Foundations of analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, FL
Chapman & Hall/CRC
2018
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| Edition: | First issued in paperback |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | x, 301 Seiten Illustrationen 24 cm |
| ISBN: | 9781138374928 9781482220742 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Table of Contents Preface ix 1 Number Systems 1.1 The Real Numbers.................. APPENDIX: Construction of the Real Numbers ................... 1.2 The Complex Numbers . .................................. 1 1 6 11 2 Sequences 2.1 Convergence of Sequences . ......................... 2.2 Subsequences ........................................... 2.3 Limsup and Liminf.............................................. 2.4 Some Special Sequences................................................. 19 19 27 31 35 3 Series of Numbers 41 3.1 Convergence of Series ..................... 41 3.2 Elementary Convergence Tests ..................................................... 48 3.3 Advanced Convergence Tests........................................................ 57 3.4 Some Special Series . . . .................................................... 65 3.5 Operations on Series . .................. 69 4 Basic Topology 75 4.1 Open and Closed Sets........................... 75 4.2 Further Properties of Open and Closed Sets............................... 82 4.3 Compact Sets....................................................................... 87 4.4 The Cantor Set ................................................................................. 90 4.5 Connected and Disconnected Sets.................................................. 95 4.6 Perfect Sets . . . . . ........................................................................ 98 vii
Vill 5 Limits and Continuity of Functions 101 5.1 Basic Properties of the Limit of a Function . . . . . ...... 101 5.2 Continuous Functions . . . . ......................... .................. .108 5.3 Topological Properties andContinuity..........................................113 5.4 Classifying Discontinuities and Monotonicity............................120 6 Differentiation of Functions 127 6.1 The Concept of Derivative . . . . . . . ... . . . . . . . .... 127 6.2 The Mean Value Theorem and Applications ................................134 6.3 More on the Theory of Differentiation ......................................... 142 APPENDIX: Proof of Theorem 6.7 (The Weierstrass Nowhere Dif ferentiable Function) ........................ 148 7 The Integral 151 7.1 Partitions and the Concept of Integral .............. 151 7.2 Properties of the Riemann Integral............................ . ..... 158 8 Sequences and Series of Functions 169 8.1 Convergence of a Sequence of Functions................... . . 169 8.2 More on Uniform Convergence..................... 175 8.3 Series of Functions .... .... .... .... ............. 180 8.4 The Weierstrass Approximation Theorem................... 185 APPENDIX: Proof of the Weierstrass Approximation Theorem . . . 189 9 Elementary Transcendental Functions 193 9.1 Power Series............ ............................................................................ 193 9.2 More on Power Series: Convergence Issues................... 200 9.3 The Exponential and Trigonometric Functions ........................... 206 9.4 Logarithms and Powers of
Real Numbers . ................................213 APPENDIX I: Elementary Number Systems............ ... ................ ... . 217 APPENDIX II: Logic and Set Theory.................. 235 Table of Notation......................................................................................... 273 Glossary.................................................................... ... . ................ ... 277 Bibliography.......................................................... 293 Index . ......................................................................................................... 295
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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 | First issued in paperback |
| format | Book |
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| spelling | Krantz, Steven G. 1951- Verfasser (DE-588)130535907 aut Foundations of analysis Steven G. Krantz First issued in paperback 201905 Boca Raton, FL Chapman & Hall/CRC 2018 x, 301 Seiten Illustrationen 24 cm txt rdacontent n rdamedia nc rdacarrier Analysis (DE-588)4001865-9 gnd rswk-swf Mathematical analysis Mathematical analysis / Problems, exercises, etc 1\p (DE-588)4123623-3 Lehrbuch 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=031537516&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 |
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| title | Foundations of analysis |
| title_auth | Foundations of analysis |
| title_exact_search | Foundations of analysis |
| title_full | Foundations of analysis Steven G. Krantz |
| title_fullStr | Foundations of analysis Steven G. Krantz |
| title_full_unstemmed | Foundations of analysis Steven G. Krantz |
| title_short | Foundations of analysis |
| title_sort | foundations of analysis |
| topic | Analysis (DE-588)4001865-9 gnd |
| topic_facet | Analysis Lehrbuch |
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