. What you will find in this book: A systematic development of complex analysis from first principles Clear explanations of key concepts like holomorphic functions, contour integration, and residue theory Geometric interpretations that build intuition and understanding Powerful techniques for solving integrals and differential equations Applications to physics, engineering, and pure mathematics Historical notes highlighting the development of important ideas Carefully selected exercises ranging from computational practice to theoretical explorations Connections between complex analysis and other branches of mathematics Transform your mathematical thinking with complex analysis—where algebraic, geometric, and analytic aspects of mathematics unite in perfect harmony. Whether you're encountering these ideas for the first time or seeking a deeper understanding, this book will open your eyes to the remarkable world where mathematics achieves its most beautiful and powerful expression.
Complex Analysis
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Author : Lars Ahlfors
language : en
Publisher:
Release Date : 1979
Complex Analysis written by Lars Ahlfors and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Education categories.
A standard source of information of functions of one complex variable, this text has retained its wide popularity in this field by being consistently rigorous without becoming needlessly concerned with advanced or overspecialized material. Difficult points have been clarified, the book has been reviewed for accuracy, and notations and terminology have been modernized. Chapter 2, Complex Functions, features a brief section on the change of length and area under conformal mapping, and much of Chapter 8, Global-Analytic Functions, has been rewritten in order to introduce readers to the terminology of germs and sheaves while still emphasizing that classical concepts are the backbone of the theory. Chapter 4, Complex Integration, now includes a new and simpler proof of the general form of Cauchy's theorem. There is a short section on the Riemann zeta function, showing the use of residues in a more exciting situation than in the computation of definite integrals.
Complex Analysis
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Author : Murali Rao
language : en
Publisher: World Scientific
Release Date : 1991
Complex Analysis written by Murali Rao and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
This is a rigorous introduction to the theory of complex functions of one complex variable. The authors have made an effort to present some of the deeper and more interesting results, for example, Picard's theorems, Riemann mapping theorem, Runge's theorem in the first few chapters. However, the very basic theory is nevertheless given a thorough treatment so that readers should never feel lost. After the first five chapters, the order may be adapted to suit the course. Each chapter finishes with exercises.
An Introduction To Complex Analysis In Several Variables
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Author : L. Hormander
language : en
Publisher: Elsevier
Release Date : 1973-02-12
An Introduction To Complex Analysis In Several Variables written by L. Hormander and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973-02-12 with Mathematics categories.
An Introduction to Complex Analysis in Several Variables
Introduction To Complex Analysis
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Author : Boris Vladimirovich Shabat
language : en
Publisher: American Mathematical Soc.
Release Date : 1992-11-04
Introduction To Complex Analysis written by Boris Vladimirovich Shabat and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-11-04 with Mathematics categories.
Since the 1960s, there has been a flowering in higher-dimensional complex analysis. Both classical and new results in this area have found numerous applications in analysis, differential and algebraic geometry, and, in particular, contemporary mathematical physics. In many areas of modern mathematics, the mastery of the foundations of higher-dimensional complex analysis has become necessary for any specialist. Intended as a first study of higher-dimensional complex analysis, this book covers the theory of holomorphic functions of several complex variables, holomorphic mappings, and submanifolds of complex Euclidean space.
An Introduction To Complex Analysis
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Author : Wolfgang Tutschke
language : en
Publisher: CRC Press
Release Date : 2004-06-25
An Introduction To Complex Analysis written by Wolfgang Tutschke and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-25 with Mathematics categories.
Like real analysis, complex analysis has generated methods indispensable to mathematics and its applications. Exploring the interactions between these two branches, this book uses the results of real analysis to lay the foundations of complex analysis and presents a unified structure of mathematical analysis as a whole. To set the groundwork and mitigate the difficulties newcomers often experience, An Introduction to Complex Analysis begins with a complete review of concepts and methods from real analysis, such as metric spaces and the Green-Gauss Integral Formula. The approach leads to brief, clear proofs of basic statements - a distinct advantage for those mainly interested in applications. Alternate approaches, such as Fichera's proof of the Goursat Theorem and Estermann's proof of the Cauchy's Integral Theorem, are also presented for comparison. Discussions include holomorphic functions, the Weierstrass Convergence Theorem, analytic continuation, isolated singularities, homotopy, Residue theory, conformal mappings, special functions and boundary value problems. More than 200 examples and 150 exercises illustrate the subject matter and make this book an ideal text for university courses on complex analysis, while the comprehensive compilation of theories and succinct proofs make this an excellent volume for reference.
An Introduction To Complex Function Theory
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Author : Bruce P. Palka
language : en
Publisher: Springer
Release Date : 1990-11-26
An Introduction To Complex Function Theory written by Bruce P. Palka and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-11-26 with Mathematics categories.
This book provides a rigorous yet elementary introduction to the theory of analytic functions of a single complex variable. While presupposing in its readership a degree of mathematical maturity, it insists on no formal prerequisites beyond a sound knowledge of calculus. Starting from basic definitions, the text slowly and carefully develops the ideas of complex analysis to the point where such landmarks of the subject as Cauchy's theorem, the Riemann mapping theorem, and the theorem of Mittag-Leffler can be treated without sidestepping any issues of rigor. The emphasis throughout is a geometric one, most pronounced in the extensive chapter dealing with conformal mapping, which amounts essentially to a "short course" in that important area of complex function theory. Each chapter concludes with a wide selection of exercises, ranging from straightforward computations to problems of a more conceptual and thought-provoking nature.
An Introduction To Complex Analysis
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Author : Ravi P. Agarwal
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-07-01
An Introduction To Complex Analysis written by Ravi P. Agarwal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-01 with Mathematics categories.
This textbook introduces the subject of complex analysis to advanced undergraduate and graduate students in a clear and concise manner. Key features of this textbook: effectively organizes the subject into easily manageable sections in the form of 50 class-tested lectures, uses detailed examples to drive the presentation, includes numerous exercise sets that encourage pursuing extensions of the material, each with an “Answers or Hints” section, covers an array of advanced topics which allow for flexibility in developing the subject beyond the basics, provides a concise history of complex numbers. An Introduction to Complex Analysis will be valuable to students in mathematics, engineering and other applied sciences. Prerequisites include a course in calculus.
Complex Analysis
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Author : John Stalker
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-10-16
Complex Analysis written by John Stalker and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-16 with Mathematics categories.
In this concise introduction to the classical theory of one complex variable the content is driven by techniques and examples, rather than definitions and theorems.
Introduction To Complex Analysis
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Author : Rolf Nevanlinna
language : en
Publisher: American Mathematical Society
Release Date : 2007-10-09
Introduction To Complex Analysis written by Rolf Nevanlinna and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-09 with Mathematics categories.
This textbook, based on lectures given by the authors, presents the elements of the theory of functions in a precise fashion. This introduction is ideal for the third or fourth year of undergraduate study and for graduate students learning complex analysis. Over 300 exercises offer important insight into the subject.