A Second Course In Complex Analysis

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A Second Course In Complex Analysis

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Author : William A. Veech
language : en
Publisher: Courier Corporation
Release Date : 2008-01-24

A Second Course In Complex Analysis written by William A. Veech and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-24 with Mathematics categories.

A clear, self-contained treatment of important areas in complex analysis, this text is geared toward upper-level undergraduates and graduate students. Chiefly classical in content, it emphasizes the geometry of complex mappings. Additional topics include modular function, Hadamard product theorem, and prime number theorem. 1967 edition.

A Second Course In Complex Analysis

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Author : William A. Veech
language : en
Publisher: Courier Corporation
Release Date : 2014-08-04

A Second Course In Complex Analysis written by William A. Veech and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-04 with Mathematics categories.

A clear, self-contained treatment of important areas in complex analysis, this text is geared toward upper-level undergraduates and graduate students. The material is largely classical, with particular emphasis on the geometry of complex mappings. Author William A. Veech, the Edgar Odell Lovett Professor of Mathematics at Rice University, presents the Riemann mapping theorem as a special case of an existence theorem for universal covering surfaces. His focus on the geometry of complex mappings makes frequent use of Schwarz's lemma. He constructs the universal covering surface of an arbitrary planar region and employs the modular function to develop the theorems of Landau, Schottky, Montel, and Picard as consequences of the existence of certain coverings. Concluding chapters explore Hadamard product theorem and prime number theorem.

A Second Course In Analysis

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Author : M. Ram Murty
language : en
Publisher:
Release Date : 2022

A Second Course In Analysis written by M. Ram Murty and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with categories.

This book discusses major topics in measure theory, Fourier transforms, complex analysis and algebraic topology. It presents material from a mature mathematical perspective. The text is suitable for a two-semester graduate course in analysis and will help students prepare for a research career in mathematics. After a short survey of undergraduate analysis and measure theory, the book highlights the essential theorems that have now become ubiquitous in mathematics. It studies Fourier transforms, derives the inversion theorem and gives diverse applications ranging from probability theory to mathematical physics. It reviews topics in complex analysis and gives a synthetic, rigorous development of the calculus of residues as well as applications to a wide array of problems. It also introduces algebraic topology and shows the symbiosis between algebra and analysis. Indeed, algebraic archetypes were providing foundational support from the start. Multivariable calculus is comprehended in a single glance through the algebra of differential forms. Advanced complex analysis inevitably leads one to the study of Riemann surfaces, and so the final chapter gives the student a hint of these motifs and underlying algebraic patterns.

Function Theory On Planar Domains

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Author : Stephen D. Fisher
language : en
Publisher: Courier Corporation
Release Date : 2014-06-10

Function Theory On Planar Domains written by Stephen D. Fisher and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-10 with Mathematics categories.

A high-level treatment of complex analysis, this text focuses on function theory on a finitely connected planar domain. Clear and complete, it emphasizes domains bounded by a finite number of disjoint analytic simple closed curves. The first chapter and parts of Chapters 2 and 3 offer background material, all of it classical and important in its own right. The remainder of the text presents results in complex analysis from the far, middle, and recent past, all selected for their interest and merit as substantive mathematics. Suitable for upper-level undergraduates and graduate students, this text is accessible to anyone with a background in complex and functional analysis. Author Stephen D. Fisher, a professor of mathematics at Northwestern University, elaborates upon and extends results with a set of exercises at the end of each chapter.

Geometric Function Theory

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Author : Tom Carroll
language : en
Publisher: Springer Nature
Release Date : 2024-12-11

Geometric Function Theory written by Tom Carroll and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-11 with Mathematics categories.

This textbook provides a second course in complex analysis with a focus on geometric aspects. It covers topics such as the spherical geometry of the extended complex plane, the hyperbolic geometry of the Poincaré disk, conformal mappings, the Riemann Mapping Theorem and uniformisation of planar domains, characterisations of simply connected domains, the convergence of Riemann maps in terms of Carathéodory convergence of the image domains, normal families and Picard's theorems on value distribution, as well as the fundamentals of univalent function theory. Throughout the text, the synergy between analysis and geometry is emphasised, with proofs chosen for their directness. The textbook is self-contained, requiring only a first undergraduate course in complex analysis. The minimal topology needed is introduced as necessary. While primarily aimed at upper-level undergraduates, the book also serves as a concise reference for graduates working in complex analysis.

A Second Course In Complex Analysis

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Author : Peter V Dovbush
language : en
Publisher:
Release Date : 2026-04-27

A Second Course In Complex Analysis written by Peter V Dovbush and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2026-04-27 with Mathematics categories.

This book covers more modern topics on complex analysis and is more geometric in focus. Topics covered include: harmonic measure, extremal length, Riemann surfaces, and uniformization, among others. It will benefit students and introduce new topics that they might not otherwise experience.

A First Course In Complex Analysis With Applications

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Author : Dennis G. Zill
language : en
Publisher: Jones & Bartlett Learning
Release Date : 2006-07

A First Course In Complex Analysis With Applications written by Dennis G. Zill and has been published by Jones & Bartlett Learning this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07 with Mathematics categories.

A First Course In Complex Analysis With Applications Limits Theoretical Coverage To Only What Is Necessary, And Conveys It In A Student-Friendly Style. Its Aim Is To Introduce The Basic Principles And Applications Of Complex Analysis To Undergraduates Who Have No Prior Knowledge Of This Subject. Contents Of The Book Include The Complex Number System, Complex Functions And Sequences, As Well As Real Integrals; In Addition To Other Concepts Of Calculus, And The Functions Of A Complex Variable. This Text Is Written For Junior-Level Undergraduate Students Who Are Majoring In Math, Physics, Computer Science, And Electrical Engineering.

A Course In Complex Analysis

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Author : Wolfgang Fischer
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-10-21

A Course In Complex Analysis written by Wolfgang Fischer 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 2011-10-21 with Mathematics categories.

This carefully written textbook is an introduction to the beautiful concepts and results of complex analysis. It is intended for international bachelor and master programmes in Germany and throughout Europe; in the Anglo-American system of university education the content corresponds to a beginning graduate course. The book presents the fundamental results and methods of complex analysis and applies them to a study of elementary and non-elementary functions (elliptic functions, Gamma- and Zeta function including a proof of the prime number theorem ...) and – a new feature in this context! – to exhibiting basic facts in the theory of several complex variables. Part of the book is a translation of the authors’ German text “Einführung in die komplexe Analysis”; some material was added from the by now almost “classical” text “Funktionentheorie” written by the authors, and a few paragraphs were newly written for special use in a master’s programme.

A Second Course In Complex Analysis Von William A Veech

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Author : William A. Veech
language : en
Publisher:
Release Date : 1967

A Second Course In Complex Analysis Von William A Veech written by William A. Veech and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with categories.

Nine Introductions In Complex Analysis Revised Edition

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Author : Sanford L. Segal
language : en
Publisher: Elsevier
Release Date : 2007-10-10

Nine Introductions In Complex Analysis Revised Edition written by Sanford L. Segal and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-10 with Mathematics categories.

The book addresses many topics not usually in "second course in complex analysis" texts. It also contains multiple proofs of several central results, and it has a minor historical perspective. - Proof of Bieberbach conjecture (after DeBranges) - Material on asymptotic values - Material on Natural Boundaries - First four chapters are comprehensive introduction to entire and metomorphic functions - First chapter (Riemann Mapping Theorem) takes up where "first courses" usually leave off