| 000 -LEADER |
|---|
| fixed length control field |
06368cam a2200325 i 4500 |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
|---|
| control field |
20260624163616.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
|---|
| fixed length control field |
260626s2022 flua b 001 0 eng |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
|---|
| International Standard Book Number |
9781032102726 |
| 041 ## - LANGUAGE CODE |
|---|
| Language code of text/sound track or separate title |
eng |
| 050 00 - LIBRARY OF CONGRESS CALL NUMBER |
|---|
| Classification number |
QA331.5 |
| Item number |
.K7134 2022 |
| 082 00 - DEWEY DECIMAL CLASSIFICATION NUMBER |
|---|
| Classification number |
515/.8 |
| Edition number |
23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
|---|
| Preferred name for the person |
Krantz, Steven G. |
| Fuller form of name |
(Steven George), |
| Dates associated with a name |
1951- |
| 245 10 - TITLE STATEMENT |
|---|
| Title |
Real analysis and foundations / |
| Statement of responsibility, etc |
Steven G. Krantz. |
| 250 ## - EDITION STATEMENT |
|---|
| Edition statement |
Fifth edition. |
| 264 #1 - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
|---|
| Place of publication, distribution, etc |
Boca Raton : |
| Name of publisher, distributor, etc |
CRC Press, Taylor & Francis Group, |
| Date of publication, distribution, etc |
2022 |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
xiv, 484 pages : |
| Other physical details |
illustrations ; |
| Dimensions |
24 cm |
| 336 ## - CONTENT TYPE |
|---|
| Content type term |
text |
| Content type code |
txt |
| Source |
rdacontent |
| 337 ## - MEDIA TYPE |
|---|
| Media type term |
unmediated |
| Media type code |
n |
| Source |
rdamedia |
| 338 ## - CARRIER TYPE |
|---|
| Carrier type term |
volume |
| Carrier type code |
nc |
| Source |
rdacarrier |
| 490 0# - SERIES STATEMENT |
|---|
| Series statement |
Textbooks in mathematics |
| 500 ## - GENERAL NOTE |
|---|
| General note |
"A Chapman & Hall book." |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
|---|
| Bibliography, etc |
Includes bibliographical references and index. |
| 505 0# - CONTENTS |
|---|
| Formatted contents note |
Preface<br/><br/>0 Background Material<br/>0.1 Number Systems<br/>0.1.1 The Natural Numbers<br/>0.1.2 The Integers<br/>0.1.3 The Rational Numbers<br/><br/>02 Logic and Set<br/>0.2.1 And” and “Or”<br/>0.2.2 “not” and “if then”<br/>0.2.3 Contrapositive, Converse, and “Iff”<br/>0.2.4 Quantifiers<br/>0.2.5 Set Theory and Venn Diagrams<br/>0.2.6 Relations and Functions<br/>0.2.7 Countable and Uncountable Sets<br/><br/>1 Real and Complex Numbers<br/>1.1 The Real Numbers<br/>Appendix: Construction of the Real Numbers<br/>1.2 The Complex Numbers<br/>2 Sequences 71<br/>2.1 Convergence of Sequences<br/>2.2 Subsequences<br/>2.3 Limsup and Liminf<br/>2.4 Some Special Sequences<br/><br/>3 Series of Numbers<br/>3.1 Convergence of Series<br/>3.2 Elementary Convergence Tests<br/>3.3 Advanced Convergence Tests<br/>3.4 Some Special Series<br/>3.5 Operations on Series<br/><br/>4 Basic Topology<br/>4.1 Open and Closed Sets<br/>4.2 Further Properties of Open and Closed Sets<br/>4.3 Compact Sets<br/>4.4 The Cantor Set<br/>4.5 Connected and Disconnected Sets<br/>4.6 Perfect Sets<br/><br/>5 Limits and Continuity of Functions<br/>5.1 Basic Properties of the Limit of a Function<br/>5.2 Continuous Functions<br/>5.3 Topological Properties and Continuity<br/>5.4 Classifying Discontinuities and Monotonicity<br/><br/>6 Differentiation of Functions<br/>6.1 The Concept of Derivative<br/>6.2 The Mean Value Theorem and Applications<br/>6.3 More on the Theory of Differentiation<br/><br/>7 The Integral<br/>7.1 Partitions and the Concept of Integral<br/>7.2 Properties of the Riemann Integral<br/>7.3 Change of Variable and Related Ideas<br/>7.4 Another Look at the Integral<br/>7.5 Advanced Results on Integration Theory<br/><br/>8 Sequences and Series of Functions<br/>8.1 Partial Sums and Pointwise Convergence<br/>8.2 More on Uniform Convergence<br/>8.3 Series of Functions<br/>8.4 The Weierstrass Approximation Theorem<br/><br/>9 Elementary Transcendental Functions<br/>9.1 Power Series<br/>9.2 More on Power Series: Convergence Issues<br/>9.3 The Exponential and Trigonometric Functions<br/>9.4 Logarithms and Powers of Real Numbers<br/><br/>10 Functions of Several Variables<br/>10.1 A New Look at the Basic Concepts of Analysis<br/>10.2 Properties of the Derivative<br/>10.3 The Inverse and Implicit Function Theorems<br/><br/>11 Advanced Topics<br/>11.1 Metric Spaces<br/>11.2 Topology in a Metric Space<br/>11.3 The Baire Category Theorem<br/>11.4 The Ascoli-Arzela Theorem<br/><br/>12 Differential Equations<br/>12.1 Picard’s Existence and Uniqueness Theorem<br/>12.1.1 The Form of a Differential Equation<br/>12.1.2 Picard’s Iteration Technique<br/>12.1.3 Some Illustrative Examples<br/>12.1.4 Estimation of the Picard Iterates<br/>12.2 Power Series Methods<br/><br/>13 Introduction to Harmonic Analysis<br/>13.1 The Idea of Harmonic Analysis<br/>13.2 The Elements of Fourier Series<br/>13.3 An Introduction to the Fourier Transform<br/>Appendix: Approximation by Smooth Functions<br/>13.4 Fourier Methods and Differential Equations<br/>13.4.1 Remarks on Different Fourier Notations<br/>13.4.2 The Dirichlet Problem on the Disc<br/>13.4.3 Introduction to the Heat and Wave Equations<br/>13.4.4 Boundary Value Problems<br/>13.4.5 Derivation of the Wave Equation<br/>13.4.6 Solution of the Wave Equation<br/>13.5 The Heat Equation<br/><br/>Appendix: Review of Linear Algebra<br/>Table of Notation<br/>Glossary<br/>Bibliography<br/>Index |
| 520 ## - SUMMARY, ETC. |
|---|
| Summary, etc |
Through four editions this popular textbook attracted a loyal readership and widespread use. Students find the book to be concise, accessible, and complete. Instructors find the book to be clear, authoritative, and dependable.<br/><br/>The primary goal of this new edition remains the same as in previous editions. It is to make real analysis relevant and accessible to a broad audience of students with diverse backgrounds while also maintaining the integrity of the course. This text aims to be the generational touchstone for the subject and the go-to text for developing young scientists.<br/><br/>This new edition continues the effort to make the book accessible to a broader audience. Many students who take a real analysis course do not have the ideal background. The new edition offers chapters on background material like set theory, logic, and methods of proof. The more advanced material in the book is made more apparent.<br/><br/>This new edition offers a new chapter on metric spaces and their applications. Metric spaces are important in many parts of the mathematical sciences, including data mining, web searching, and classification of images.<br/><br/>The author also revised the material on sequences and series adding examples and exercises that compare convergence tests and give additional tests.<br/><br/>The text includes rare topics such as wavelets and applications to differential equations. The level of difficulty moves slowly, becoming more sophisticated in later chapters. Students have commented on the progression as a favorite aspect of the textbook.<br/><br/>The author is perhaps the most prolific expositor of upper division mathematics. With over seventy books in print, thousands of students have been taught and learned from his books. |
| Assigning source |
Provided by the publisher. |
| 545 0# - BIOGRAPHICAL OR HISTORICAL DATA |
|---|
| Biographical or historical note |
Biography<br/><br/>Steven G. Krantz is a professor of mathematics at Washington University in St. Louis. He has previously taught at UCLA, Princeton University, and Pennsylvania State University. He has written more than 130 books and more than 250 scholarly papers and is the founding editor of the Journal of Geometric Analysis. An AMS Fellow, Dr. Krantz has been a recipient of the Chauvenet Prize, Beckenbach Book Award, and Kemper Prize. He received a Ph.D. from Princeton University. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Functions of real variables. |
| 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 |
Numbers, Real. |
| 942 ## - ADDED ENTRY ELEMENTS |
|---|
| Source of classification or shelving scheme |
|
| Item type |
BOOK |