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Cover: 9781441931351 | Complex Analysis | Serge Lang | Taschenbuch | xiv | Englisch | 2010
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Complex Analysis
Taschenbuch von Serge Lang
Sprache: Englisch

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Beschreibung
The present book is meant as a text for a course on complex analysis at the advanced undergraduate level, or first-year graduate level. The first half, more or less, can be used for a one-semester course addressed to undergraduates. The second half can be used for a second semester, at either level. Somewhat more material has been included than can be covered at leisure in one or two terms, to give opportunities for the instructor to exercise individual taste, and to lead the course in whatever directions strikes the instructor's fancy at the time as well as extra read­ ing material for students on their own. A large number of routine exer­ cises are included for the more standard portions, and a few harder exercises of striking theoretical interest are also included, but may be omitted in courses addressed to less advanced students. In some sense, I think the classical German prewar texts were the best (Hurwitz-Courant, Knopp, Bieberbach, etc. ) and I would recommend to anyone to look through them. More recent texts have emphasized connections with real analysis, which is important, but at the cost of exhibiting succinctly and clearly what is peculiar about complex analysis: the power series expansion, the uniqueness of analytic continuation, and the calculus of residues.
The present book is meant as a text for a course on complex analysis at the advanced undergraduate level, or first-year graduate level. The first half, more or less, can be used for a one-semester course addressed to undergraduates. The second half can be used for a second semester, at either level. Somewhat more material has been included than can be covered at leisure in one or two terms, to give opportunities for the instructor to exercise individual taste, and to lead the course in whatever directions strikes the instructor's fancy at the time as well as extra read­ ing material for students on their own. A large number of routine exer­ cises are included for the more standard portions, and a few harder exercises of striking theoretical interest are also included, but may be omitted in courses addressed to less advanced students. In some sense, I think the classical German prewar texts were the best (Hurwitz-Courant, Knopp, Bieberbach, etc. ) and I would recommend to anyone to look through them. More recent texts have emphasized connections with real analysis, which is important, but at the cost of exhibiting succinctly and clearly what is peculiar about complex analysis: the power series expansion, the uniqueness of analytic continuation, and the calculus of residues.
Zusammenfassung
This is the fourth edition of Serge Lang's Complex Analysis. The
first part of the book covers the basic material of complex analysis,
and the second covers many special topics, such as the Riemann Mapping
Theorem, the gamma function, and analytic continuation. Power series
methods are used more systematically than in other texts, and the
proofs using these methods often shed more light on the results than
the standard proofs do.
Inhaltsverzeichnis
I: BASIC THEORY. 1: Complex Numbers and Functions. 2: Power Series. 3: Cauchy's Theorem, First Part. 4: Winding Numbers and Cauchy's Theorem. 5: Applications of Cauchy's Integral Formula. 6: Calculus of Residues. 7: Conformal Mappings. 8: Harmonic Functions. II: GEOMETRIC FUNCTION THEORY. 9: Schwarz Reflection. 10: The Riemann Mapping Theorem. 11: Analytic Continuation Along Curves. III: VARIOUS ANALYTIC TOPICS. 12: Applications of the Maximum Modulus Principle and Jensen's Formula. 13: Entire and Meromorphic Functions. 14: Elliptic Functions. 15: The Gamma and Zeta Functions. 16: The Prime Number Theorem.
Details
Erscheinungsjahr: 2010
Fachbereich: Analysis
Genre: Importe, Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: xiv
489 S.
ISBN-13: 9781441931351
ISBN-10: 144193135X
Sprache: Englisch
Einband: Kartoniert / Broschiert
Autor: Lang, Serge
Auflage: Softcover reprint of hardcover 4th edition 1999
Hersteller: Springer US
Springer New York
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 235 x 155 x 28 mm
Von/Mit: Serge Lang
Erscheinungsdatum: 19.11.2010
Gewicht: 0,762 kg
Artikel-ID: 107152377
Zusammenfassung
This is the fourth edition of Serge Lang's Complex Analysis. The
first part of the book covers the basic material of complex analysis,
and the second covers many special topics, such as the Riemann Mapping
Theorem, the gamma function, and analytic continuation. Power series
methods are used more systematically than in other texts, and the
proofs using these methods often shed more light on the results than
the standard proofs do.
Inhaltsverzeichnis
I: BASIC THEORY. 1: Complex Numbers and Functions. 2: Power Series. 3: Cauchy's Theorem, First Part. 4: Winding Numbers and Cauchy's Theorem. 5: Applications of Cauchy's Integral Formula. 6: Calculus of Residues. 7: Conformal Mappings. 8: Harmonic Functions. II: GEOMETRIC FUNCTION THEORY. 9: Schwarz Reflection. 10: The Riemann Mapping Theorem. 11: Analytic Continuation Along Curves. III: VARIOUS ANALYTIC TOPICS. 12: Applications of the Maximum Modulus Principle and Jensen's Formula. 13: Entire and Meromorphic Functions. 14: Elliptic Functions. 15: The Gamma and Zeta Functions. 16: The Prime Number Theorem.
Details
Erscheinungsjahr: 2010
Fachbereich: Analysis
Genre: Importe, Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: xiv
489 S.
ISBN-13: 9781441931351
ISBN-10: 144193135X
Sprache: Englisch
Einband: Kartoniert / Broschiert
Autor: Lang, Serge
Auflage: Softcover reprint of hardcover 4th edition 1999
Hersteller: Springer US
Springer New York
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 235 x 155 x 28 mm
Von/Mit: Serge Lang
Erscheinungsdatum: 19.11.2010
Gewicht: 0,762 kg
Artikel-ID: 107152377
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