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Características del artículo
- Estado
- Book Title
- Problems and Solutions for Complex Analysis
- ISBN-13
- 9780387988313
- ISBN
- 9780387988313
Acerca de este producto
Product Identifiers
Publisher
Springer New York
ISBN-10
0387988319
ISBN-13
9780387988313
eBay Product ID (ePID)
370448
Product Key Features
Number of Pages
Xi, 246 Pages
Language
English
Publication Name
Problems and Solutions for Complex Analysis
Subject
Complex Analysis, Mathematical Analysis
Publication Year
1999
Type
Textbook
Subject Area
Mathematics
Format
Trade Paperback
Dimensions
Item Height
0.2 in
Item Weight
28.9 Oz
Item Length
9.3 in
Item Width
6.1 in
Additional Product Features
Intended Audience
Scholarly & Professional
LCCN
99-013255
Dewey Edition
21
Number of Volumes
1 vol.
Illustrated
Yes
Dewey Decimal
515/.9
Table Of Content
I Complex Numbers and Functions.- I.1 Definition.- I.2 Polar Form.- I.3 Complex Valued Functions.- I.4 Limits and Compact Sets.- I.6 The Cauchy-Riemann Equations.- II Power Series.- II.1 Formal Power Series.- II.2 Convergent Power Series.- II.3 Relations Between Formal and Convergent Series.- II.4 Analytic Functions.- II.5 Differentiation of Power Series.- II.6 The Inverse and Open Mapping Theorems.- III Cauchy's Theorem, First Part.- III.1 Holomorphic Functions on Connected Sets.- III.2 Integrals over Paths.- III.5 The Homotopy Form of Cauchy's Theorem.- III.6 Existence of Global Primitives Definition of the Logarithm.- III.7 The Local Cauchy Formula.- IV Winding Numbers and Cauchy's Theorem.- IV.2 The Global Cauchy Theorem.- V Applications of Cauchy's Integral Formula.- V.1 Uniform Limits of Analytic Functions.- V.2 Laurent Series.- V.3 Isolated Singularities.- VI Calculus of Residues.- VI.1 The Residue Formula.- VI.2 Evaluation of Definite Integrals.- VII Conformal Mappings.- VII.2 Analytic Automorphisms of the Disc.- VII.3 The Upper Half Plane.- VII.4 Other Examples.- VII.5 Fractional Linear Transformations.- VIII Harmonic Functions.- VIII.1 Definition.- VIII.2 Examples.- VIII.3 Basic Properties of Harmonic Functions.- VIII.4 The Poisson Formula.- VIII.5 Construction of Harmonic Functions.- IX Schwarz Reflection.- IX.2 Reflection Across Analytic Arcs.- X The Riemann Mapping Theorema.- X.1 Statement of the Theorem.- X.2 Compact Sets in Function Spaces.- XI Analytic Continuation along Curves.- XI.1 Continuation Along a Curve.- XI.2 The Dilogarithm.- XII Applications of the Maximum Modulus Principle and Jensen's Formula.- XII.1 Jensen's Formula.- XII.2 The Picard-Borel Theorem.- XII.6 The Phragmen-Lindelof and Hadamard Theorems.- XIII Entire and MeromorphicFunctions.- XIII.1 Infinite Products.- XIII.2 Weierstrass Products.- XIII.3 Functions of Finite Order.- XIII.4 Meromorphic Functions, Mittag-Leffler Theorem.- XV The Gamma and Zeta Functions.- XV.1 The Differentiation Lemma.- XV.2 The Gamma Function.- XV.3 The Lerch Formula.- XV.4 Zeta Functions.- XVI The Prime Number Theorem.- XVI.1 Basic Analytic Properties of the Zeta Function.- XVI.2 The Main Lemma and its Application.
Synopsis
This book contains all the exercises and solutions of Serge Lang's Complex Analy- sis. Chapters I through VITI of Lang's book contain the material of an introductory course at the undergraduate level and the reader will find exercises in all of the fol- lowing topics: power series, Cauchy's theorem, Laurent series, singularities and meromorphic functions, the calculus of residues, conformal mappings and har- monic functions. Chapters IX through XVI, which are suitable for a more advanced course at the graduate level, offer exercises in the following subjects: Schwarz re- flection, analytic continuation, Jensen's formula, the Phragmen-LindelOf theorem, entire functions, Weierstrass products and meromorphic functions, the Gamma function and the Zeta function. This solutions manual offers a large number of worked out exercises of varying difficulty. I thank Serge Lang for teaching me complex analysis with so much enthusiasm and passion, and for giving me the opportunity to work on this answer book. Without his patience and help, this project would be far from complete. I thank my brother Karim for always being an infinite source of inspiration and wisdom. Finally, I want to thank Mark McKee for his help on some problems and Jennifer Baltzell for the many years of support, friendship and complicity. Rami Shakarchi Princeton, New Jersey 1999 Contents Preface vii I Complex Numbers and Functions 1 1. 1 Definition . . . . . . . . . . 1 1. 2 Polar Form . . . . . . . . . 3 1. 3 Complex Valued Functions . 8 1. 4 Limits and Compact Sets . . 9 1. 6 The Cauchy-Riemann Equations ., This book is an independent source of problems with detailed answers beneficial for anyone interested in learning complex analysis. The problems cover such topics as: power series, Cauchys theorem, Laurent series, singularities and meromorphic functions, the calculus of residues, conformal mappings, harmonic functions, and Jensens formula. All the exercises from this volume were derived from Serge Langs fourth edition of Complex Analysis and can also serve as a companion guide to it., This volume contains all the exercises, and their solutions, for Serge Lang's fourth edition of "Complex Analysis." It also serves as an independent source of problems with detailed answers beneficial for anyone interested in learning complex analysis., This book contains all the exercises and solutions of Serge Lang's Complex Analy sis. Chapters I through VITI of Lang's book contain the material of an introductory course at the undergraduate level and the reader will find exercises in all of the fol lowing topics: power series, Cauchy's theorem, Laurent series, singularities and meromorphic functions, the calculus of residues, conformal mappings and har monic functions. Chapters IX through XVI, which are suitable for a more advanced course at the graduate level, offer exercises in the following subjects: Schwarz re flection, analytic continuation, Jensen's formula, the Phragmen-LindelOf theorem, entire functions, Weierstrass products and meromorphic functions, the Gamma function and the Zeta function. This solutions manual offers a large number of worked out exercises of varying difficulty. I thank Serge Lang for teaching me complex analysis with so much enthusiasm and passion, and for giving me the opportunity to work on this answer book. Without his patience and help, this project would be far from complete. I thank my brother Karim for always being an infinite source of inspiration and wisdom. Finally, I want to thank Mark McKee for his help on some problems and Jennifer Baltzell for the many years of support, friendship and complicity. Rami Shakarchi Princeton, New Jersey 1999 Contents Preface vii I Complex Numbers and Functions 1 1. 1 Definition . . . . . . . . . . 1 1. 2 Polar Form . . . . . . . . . 3 1. 3 Complex Valued Functions . 8 1. 4 Limits and Compact Sets . . 9 1. 6 The Cauchy-Riemann Equations .
LC Classification Number
QA299.6-433
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100% de votos positivos•8,2 mil artículos vendidos
Registrado como vendedor particularPor tanto, no se aplican los derechos de los consumidores derivados de las leyes de protección de los consumidores de la UE. La Garantía al cliente de eBay sigue aplicando a la mayoría de compras. Más informaciónMás información
Votos de vendedor (3.331)
- 1***p (459)- Votos emitidos por el comprador.Últimos 6 mesesCompra verificadaArrived yesterday safe and sound and well packaged. Was placed insides a very sturdy box and a bubble mailer. Was exactly as described and what I have been looking for to replace the one that was stolen from my apartment while I was in the hospital last year. Well worth the price I paid for it. It is one of my most favorite unicorn bookmarks I own! Thank you so very, very much for having one available for purchase!Vintage 1988 Unicorn Bookmark Embroidered Taperstry Flowers Brass w/Original Box (#326471685441)
- r***e (2)- Votos emitidos por el comprador.Mes pasadoCompra verificadaCandlesticks were as described and are in perfect condition. Excellent value! The packaging was secure and shipping was fast. Seller did an awesome job with my order.
- 8***g (75)- Votos emitidos por el comprador.Mes pasadoCompra verificadaPackaging was very good, shipping price was fair, item as described, a great value. Shipping time was good. Great lamp in excellent condition. I would buy from this seller again and would definitely recommend this seller to anyone!!! AAA+++!!