Complex Analysis

AvSerge Lang

Inbunden, Engelska, 1998

Del i serien Graduate Texts in Mathematics

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Beskrivning

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. The first part of Complex Analysis is suitable for an introductory course on the undergraduate level, and the additional topics covered in the second part give the instructor of a graduate course a great deal of flexibility in structuring a more advanced course. This is a revised edition, new examples and exercises have been added, and many minor improvements have been made throughout the text.

Produktinformation

Utgivningsdatum:1998-12-07
Mått:155 x 235 x 37 mm
Vikt:894 g
Format:Inbunden
Språk:Engelska
Serie:Graduate Texts in Mathematics
Antal sidor:489
Upplaga:4
Förlag:Springer-Verlag New York Inc.
ISBN:9780387985923

Utforska kategorier

Beräkning och matematisk analys inom Naturvetenskap och teknik

Recensioner i media

"The very understandable style of explanation, which is typical for this author, makes the book valuable for both students and teachers." EMS Newsletter, Vol. 37, Sept. 2000 Fourth Edition S. Lang Complex Analysis "A highly recommendable book for a two semester course on complex analysis." -ZENTRALBLATTMATH

Innehållsförteckning

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.