Introduction to analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton
CRC Press
2017
|
| Schriftenreihe: | Textbooks in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XX, 398 S. Diagramme |
| ISBN: | 9781498732017 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804177706563141632 |
|---|---|
| adam_text | Contents
Preface xi
List of Figures xix
1 Sets, Functions, and Proofs 1
1.1 Logic and an Introduction to Proof ......................... 2
1.2 Sets and Their Operations ................................. 11
1.3 Mathematical Induction..................................... 22
1.4 Functions.................................................. 29
1.5 Cardinality................................................ 39
1.6 Troubleshooting Guide for Sets, Functions, and Proofs ... 55
2 The Real Numbers 59
2.1 The Real and Extended Real Number System .................. 60
2.2 The Supremum and Infimum................................... 75
2.3 The Completeness Axiom..................................... 82
2.4 Troubleshooting Guide for The Real Numbers ................ 90
3 Sequences and Their Limits 93
3.1 Sequences................................................ 95
3.2 Limits and Convergence.................................... 106
3.3 Limit Theorems ........................................... 124
3.4 Subsequences.............................................. 143
3.5 Monotone Sequences........................................ 149
3.6 The Bolzano-Weierstrass Theorems ......................... 161
3.7 Cauchy Sequences ......................................... 171
3.8 Infinite Limits .......................................... 182
3.9 The limsup and liminf .................................... 195
3.10 Troubleshooting guide for Sequences and Their Limits .... 211
4 Series of Real Numbers 219
4.1 Infinite Series .......................................... 220
4.2 Convergence Tests for Series with Nonnegative Terms .... 227
4.3 Other Convergence Tests for Series ....................... 235
4.4 Rearrangements ........................................... 245
4.5 Troubleshooting Guide for Series of Real Numbers.......... 251
ix
x Contents
5 Limits and Continuity 253
5.1 Limits of Functions ...................................... 254
5.2 Properties of Limits ..................................... 263
5.3 Infinite Limits .......................................... 274
5.4 Continuity and Discontinuity.............................. 281
5.5 Consequences of Continuity................................ 288
5.6 Uniform Continuity ....................................... 296
5.7 Troubleshooting Guide for Limits and Continuity .......... 304
6 Differentiation 309
6.1 The Derivative............................................ 310
6.2 The Mean Value Theorem ................................... 324
6.3 Taylor Polynomials ....................................... 334
6.4 L Hopital’s Rule ......................................... 340
6.5 Troubleshooting Guide for Differentiation................. 348
7 Sequences and Series of Functions 351
7.1 Sequences of Functions ................................... 352
7.2 Consequences of Uniform Convergence ...................... 360
7.3 Infinite Series of Functions ............................. 367
7.4 Power Series ............................................. 375
7.5 Troubleshooting Guide for Series of Real Numbers.......... 387
Appendix A List of Commonly Used Symbols 389
Bibliography 393
Index
395
|
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| spelling | Dunn, Corey M. 1978- Verfasser aut Introduction to analysis Corey M. Dunn Boca Raton CRC Press 2017 XX, 398 S. Diagramme txt rdacontent n rdamedia nc rdacarrier Textbooks in mathematics Mathematical analysis Textbooks Numbers, Real Textbooks Analysis (DE-588)4001865-9 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Analysis (DE-588)4001865-9 s DE-604 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029816741&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| title | Introduction to analysis |
| title_auth | Introduction to analysis |
| title_exact_search | Introduction to analysis |
| title_full | Introduction to analysis Corey M. Dunn |
| title_fullStr | Introduction to analysis Corey M. Dunn |
| title_full_unstemmed | Introduction to analysis Corey M. Dunn |
| title_short | Introduction to analysis |
| title_sort | introduction to analysis |
| topic | Mathematical analysis Textbooks Numbers, Real Textbooks Analysis (DE-588)4001865-9 gnd |
| topic_facet | Mathematical analysis Textbooks Numbers, Real Textbooks Analysis Einführung |
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