A first course in analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York u.a.
Springer
1994
|
| Schriftenreihe: | Undergraduate texts in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXI, 278 S. graph. Darst. |
| ISBN: | 3540941088 0387941088 |
Internformat
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Datensatz im Suchindex
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| adam_text | GEORGE PEDRICK A FIRST COURSE IN ANALYSIS WITH 62 ILLUSTRATIONS
SPRINGER-VERLAG NEW YORK BERLIN HEIDELBERG LONDON PARIS TOKYO HONG KQNG
BARCELONA BUDAPEST CONTENTS PREFACE VII NOTATIONS AND CONVENTIONS XV
INTRODUCTION XIX BACKGROUND NUMBER SYSTEMS 1 §1. COUNTING: THE NATURAL
.NUMBERS 1 §2. MEASUREMENT: THE RATIONAL NUMBERS 13 THE AXIOMS OF
ORDERED FIELDS 19 §3. DECIMAL REPRESENTATION. IRRATIONALS 25 PART I
ANALYSIS 35 CHAPTER 1 APPROXIMATION: THE REAL NUMBERS 37 §1. LEAST UPPER
BOUND 38 §2. COMPLETENESS. NESTED INTERVALS 40 §3. BOUNDED MONOTONIC
SEQUENCES 42 §4. CAUCHY SEQUENCES 47 §5. THE REAL NUMBER SYSTEM 50 §6.
COUNTABILITY 52 APPENDIX. THE FUNDAMENTAL THEOREM OF ALGEBRA. COMPLEX
NUMBERS 55 XII CONTENTS CHAPTER 2 THE EXTREME-VALUE PROBLEM 64 §1.
CONTINUITY, COMPACTNESS, AND THE EXTREME-VALUE THEOREM 65 §2. CONTINUITY
OF RATIONAL FUNCTIONS. LIMITS OF SEQUENCES 72 APPENDIX. COMPLETION OF
THE PROOF OF THE FUNDAMENTAL THEOREM OF ALGEBRA 76 §3. SEQUENCES AND
SERIES OF REALS. THE NUMBER E 78 §4. SETS OF REALS. LIMITS OF FUNCTIONS
90 CHAPTER 3 CONTINUOUS FUNCTIONS 97 §1. IMPLICIT FUNCTIONS, F/X. THE
INTERMEDIATE-VALUE THEOREM 97 §2. INVERSE FUNCTIONS. X R FOR R E Q 101
§3. CONTINUOUS EXTENSION. UNIFORM CONTINUITY. THE EXPONENTIAL AND
LOGARITHM 104 §4. THE ELEMENTARY FUNCTIONS 109 §5. UNIFORMITY. THE
HEINE-BOREL THEOREM 112 §6. UNIFORM CONVERGENCE. A NOWHERE
DIFFERENTIABLE CONTINUOUS FUNCTION 118 §7. THE WEIERSTRASS APPROXIMATION
THEOREM 124 SUMMARY OF THE MAIN PROPERTIES OF CONTINUOUS FUNCTIONS 128
APPENDIX. A SPACE-FILLING CONTINUOUS CURVE 128 PART II FOUNDATIONS OF
CALCULUS 131 CHAPTER 4 DIFFERENTIATION 133 §1. DIFFERENTIAL AND
DERIVATIVE. TANGENT LINE 135 §2. THE FOUNDATIONS OF DIFFERENTIATION 140
§3. CURVE SKETCHING. THE MEAN-VALUE THEOREM 146 §4. TAYLOR S THEOREM 154
§5. FUNCTIONS DEFINED IMPLICITLY 160 CHAPTER 5 INTEGRATION 169 §1.
DEFINITIONS. DARBOUX THEOREM 171 §2. FOUNDATIONS OF INTEGRAL CALCULUS.
THE FUNDAMENTAL THEOREM OF CALCULUS 179 §3. THE NATURE OF INTEGRABILITY.
LEBESGUE S THEOREM 189 §4. IMPROPER INTEGRAL 197 §5. ARCLENGTH. BOUNDED
VARIATION 206 A WORD ABOUT THE STIELTJES INTEGRAL AND MEASURE THEORY 215
CONTENTS XIII CHAPTER 6 INFINITE SERIES 218 §1. THE VIBRATING STRING 219
§2. CONVERGENCE: GENERAL CONSIDERATIONS 224 §3. CONVERGENCE: SERIES OF
POSITIVE TERMS 230 §4. COMPUTATION WITH SERIES 237 §5. POWER SERIES 244
§6. FOURIER SERIES 254 BIBLIOGRAPHY 266 INDEX 269
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T17:38:41Z |
| institution | BVB |
| isbn | 3540941088 0387941088 |
| language | English |
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| physical | XXI, 278 S. graph. Darst. |
| publishDate | 1994 |
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| series2 | Undergraduate texts in mathematics |
| spelling | Pedrick, George Verfasser aut A first course in analysis George Pedrick New York u.a. Springer 1994 XXI, 278 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in mathematics Analyse mathématique ram Mathematical analysis Infinitesimalrechnung (DE-588)4072798-1 gnd rswk-swf Infinitesimalrechnung (DE-588)4072798-1 s DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006384282&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pedrick, George A first course in analysis Analyse mathématique ram Mathematical analysis Infinitesimalrechnung (DE-588)4072798-1 gnd |
| subject_GND | (DE-588)4072798-1 |
| title | A first course in analysis |
| title_auth | A first course in analysis |
| title_exact_search | A first course in analysis |
| title_full | A first course in analysis George Pedrick |
| title_fullStr | A first course in analysis George Pedrick |
| title_full_unstemmed | A first course in analysis George Pedrick |
| title_short | A first course in analysis |
| title_sort | a first course in analysis |
| topic | Analyse mathématique ram Mathematical analysis Infinitesimalrechnung (DE-588)4072798-1 gnd |
| topic_facet | Analyse mathématique Mathematical analysis Infinitesimalrechnung |
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