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Introduction to real analysis / (Record no. 2183)

000 -LEADER
fixed length control field 03983cam a22003494a 4500
001 - CONTROL NUMBER
control field 16513689
003 - CONTROL NUMBER IDENTIFIER
control field BD-DhUL
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20220619201112.0
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 101022s2011 njua b 001 0 eng
010 ## - LIBRARY OF CONGRESS CONTROL NUMBER
LC control number 2010045251
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9780471433316 (hardback)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 0471433314 (hardback)
035 ## - SYSTEM CONTROL NUMBER
System control number (OCoLC)ocn671573454
040 ## - CATALOGING SOURCE
Original cataloging agency DLC
Transcribing agency DLC
Modifying agency YDX
-- YDXCP
-- BWX
-- CUS
-- CDX
-- IUL
-- DLC
-- BD-DhUL
042 ## - AUTHENTICATION CODE
Authentication code pcc
050 00 - LIBRARY OF CONGRESS CALL NUMBER
Classification number QA300
Item number .B294 2011
082 00 - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 515
Edition number 22
Item number BAI
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Bartle, Robert Gardner,
Dates associated with a name 1927-
245 10 - TITLE STATEMENT
Title Introduction to real analysis /
Statement of responsibility, etc. Robert G. Bartle, Donald R. Sherbert.
250 ## - EDITION STATEMENT
Edition statement 4th ed.
260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT)
Place of publication, distribution, etc. Hoboken, NJ :
Name of publisher, distributor, etc. Wiley,
Date of publication, distribution, etc. c2011.
300 ## - PHYSICAL DESCRIPTION
Extent xiii, 402 p. :
Other physical details ill. ;
Dimensions 26 cm.
504 ## - BIBLIOGRAPHY, ETC. NOTE
Bibliography, etc Includes bibliographical references and index.
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note Ch. 1.Preliminaries: 1.1. Sets and functions; 1.2. Mathematical induction; 1.3. Finite and infinite sets -- Ch. 2. The Real Numbers: 2.1. The algebraic and order properties of R; 2.2. Absolute value and real line; 2.3. The completeness property of R; 2.4. Applications of the supremum property; 2.5. Intervals -- Ch. 3. Sequences and series: 3.1. Sequences and their limits; 3.2. Limit theorems; 3.3. Monotone sequences; 3.4. Subsequences and the Bolzano-Weierstrass theorem; 3.5. The Cauchy criterion; 3.6. Properly divergent sequences; 3.7. Introduction to infinite series -- Ch. 4. Limits: 4.1. Limits of functions; 4.2. Limit theorems; 4.3. Some extensions of the limit concept -- Ch. 5. Continuous functions: 5.1. Continuous runctions; 5.2 . Combinations of continuous runctions; 5.3. Continuous functions on intervals; 5.4. Uniform continuity; 5.5. Continuity and gauges; 5.6. Monotone and inverse functions -- Ch. 6. Differentiation: 6.1. The derivative; 6.2. The mean value theorem; 6.3. L'Hospital's rules; 6.4. Taylor's Theorem -- Ch. 7. The Riemann integral: 7.1. Riemann integral; 7.2. Riemann integrable functions; 7.3. The fundamental theorem; 7.4. The Darboux integral; 7.5. Approximate integration -- Ch. 8. Sequences of functions: 8.1. Pointwise and uniform convergence; 8.2. Interchange of limits; 8.3. The exponential and logarithmic functions; 8.4. The trigonometric functions -- Ch. 9. Infinite series: 9.1. Absolute convergence; 9.2. Tests for absolute convergence; 9.3. Tests for nonabsolute convergence; 9.4. Series of functions -- Ch. 10. The generalized Riemann integral: 10.1. Definition and main poperties; 10.2. Improper and Lebesgue integrals; 10.3. Infinite intervals; 10.4. Convergence theorems -- Ch. 11. A glimpse into topology: 11.1. Open and closed sets in R; 11.2 Compact sets; 11.3. Continuous functions; 11.4. Metrtic Spaces -- Appendix A. Logic and proofs -- Appendix B. Finite and countable sets -- Appendix C. The Riemann and Lebesgue criteria -- Appendix D. Approximate integration -- Appendix E. Two examples.
520 ## - SUMMARY, ETC.
Summary, etc. "This text provides the fundamental concepts and techniques of real analysis for students in all of these areas. It helps one develop the ability to think deductively, analyse mathematical situations and extend ideas to a new context. Like the first three editions, this edition maintains the same spirit and user-friendly approach with addition examples and expansion on Logical Operations and Set Theory. There is also content revision in the following areas: introducing point-set topology before discussing continuity, including a more thorough discussion of limsup and limimf, covering series directly following sequences, adding coverage of Lebesgue Integral and the construction of the reals, and drawing student attention to possible applications wherever possible"--
Assigning source Provided by publisher.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Mathematical analysis.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Functions of real variables.
700 1# - ADDED ENTRY--PERSONAL NAME
Personal name Sherbert, Donald R.,
Dates associated with a name 1935-
906 ## - LOCAL DATA ELEMENT F, LDF (RLIN)
a 7
b cbc
c orignew
d 1
e ecip
f 20
g y-gencatlg
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Source of classification or shelving scheme
Koha item type Books

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