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Complex Analysis: Fundamentals of the Classical Theory of Functions (Modern Birkhäuser Classics) - Softcover
Inhaltsangabe
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.
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This clear, concise introduction to the classical theory of one complex variable is based on the premise that "anything worth doing is worth doing with interesting examples." The content is driven by techniques and examples rather than definitions and theorems. This self-contained monograph is an excellent resource for a self-study guide and should appeal to a broad audience. The only prerequisite is a standard calculus course.
The first chapter deals with a beautiful presentation of special functions. . . . The third chapter covers elliptic and modular functions. . . in much more detail, and from a different point of view, than one can find in standard introductory books. . . . For [the] subjects that are omitted, the author has suggested some excellent references for the reader who wants to go through these topics. The book is read easily and with great interest. It can be recommended to both students as a textbook and to mathematicians and physicists as a useful reference. ---Mathematical Reviews
Mainly original papers are cited to support the historical remarks. The book is well readable. ---Zentralblatt für Mathematik
This is an unusual textbook, incorporating material showing how classical function theory can be used. . . . The general scheme is to show the reader how things were developed without following the traditional approach of most books on functional theory. . . . This book can be recommended to those who like to see applications of the theory taught in classical courses. ---EMS
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Complex Analysis: Fundamentals of the Classical Theory of Functions
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Zustand: New. Brand New. Soft Cover International Edition. Different ISBN and Cover Image. Priced lower than the standard editions which is usually intended to make them more affordable for students abroad. The core content of the book is generally the same as the standard edition. The country selling restrictions may be printed on the book but is no problem for the self-use. This Item maybe shipped from US or any other country as we have multiple locations worldwide. Artikel-Nr. ABNR-241707
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Complex Analysis: Fundamentals of the Classical Theory of Functions (Modern Birkhäuser Classics)
Anbieter: Ria Christie Collections, Uxbridge, Vereinigtes Königreich
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Complex Analysis
Verlag:
Birkhäuser Boston, Birkhäuser Boston Okt 2009, 2009
ISBN 10: 0817649182
ISBN 13: 9780817649180
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Taschenbuch. Zustand: Neu. Neuware -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.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 244 pp. Englisch. Artikel-Nr. 9780817649180
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Complex Analysis : Fundamentals of the Classical Theory of Functions
Anbieter: AHA-BUCH GmbH, Einbeck, Deutschland
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Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Artikel-Nr. 9780817649180
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