Verfügbarkeit: Introduction to real analysis | Technische Universität München

Introduction to real analysis:

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Bibliographische Detailangaben
Beteiligte Personen:	Bartle, Robert G. (VerfasserIn), Sherbert, Donald R. (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	New York [u.a.] Wiley 2000
Ausgabe:	3. ed.
Schlagwörter:	Analyse mathématique Análise real Fonctions de variables réelles Matemática Functions of real variables Mathematical analysis Analysis Reelle Analysis Einführung
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009001649&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	XI, 388 S. graph. Darst.
ISBN:	0471321486

Internformat

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Datensatz im Suchindex

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adam_text	Titel: Introduction to real analysis Autor: Bartle, Robert G Jahr: 2000 CONTENTS CHAPTER 1 PRELIMINARIES 1 1.1 Sets and Functions 1 1.2 Mathematical Induction 12 1 .3 Finite and Infinite Sets 16 CHAPTER 2 THE REAL NUMBERS 22 2.1 The Algebraic and Order Properties of R 22 2.2 Absolute Value and Real Line 31 2.3 The Completeness Property of R 34 2.4 Applications of the Supremum Property 38 2.5 Intervals 44 CHAPTER 3 SEQUENCES AND SERIES 52 3.1 Sequences and Their Limits 53 3.2 Limit Theorems 60 3.3 Monotone Sequences 68 3.4 Subsequences and the Bolzano-Weierstrass Theorem 75 3.5 The Cauchy Criterion 80 3.6 Properly Divergent Sequences 86 3.7 Introduction to Series 89 CHAPTER 4 LIMITS 96 4.1 Limits of Functions 97 4.2 Limit Theorems 105 4.3 Some Extensions of the Limit Concept 111 CHAPTER 5 CONTINUOUS FUNCTIONS 119 5.1 Continuous Functions 120 5.2 Combinations of Continuous Functions 125 5.3 Continuous Functions on Intervals 129 5.4 Uniform Continuity 136 5.5 Continuity and Gauges 145 5.6 Monotone and Inverse Functions 149 ix x CONTENTS CHAPTER 6 DIFFERENTIATION 157 6.1 The Derivative 158 6.2 The Mean Value Theorem 168 6.3 L Hospital Rules 176 6.4 Taylor s Theorem 183 CHAPTER 7 THE RIEMANN INTEGRAL 193 7.1 The Riemann Integral 194 7.2 Riemann Integrable Functions 202 7.3 The Fundamental Theorem 210 7.4 Approximate Integration 219 CHAPTER 8 SEQUENCES OF FUNCTIONS 227 8.1 Pointwise and Uniform Convergence 227 8.2 Interchange of Limits 233 8.3 The Exponential and Logarithmic Functions 239 8.4 The Trigonometric Functions 246 CHAPTER 9 INFINITE SERIES 253 9.1 Absolute Convergence 253 9.2 Tests for Absolute Convergence 257 9.3 Tests for Nonabsolute Convergence 263 9.4 Series of Functions 266 CHAPTER 10 THE GENERALIZED RIEMANN INTEGRAL 274 10.1 Definition and Main Properties 275 10.2 Improper and Lebesgue Integrals 287 10.3 Infinite Intervals 294 10.4 Convergence Theorems 301 CHAPTER 11 A GLIMPSE INTO TOPOLOGY 312 11.1 Open and Closed Sets in R 312 11.2 Compact Sets 319 11.3 Continuous Functions 323 11.4 Metric Spaces 327 APPENDIX A APPENDIX B APPENDIX C LOGIC AND PROOFS 334 FINITE AND COUNTABLE SETS 343 THE RIEMANN AND LEBESGUE CRITERIA 347 APPENDIX D APPROXIMATE INTEGRATION 351 APPENDIX E TWO EXAMPLES 354 REFERENCES 357 PHOTO CREDITS 358 HINTS FOR SELECTED EXERCISES 359 INDEX 381
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spellingShingle	Bartle, Robert G. Sherbert, Donald R. Introduction to real analysis Analyse mathématique Análise real larpcal Fonctions de variables réelles Matemática larpcal Functions of real variables Mathematical analysis Analysis (DE-588)4001865-9 gnd Reelle Analysis (DE-588)4627581-2 gnd
subject_GND	(DE-588)4001865-9 (DE-588)4627581-2 (DE-588)4151278-9
title	Introduction to real analysis
title_auth	Introduction to real analysis
title_exact_search	Introduction to real analysis
title_full	Introduction to real analysis Robert G. Bartle ; Donald R. Sherbert
title_fullStr	Introduction to real analysis Robert G. Bartle ; Donald R. Sherbert
title_full_unstemmed	Introduction to real analysis Robert G. Bartle ; Donald R. Sherbert
title_short	Introduction to real analysis
title_sort	introduction to real analysis
topic	Analyse mathématique Análise real larpcal Fonctions de variables réelles Matemática larpcal Functions of real variables Mathematical analysis Analysis (DE-588)4001865-9 gnd Reelle Analysis (DE-588)4627581-2 gnd
topic_facet	Analyse mathématique Análise real Fonctions de variables réelles Matemática Functions of real variables Mathematical analysis Analysis Reelle Analysis Einführung
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work_keys_str_mv	AT bartlerobertg introductiontorealanalysis AT sherbertdonaldr introductiontorealanalysis

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