Introduction to real analysis:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Wiley
2000
|
| Ausgabe: | 3. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 388 S. graph. Darst. |
| ISBN: | 0471321486 |
Internformat
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| 245 | 1 | 0 | |a Introduction to real analysis |c Robert G. Bartle ; Donald R. Sherbert |
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Datensatz im Suchindex
| _version_ | 1804127967050203136 |
|---|---|
| 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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| discipline | Mathematik |
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| spelling | Bartle, Robert G. Verfasser aut Introduction to real analysis Robert G. Bartle ; Donald R. Sherbert 3. ed. New York [u.a.] Wiley 2000 XI, 388 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Analyse mathématique Análise real larpcal Fonctions de variables réelles Matemática larpcal Functions of real variables Mathematical analysis Analysis (DE-588)4001865-9 gnd rswk-swf Reelle Analysis (DE-588)4627581-2 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Reelle Analysis (DE-588)4627581-2 s DE-604 Analysis (DE-588)4001865-9 s 2\p DE-604 Sherbert, Donald R. Verfasser aut HBZ Datenaustausch application/pdf 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 Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| 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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