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A First Course In Complex Analysis With Applications

Author: Dennis G. Zill
Publisher: Jones & Bartlett Publishers
ISBN: 1449668836
Size: 42.92 MB
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The new Second Edition of A First Course in Complex Analysis with Applications is a truly accessible introduction to the fundamental principles and applications of complex analysis. Designed for the undergraduate student with a calculus background but no prior experience with complex variables, this text discusses theory of the most relevant mathematical topics in a student-friendly manner. With Zill's clear and straightforward writing style, concepts are introduced through numerous examples and clear illustrations. Students are guided and supported through numerous proofs providing them with a higher level of mathematical insight and maturity. Each chapter contains a separate section on the applications of complex variables, providing students with the opportunity to develop a practical and clear understanding of complex analysis.

Complex Analysis

Author: Dennis G. Zill
Publisher:
ISBN:
Size: 31.82 MB
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Designed for the undergraduate student with a calculus background but no prior experience with complex analysis, this text discusses the theory of the most relevant mathematical topics in a student-friendly manner. With a clear and straightforward writing style, concepts are introduced through numerous examples, illustrations, and applications. Each section of the text contains an extensive exercise set containing a range of computational, conceptual, and geometric problems. In the text and exercises, students are guided and supported through numerous proofs providing them with a higher level of mathematical insight and maturity. Each chapter contains a separate section devoted exclusively to the applications of complex analysis to science and engineering, providing students with the opportunity to develop a practical and clear understanding of complex analysis. The Mathematica syntax from the second edition has been updated to coincide with version 8 of the software. --

A First Course In Complex Analysis With Applications

Author: Patrick D. Shanahan
Publisher: Jones & Bartlett Learning
ISBN: 9780763778347
Size: 77.46 MB
Format: PDF, Mobi
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The new Second Edition of A First Course in Complex Analysis with Applications is a truly accessible introduction to the fundamental principles and applications of complex analysis. Designed for the undergraduate student with a calculus background but no prior experience with complex variables, this text discusses theory of the most relevant mathematical topics in a student-friendly manner. With Zill's clear and straightforward writing style, concepts are introduced through numerous examples and clear illustrations. Students are guided and supported through numerous proofs providing them with a higher level of mathematical insight and maturity. Each chapter contains a separate section on the applications of complex variables, providing students with the opportunity to develop a practical and clear understanding of complex analysis.

Einf Hrung In Die Komplexe Analysis

Author: Wolfgang Fischer
Publisher: Springer-Verlag
ISBN: 3834893773
Size: 10.24 MB
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In den Bachelor-Studiengängen der Mathematik steht für die Komplexe Analysis (Funktionentheorie) oft nur eine einsemestrige 2-stündige Vorlesung zur Verfügung. Dieses Buch eignet sich als Grundlage für eine solche Vorlesung im 2. Studienjahr. Mit einer guten thematischen Auswahl, vielen Beispielen und ausführlichen Erläuterungen gibt dieses Buch eine Darstellung der Komplexen Analysis, die genau die Grundlagen und den wesentlichen Kernbestand dieses Gebietes enthält. Das Buch bietet über diese Grundausbildung hinaus weiteres Lehrmaterial als Ergänzung, sodass es auch für eine 3- oder 4 –stündige Vorlesung geeignet ist. Je nach Hörerkreis kann der Stoff unterschiedlich erweitert werden. So wurden für den „Bachelor Lehramt“ die geometrischen Aspekte der Komplexen Analysis besonders herausgearbeitet.

Funktionentheorie

Author: Eberhard Freitag
Publisher: Springer-Verlag
ISBN: 3662073498
Size: 21.52 MB
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Die komplexen Zahlen haben ihre historischen Wurzeln im 16. Jahrhundert, sie entstanden bei dem Versuch, algebmische Gleichungen zu lösen. So führte schon G. CARDANO (1545) formale Ausdrücke wie zum Beispiel 5 ± v'-15 ein, um Lösungen quadratischer und kubischer Gleichungen angeben zu können. R. BOMBELLI rechnete um 1560 bereits systematisch mit diesen Ausdrücken 3 und fand 4 als Lösung der Gleichung x = 15x + 4 in der verschlüsselten Form 4 = ~2 + v'-121 + ~2 - v'-121. Auch bei G. W. LEIBNIZ (1675) findet man Gleichungen dieser Art, wie z. B. VI + v'=3 + Vl- v'=3 = v'6. Im Jahre 1777 führte L. EULER die Bezeichnung i = A für die imaginäre Einheit ein. Der Fachausdruck "komplexe Zahl" stammt von C. F. GAUSS (1831). Die strenge Einführung der komplexen Zahlen als Paare reeller Zahlen geht auf W. R. HAMILTON (1837) zurück. Schon in der reellen Analysis ist es gelegentlich vorteilhaft, komplexe Zahlen einzuführen. Man denke beispielsweise an die Integration rationaler Funktio nen, die auf der Partialbruchentwicklung und damit auf dem Fundamentalsatz der Algebra beruht: Über dem Körper der komplexen Zahlen zerfällt jedes Polynom in ein Produkt von Linearfaktoren.

Anschauliche Funktionentheorie

Author: Tristan Needham
Publisher: Oldenbourg Wissenschaftsverlag
ISBN: 9783486709025
Size: 27.13 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 M. Howie
Publisher: Springer Science & Business Media
ISBN: 1447100271
Size: 21.26 MB
Format: PDF
View: 2010
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Complex analysis can be a difficult subject and many introductory texts are just too ambitious for today’s students. This book takes a lower starting point than is traditional and concentrates on explaining the key ideas through worked examples and informal explanations, rather than through "dry" theory.

Invitation To Complex Analysis

Author: Ralph P. Boas
Publisher: MAA
ISBN: 0883857642
Size: 35.86 MB
Format: PDF, Kindle
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An ideal choice for a first course in complex analysis, this book can be used either as a classroom text or for independent study. Written in an informal style by a master expositor, the book distills more than half a century of experience with the subject into a lucid, engaging, yet rigorous account. The book reveals both the power of complex analysis as a tool for applications and the intrinsic beauty of the subject as a fundamental part of pure mathematics. Written at the level of courses commonly taught in American universities to seniors and beginning graduate students, the book is suitable for readers acquainted with advanced calculus or introductory real analysis. The treatment goes beyond the standard material of power series, Cauchy's theorem, residues, conformal mapping, and harmonic functions by including accessible discussions of many intriguing topics that are uncommon in a book at this level. Readers will encounter notions ranging from Landau's notation to overconvergent series to the Phragmén-Lindelöf theorem. The flexibility afforded by the supplementary topics and applications makes the book adaptable either to a short, one-term course or to a comprehensive, full-year course.The writing is user-friendly in many ways. Each topic is discussed in a typical, commonly encountered situation rather than in the most general, abstract setting. There are no numbered equations. Numerous exercises interspersed in the text encourage readers to test their understanding of new concepts and techniques as they are presented. Detailed solutions of the exercises, included at the back of the book, both serve as models for students and facilitate independent study. Supplementary exercises at the ends of sections, not solved in the book, provide an additional teaching tool.This second edition of Invitation to Complex Analysis has been painstakingly revised by the author's son, himself an award-winning mathematical expositor.

A Complex Analysis Problem Book

Author: Daniel Alpay
Publisher: Birkhäuser
ISBN: 3319421816
Size: 39.72 MB
Format: PDF, Mobi
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This second edition presents a collection of exercises on the theory of analytic functions, including completed and detailed solutions. It introduces students to various applications and aspects of the theory of analytic functions not always touched on in a first course, while also addressing topics of interest to electrical engineering students (e.g., the realization of rational functions and its connections to the theory of linear systems and state space representations of such systems). It provides examples of important Hilbert spaces of analytic functions (in particular the Hardy space and the Fock space), and also includes a section reviewing essential aspects of topology, functional analysis and Lebesgue integration. Benefits of the 2nd edition Rational functions are now covered in a separate chapter. Further, the section on conformal mappings has been expanded.