Mathematical analysis and proof:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chichester
Albion Publ.
1997
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Albion mathematics & applications series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 243 S. graph. Darst. |
| ISBN: | 1898563365 |
Internformat
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Datensatz im Suchindex
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| adam_text | MATHEMATICAL ANALYSIS AND PROOF DAVID S.G. STIRLING SENIOR LECTURER IN
MATHEMATICS UNIVERSITY OF READING ALBION PUBLISHING CHICHESTER TABLE OF
CONTENTS AUTHOR S PREFACE VII CHAPTER 1 SETTING THE SCENE 1 CHAPTER 2
LOGIC AND DEDUCTION 6 2.1 INTRODUCTION 6 2.2 IMPLICATION 7 2.3 IS ALL
THIS NECESSARY - OR WORTHWHILE? 8 2.4 USING THE RIGHT WORDS 10 PROBLEMS
13 CHAPTER 3 MATHEMATICAL INDUCTION 15 3.1 INTRODUCTION 15 3.2
ARITHMETIC PROGRESSIONS 15 3.3 THE PRINCIPLE OF MATHEMATICAL INDUCTION
17 3.4 WHY ALL THE FUSS ABOUT INDUCTION? 19 3.5 EXAMPLES OF INDUCTION 19
3.6 THE BINOMIAL THEOREM 26 PROBLEMS 29 CHAPTER 4 SETS AND NUMBERS 33
4.1 SETS 33 4.2 STANDARD SETS : : 34 4.3 PROOF BY CONTRADICTION 35 4.4
SETS AGAIN 41 4.5 WHERE WE HAVE GOT TO - AND THE WAY AHEAD 41 4.6 A
DIGRESSION 42 PROBLEMS 44 CHAPTER 5 ORDER AND INEQUALITIES 45 5.1 BASIC
PROPERTIES 45 5.2 CONSEQUENCES OF THE BASIC PROPERTIES 46 5.3
BERNOULLI S INEQUALITY 52 5.4 THE MODULUS (OR ABSOLUTE VALUE) 55
PROBLEMS 60 CHAPTER 6 DECIMALS 65 6.1 DECIMAL NOTATION : 65 6.2 DECIMALS
OF REAL NUMBERS 66 6.3 SOME INTERESTING CONSEQUENCES 74 PROBLEMS 75
CHAPTER 7 LIMITS 77 7.1 THE IDEA OF A LIMIT 77 7.2 MANIPULATING LIMITS
80 7.3 DEVELOPMENTS 85 PROBLEMS 90 TABLE OF CONTENTS CHAPTER 8 INFINITE
SERIES 93 8.1 INTRODUCTION 93 8.2 CONVERGENCE TESTS 94 8.3 POWER SERIES
102 8.4 DECIMALS AGAIN 103 PROBLEMS 104 CHAPTER 9 THE STRUCTURE OF THE
REAL NUMBER SYSTEM 107 PROBLEMS 115 CHAPTER 10 CONTINUITY ..117 10.1
INTRODUCTION 117 10.2 THE LIMIT OF A FUNCTION OF A REAL VARIABLE 118
10.3 CONTINUITY 124 10.4 INVERSE FUNCTIONS 129 10.5 SOME DISCONTINUOUS
FUNCTIONS 132 PROBLEMS 133 CHAPTER 11 DIFFERENTIATION 135 11.1 BASIC
RESULTS 135 11.2 THE MEAN VALUE THEOREM AND ITS FRIENDS 139 PROBLEMS 149
CHAPTER 12 FUNCTIONS DEFINED BY POWER SERIES 152 12.1 INTRODUCTION 152
12.2 FUNCTIONS DEFINED BY POWER SERIES 153 12.3 SOME STANDARD FUNCTIONS
OF MATHEMATICS 156 12.4 FURTHER EXAMPLES 165 PROBLEMS , 167 CHAPTER 13
INTEGRATION 169 13.1 THE INTEGRAL 169 13.2 APPROXIMATING THE VALUE OF AN
INTEGRAL 184 13.3 IMPROPER INTEGRALS 186 PROBLEMS : 191 CHAPTER 14
FUNCTIONS OF SEVERAL VARIABLES 195 14.1 CONTINUITY . , 195 14.2
DIFFERENTIATION 202 14.3 RESULTS INVOLVING INTERCHANGE OF LIMITS 207
14.4 SOLVING DIFFERENTIAL EQUATIONS 211 PROBLEMS 215 APPENDIX THE
EXPRESSION OF AN INTEGER AS A DECIMAL 219 REFERENCES AND SUGGESTIONS FOR
FURTHER READING 221 HINTS AND SOLUTIONS TO SELECTED PROBLEMS 222
NOTATION INDEX 237 SUBJECT INDEX 238
|
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| id | DE-604.BV012757312 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:33:07Z |
| institution | BVB |
| isbn | 1898563365 |
| language | English |
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| physical | 243 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Albion Publ. |
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| series2 | Albion mathematics & applications series |
| spelling | Stirling, David S. G. 1947- Verfasser (DE-588)1011480530 aut Mathematical analysis and proof David S. G. Stirling 1. publ. Chichester Albion Publ. 1997 243 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Albion mathematics & applications series Analyse (wiskunde) gtt Bewijstheorie gtt Mathematical analysis Proof theory Beweis (DE-588)4132532-1 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Analysis (DE-588)4001865-9 s Beweis (DE-588)4132532-1 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008674113&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Stirling, David S. G. 1947- Mathematical analysis and proof Analyse (wiskunde) gtt Bewijstheorie gtt Mathematical analysis Proof theory Beweis (DE-588)4132532-1 gnd Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4132532-1 (DE-588)4001865-9 |
| title | Mathematical analysis and proof |
| title_auth | Mathematical analysis and proof |
| title_exact_search | Mathematical analysis and proof |
| title_full | Mathematical analysis and proof David S. G. Stirling |
| title_fullStr | Mathematical analysis and proof David S. G. Stirling |
| title_full_unstemmed | Mathematical analysis and proof David S. G. Stirling |
| title_short | Mathematical analysis and proof |
| title_sort | mathematical analysis and proof |
| topic | Analyse (wiskunde) gtt Bewijstheorie gtt Mathematical analysis Proof theory Beweis (DE-588)4132532-1 gnd Analysis (DE-588)4001865-9 gnd |
| topic_facet | Analyse (wiskunde) Bewijstheorie Mathematical analysis Proof theory Beweis Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008674113&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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