Principles of Complex Analysis

Principles of Complex Analysis
Title Principles of Complex Analysis PDF eBook
Author Serge Lvovski
Publisher Springer Nature
Pages 257
Release 2020-09-26
Genre Mathematics
ISBN 3030593657

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This is a brief textbook on complex analysis intended for the students of upper undergraduate or beginning graduate level. The author stresses the aspects of complex analysis that are most important for the student planning to study algebraic geometry and related topics. The exposition is rigorous but elementary: abstract notions are introduced only if they are really indispensable. This approach provides a motivation for the reader to digest more abstract definitions (e.g., those of sheaves or line bundles, which are not mentioned in the book) when he/she is ready for that level of abstraction indeed. In the chapter on Riemann surfaces, several key results on compact Riemann surfaces are stated and proved in the first nontrivial case, i.e. that of elliptic curves.

Complex Analysis

Complex Analysis
Title Complex Analysis PDF eBook
Author Jerry R. Muir, Jr.
Publisher John Wiley & Sons
Pages 274
Release 2015-05-26
Genre Mathematics
ISBN 1118705270

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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.

Complex Analysis: an Introduction to Theory of Analytic Functions of One Complex Variable

Complex Analysis: an Introduction to Theory of Analytic Functions of One Complex Variable
Title Complex Analysis: an Introduction to Theory of Analytic Functions of One Complex Variable PDF eBook
Author Ahlfors Lars V
Publisher
Pages 331
Release 1981
Genre
ISBN

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Theory of Complex Functions

Theory of Complex Functions
Title Theory of Complex Functions PDF eBook
Author Reinhold Remmert
Publisher Springer Science & Business Media
Pages 464
Release 2012-12-06
Genre Mathematics
ISBN 1461209390

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A lively and vivid look at the material from function theory, including the residue calculus, supported by examples and practice exercises throughout. There is also ample discussion of the historical evolution of the theory, biographical sketches of important contributors, and citations - in the original language with their English translation - from their classical works. Yet the book is far from being a mere history of function theory, and even experts will find a few new or long forgotten gems here. Destined to accompany students making their way into this classical area of mathematics, the book offers quick access to the essential results for exam preparation. Teachers and interested mathematicians in finance, industry and science will profit from reading this again and again, and will refer back to it with pleasure.

Applied Complex Variables

Applied Complex Variables
Title Applied Complex Variables PDF eBook
Author John W. Dettman
Publisher Courier Corporation
Pages 514
Release 2012-05-07
Genre Mathematics
ISBN 0486158284

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Fundamentals of analytic function theory — plus lucid exposition of 5 important applications: potential theory, ordinary differential equations, Fourier transforms, Laplace transforms, and asymptotic expansions. Includes 66 figures.

Modern Real and Complex Analysis

Modern Real and Complex Analysis
Title Modern Real and Complex Analysis PDF eBook
Author Bernard R. Gelbaum
Publisher John Wiley & Sons
Pages 506
Release 2011-02-25
Genre Mathematics
ISBN 111803080X

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Modern Real and Complex Analysis Thorough, well-written, and encyclopedic in its coverage, this textoffers a lucid presentation of all the topics essential to graduatestudy in analysis. While maintaining the strictest standards ofrigor, Professor Gelbaum's approach is designed to appeal tointuition whenever possible. Modern Real and Complex Analysisprovides up-to-date treatment of such subjects as the Daniellintegration, differentiation, functional analysis and Banachalgebras, conformal mapping and Bergman's kernels, defectivefunctions, Riemann surfaces and uniformization, and the role ofconvexity in analysis. The text supplies an abundance of exercisesand illustrative examples to reinforce learning, and extensivenotes and remarks to help clarify important points.

Elementary Theory of Analytic Functions of One or Several Complex Variables

Elementary Theory of Analytic Functions of One or Several Complex Variables
Title Elementary Theory of Analytic Functions of One or Several Complex Variables PDF eBook
Author Henri Cartan
Publisher Courier Corporation
Pages 242
Release 2013-04-22
Genre Mathematics
ISBN 0486318672

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Basic treatment includes existence theorem for solutions of differential systems where data is analytic, holomorphic functions, Cauchy's integral, Taylor and Laurent expansions, more. Exercises. 1973 edition.