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Complex Analysis
Buch 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
One Basic Theory.- I Complex Numbers and Functions.- II Power Series.- III Cauchy's Theorem, First Part.- IV Winding Numbers and Cauchy's Theorem.- V Applications of Cauchy's integral Formula.- VI Calculus of Residues.- VII Conformal Mappings.- VIII Harmonic Functions.- Two Geometric Function Theory.- IX Schwarz Reflection.- X The Riemann Mapping Theorem.- XI Analytic Continuation Along Curves.- Three Various Analytic Topics.- XII Applications of the Maximum Modulus Principle and Jensen's Formula.- XIII Entire and Meromorphic Functions.- XIV Elliptic Functions.- XV The Gamma and Zeta Functions.- XVI The Prime Number Theorem.- §1. Summation by Parts and Non-Absolute Convergence.- §2. Difference Equations.- §3. Analytic Differential Equations.- §4. Fixed Points of a Fractional Linear Transformation.- §6. Cauchy's Theorem for Locally Integrable Vector Fields.- §7. More on Cauchy-Riemann.
Details
Erscheinungsjahr: 1998
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 508
Reihe: Graduate Texts in Mathematics
Inhalt: xiv
489 S.
ISBN-13: 9780387985923
ISBN-10: 0387985921
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Lang, Serge
Auflage: 4th ed. 1999
Hersteller: Springer US
Springer New York
Graduate Texts in Mathematics
Maße: 241 x 160 x 33 mm
Von/Mit: Serge Lang
Erscheinungsdatum: 07.12.1998
Gewicht: 0,922 kg
preigu-id: 104632991
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
One Basic Theory.- I Complex Numbers and Functions.- II Power Series.- III Cauchy's Theorem, First Part.- IV Winding Numbers and Cauchy's Theorem.- V Applications of Cauchy's integral Formula.- VI Calculus of Residues.- VII Conformal Mappings.- VIII Harmonic Functions.- Two Geometric Function Theory.- IX Schwarz Reflection.- X The Riemann Mapping Theorem.- XI Analytic Continuation Along Curves.- Three Various Analytic Topics.- XII Applications of the Maximum Modulus Principle and Jensen's Formula.- XIII Entire and Meromorphic Functions.- XIV Elliptic Functions.- XV The Gamma and Zeta Functions.- XVI The Prime Number Theorem.- §1. Summation by Parts and Non-Absolute Convergence.- §2. Difference Equations.- §3. Analytic Differential Equations.- §4. Fixed Points of a Fractional Linear Transformation.- §6. Cauchy's Theorem for Locally Integrable Vector Fields.- §7. More on Cauchy-Riemann.
Details
Erscheinungsjahr: 1998
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 508
Reihe: Graduate Texts in Mathematics
Inhalt: xiv
489 S.
ISBN-13: 9780387985923
ISBN-10: 0387985921
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Lang, Serge
Auflage: 4th ed. 1999
Hersteller: Springer US
Springer New York
Graduate Texts in Mathematics
Maße: 241 x 160 x 33 mm
Von/Mit: Serge Lang
Erscheinungsdatum: 07.12.1998
Gewicht: 0,922 kg
preigu-id: 104632991
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