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20140310151445.0 |
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121120s2013 xxu| s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
|---|
| International Standard Book Number |
9781441973238 |
|
978-1-4419-7323-8 |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
|---|
| Classification number |
QA331-355 |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
|---|
| Classification number |
515.9 |
| Edition number |
23 |
| 264 #1 - |
|---|
| -- |
New York, NY : |
| -- |
Springer New York : |
| -- |
Imprint: Springer, |
| -- |
2013. |
| 912 ## - |
|---|
| -- |
ZDB-2-SMA |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
|---|
| Personal name |
Rodríguez, Rubí E. |
| Relator term |
author. |
| 245 10 - IMMEDIATE SOURCE OF ACQUISITION NOTE |
|---|
| Title |
Complex Analysis |
| Medium |
[electronic resource] : |
| Remainder of title |
In the Spirit of Lipman Bers / |
| Statement of responsibility, etc |
by Rubí E. Rodríguez, Irwin Kra, Jane P. Gilman. |
| 250 ## - EDITION STATEMENT |
|---|
| Edition statement |
2nd ed. 2013. |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
XVIII, 306 p. 27 illus. |
| Other physical details |
online resource. |
| 440 1# - SERIES STATEMENT/ADDED ENTRY--TITLE |
|---|
| Title |
Graduate Texts in Mathematics, |
| International Standard Serial Number |
0072-5285 ; |
| Volume number/sequential designation |
245 |
| 505 0# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
Preface to Second Edition -- Preface to First Edition -- Standard Notation and Commonly Used Symbols -- 1 The Fundamental Theorem in Complex Function Theory -- 2 Foundations -- 3 Power Series -- 4 The Cauchy Theory - A Fundamental Theorem -- 5 The Cauchy Theory - Key Consequences -- 6 Cauchy Theory: Local Behavior and Singularities of Holomorphic Functions -- 7 Sequences and Series of Holomorphic Functions -- 8 Conformal Equivalence and Hyperbolic Geometry -- 9 Harmonic Functions -- 10 Zeros of Holomorphic Functions -- Bibliographical Notes -- Bibliography -- Index. |
| 520 ## - SUMMARY, ETC. |
|---|
| Summary, etc |
This book is intended for a graduate course in complex analysis, where the main focus is the theory of complex-valued functions of a single complex variable. This theory is a prerequisite for the study of many areas of mathematics, including the theory of several finitely and infinitely many complex variables, hyperbolic geometry, two- and three-manifolds, and number theory. Complex analysis has connections and applications to many other subjects in mathematics and to other sciences. Thus this material will also be of interest to computer scientists, physicists, and engineers. The book covers most, if not all, of the material contained in Lipman Bers’s courses on first year complex analysis. In addition, topics of current interest, such as zeros of holomorphic functions and the connection between hyperbolic geometry and complex analysis, are explored. In addition to many new exercises, this second edition introduces a variety of new and interesting topics. New features include a section on Bers's theorem on isomorphisms between rings of holomorphic functions on plane domains; necessary and sufficient conditions for the existence of a bounded analytic function on the disc with prescribed zeros; sections on subharmonic functions and Perron's principle; and a section on the ring of holomorphic functions on a plane domain. There are three new appendices: the first is a contribution by Ranjan Roy on the history of complex analysis, the second contains background material on exterior differential calculus, and the third appendix includes an alternate approach to the Cauchy theory. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Mathematics. |
|
|---|
| Topical term or geographic name as entry element |
Functions of complex variables. |
|
|---|
| Topical term or geographic name as entry element |
Mathematics. |
|
|---|
| Topical term or geographic name as entry element |
Functions of a Complex Variable. |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
|---|
| Personal name |
Kra, Irwin. |
| Relator term |
author. |
|
|---|
| Personal name |
Gilman, Jane P. |
| Relator term |
author. |
| 710 2# - ADDED ENTRY--CORPORATE NAME |
|---|
| Corporate name or jurisdiction name as entry element |
SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY |
|---|
| Title |
Springer eBooks |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
|---|
| Display text |
Printed edition: |
| International Standard Book Number |
9781441973221 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
|---|
| Uniform Resource Identifier |
http://dx.doi.org/10.1007/978-1-4419-7323-8 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
|---|
| Source of classification or shelving scheme |
|
| Item type |
E-Book |
