Introduction to real analysis:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Hoboken, NJ
Wiley
2011
|
| Ausgabe: | 4. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XIII, 402 S. Ill., graph. Darst. 26 cm |
| ISBN: | 9780471433316 0471433314 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804149089150959616 |
|---|---|
| adam_text | INTRODUCTION TO REAL ANALYSIS
/ BARTLE, ROBERT GARDNER
: C2011
TABLE OF CONTENTS / INHALTSVERZEICHNIS
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.
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
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| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 4. ed. |
| format | Book |
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| institution | BVB |
| isbn | 9780471433316 0471433314 |
| language | English |
| lccn | 2010045251 |
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| physical | XIII, 402 S. Ill., graph. Darst. 26 cm |
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| spelling | Bartle, Robert G. 1927-2003 Verfasser (DE-588)13732877X aut Introduction to real analysis Robert G. Bartle ; Donald R. Sherbert 4. ed. Hoboken, NJ Wiley 2011 XIII, 402 S. Ill., graph. Darst. 26 cm txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Mathematical analysis Functions of real variables Reelle Analysis (DE-588)4627581-2 gnd rswk-swf Analysis (DE-588)4001865-9 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 LoC Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024983446&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. 1927-2003 Sherbert, Donald R. Introduction to real analysis Mathematical analysis Functions of real variables Reelle Analysis (DE-588)4627581-2 gnd Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4627581-2 (DE-588)4001865-9 (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 | Mathematical analysis Functions of real variables Reelle Analysis (DE-588)4627581-2 gnd Analysis (DE-588)4001865-9 gnd |
| topic_facet | Mathematical analysis Functions of real variables Reelle Analysis Analysis Einführung |
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