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Complex Analysis

Author: Jerry R. Muir
Publisher: John Wiley & Sons
ISBN: 111870522X
Size: 57.83 MB
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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.

Function Theory Of One Complex Variable

Author: Robert Everist Greene
Publisher: American Mathematical Soc.
ISBN: 9780821839621
Size: 33.71 MB
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The third edition of this textbook on one of mathematics' most central subjects includes revisions of many exercises for greater consistency, as well as clarifications of several proofs. The authors treat complex variables as a direct development from calculus, relating ideas such as the complex derivative and the Cauchy theorem to their cognate idea from calculus. Many examples, figures and exercises enrich the text.

Complex Analysis

Author: Jane P. Gilman
Publisher: Springer Science & Business Media
ISBN: 0387747141
Size: 17.95 MB
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Organizing the basic material of complex analysis in a unique manner, the authors of this versatile book aim is to present a precise and concise treatment of those parts of complex analysis that should be familiar to every research mathematician.

Geometric Function Theory

Author: Steven G. Krantz
Publisher: Springer Science & Business Media
ISBN: 0817644407
Size: 47.98 MB
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* Presented from a geometric analytical viewpoint, this work addresses advanced topics in complex analysis that verge on modern areas of research * Methodically designed with individual chapters containing a rich collection of exercises, examples, and illustrations

Anschauliche Funktionentheorie

Author: Tristan Needham
Publisher: Oldenbourg Verlag
ISBN: 348670902X
Size: 21.98 MB
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Needhams neuartiger Zugang zur Funktionentheorie wurde von der Fachpresse begeistert aufgenommen. Mit über 500 zum großen Teil perspektivischen Grafiken vermittelt er im wahrsten Sinne des Wortes eine Anschauung von der sonst oft als trocken empfundenen Funktionentheorie. "Anschauliche Funktionentheorie ist eine wahre Freude und ein Buch so recht nach meinem Herzen. Indem er ausschließlich seine neuartige geometrische Perspektive verwendet, enthüllt Tristan Needham viele überraschende und bisher weitgehend unbeachtete Facetten der Schönheit der Funktionentheorie." (Sir Roger Penrose)

Complex Analysis

Author: John Stalker
Publisher: Springer Science & Business Media
ISBN: 0817649190
Size: 66.36 MB
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All modem introductions to complex analysis follow, more or less explicitly, the pattern laid down in Whittaker and Watson [75]. In "part I'' we find the foundational material, the basic definitions and theorems. In "part II" we find the examples and applications. Slowly we begin to understand why we read part I. Historically this is an anachronism. Pedagogically it is a disaster. Part II in fact predates part I, so clearly it can be taught first. Why should the student have to wade through hundreds of pages before finding out what the subject is good for? In teaching complex analysis this way, we risk more than just boredom. Beginning with a series of unmotivated definitions gives a misleading impression of complex analy sis in particular and of mathematics in general. The classical theory of analytic functions did not arise from the idle speculation of bored mathematicians on the possible conse quences of an arbitrary set of definitions; it was the natural, even inevitable, consequence of the practical need to answer questions about specific examples. In standard texts, after hundreds of pages of theorems about generic analytic functions with only the rational and trigonometric functions as examples, students inevitably begin to believe that the purpose of complex analysis is to produce more such theorems. We require introductory com plex analysis courses of our undergraduates and graduates because it is useful both within mathematics and beyond.

A Course Of Modern Analysis

Author: E. T. Whittaker
Publisher: Cambridge University Press
ISBN: 9780521588072
Size: 49.74 MB
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This classic text has entered and held the field as the standard book on the applications of analysis to the transcendental functions. The authors explain the methods of modern analysis in the first part of the book and then proceed to a detailed discussion of the transcendental function, unhampered by the necessity of continually proving new theorems for special applications. In this way the authors have succeeded in being rigorous without imposing on the reader the mass of detail that so often tends to make a rigorous demonstration tedious. Researchers and students will find this book as valuable as ever.

Advanced Real Analysis

Author: Anthony W. Knapp
Publisher: Springer Science & Business Media
ISBN: 9780817644420
Size: 10.42 MB
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* Presents a comprehensive treatment with a global view of the subject * Rich in examples, problems with hints, and solutions, the book makes a welcome addition to the library of every mathematician

Hidden Harmony Geometric Fantasies

Author: Umberto Bottazzini
Publisher: Springer Science & Business Media
ISBN: 1461457254
Size: 14.63 MB
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​This book is a history of complex function theory from its origins to 1914, when the essential features of the modern theory were in place. It is the first history of mathematics devoted to complex function theory, and it draws on a wide range of published and unpublished sources. In addition to an extensive and detailed coverage of the three founders of the subject – Cauchy, Riemann, and Weierstrass – it looks at the contributions of authors from d’Alembert to Hilbert, and Laplace to Weyl. Particular chapters examine the rise and importance of elliptic function theory, differential equations in the complex domain, geometric function theory, and the early years of complex function theory in several variables. Unique emphasis has been devoted to the creation of a textbook tradition in complex analysis by considering some seventy textbooks in nine different languages. The book is not a mere sequence of disembodied results and theories, but offers a comprehensive picture of the broad cultural and social context in which the main actors lived and worked by paying attention to the rise of mathematical schools and of contrasting national traditions. The book is unrivaled for its breadth and depth, both in the core theory and its implications for other fields of mathematics. It documents the motivations for the early ideas and their gradual refinement into a rigorous theory.​

Geometric Analysis And Function Spaces

Author: Steven George Krantz
Publisher: American Mathematical Soc.
ISBN: 9780821889251
Size: 76.79 MB
Format: PDF
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This book brings into focus the synergistic interaction between analysis and geometry by examining a variety of topics in function theory, real analysis, harmonic analysis, several complex variables, and group actions. Krantz's approach is motivated by examples, both classical and modern, which highlight the symbiotic relationship between analysis and geometry. Creating a synthesis among a host of different topics, this book is useful to researchers in geometry and analysis and may be of interest to physicists, astronomers, and engineers in certain areas. The book is based on lectures presented at an NSF-CBMS Regional Conference held in May 1992.