Basic elements of real analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
New York ; Berlin ; Heidelberg ; Barcelona ; Budapest ; Hong Kong ; London ; Milan ; Paris ; Singapore ; Tokyo
Springer
[1998]
|
| Series: | Undergraduate texts in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xl, 273 Seiten Diagramme |
| ISBN: | 9780387984797 0387984798 9780387227498 |
Staff View
MARC
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Record in the Search Index
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| adam_text | MURRAY H. PROTTER BASIC ELEMENTS OF REAL ANALYSIS WITH 48 ILLUSTRATIONS
SPRINGER CONTENTS PREFACE VII CHAPTER 1 THE REAL NUMBER SYSTEM 1 1.1
AXIOMS FOR A FIELD 1 1.2 NATURAL NUMBERS AND SEQUENCES 7 1.3
INEQUALITIES 11 1.4 MATHEMATICAL INDUCTION 19 CHAPTER 2 CONTINUITY AND
LIMITS 23 2.1 CONTINUITY 23 2.2 LIMITS 28 2.3 ONE-SIDED LIMITS 33 2.4
LIMITS AT INFINITY; INFINITE LIMITS 37 2.5 LIMITS OF SEQUENCES 42
CHAPTER 3 BASIC PROPERTIES OF FUNCTIONS ON R 1 45 3.1 THE
INTERMEDIATE-VALUE THEOREM 45 3.2 LEAST UPPER BOUND; GREATEST LOWER
BOUND 48 3.3 THE BOLZANO-WEIERSTRASS THEOREM 54 3.4 THE BOUNDEDNESS AND
EXTREME-VALUE THEOREMS 56 3.5 UNIFORM CONTINUITY 57 3.6 THE CAUCHY
CRITERION 61 3.7 THE HEINE-BOREL THEOREM 63 IX X CONTENTS CHAPTER 4
ELEMENTARY THEORY OF DIFFERENTIATION 67 4.1 THE DERIVATIVE IN R 1 67 4.2
INVERSE FUNCTIONS IN R 1 77 CHAPTER 5 ELEMENTARY THEORY OF INTEGRATION
81 5.1 THE DARBOUX INTEGRAL FOR FUNCTIONS ON R 1 81 5.2 THE RIEMANN
INTEGRAL 91 5.3 THE LOGARITHM AND EXPONENTIAL FUNCTIONS 96 CHAPTER 6
ELEMENTARY THEORY OF METRIC SPACES 101 6.1 THE SCHWARZ AND TRIANGLE
INEQUALITIES; METRIC SPACES 101 6.2 TOPOLOGY IN METRIC SPACES 106 6.3
COUNTABLE AND UNCOUNTABLE SETS 114 6.4 COMPACT SETS AND THE HEINE-BOREL
THEOREM 118 6.5 FUNCTIONS ON COMPACT SETS 122 CHAPTER 7 DIFFERENTIATION
AND INTEGRATION IN R^ 125 7.1 PARTIAL DERIVATIVES AND THE CHAIN RULE 125
7.2 TAYLOR S THEOREM; MAXIMA AND MINIMA 130 7.3 THE DERIVATIVE IN R N
136 7.4 THE DARBOUX INTEGRAL IN R N 141 7.5 THE RIEMANN INTEGRAL IN R N
145 CHAPTER 8 INFINITE SERIES 150 8.1 TESTS FOR CONVERGENCE AND
DIVERGENCE 150 8.2 SERIES OF POSITIVE AND NEGATIVE TERMS; POWER SERIES
155 8.3 UNIFORM CONVERGENCE 162 8.4 UNIFORM CONVERGENCE OF SERIES; POWER
SERIES 168 CHAPTER 9 THE DERIVATIVE OF AN INTEGRAL. IMPROPER INTEGRALS
178 9.1 THE DERIVATIVE OF A FUNCTION DEFINED BY AN INTEGRAL. THE LEIBNIZ
RULE 178 9.2 CONVERGENCE AND DIVERGENCE OF IMPROPER INTEGRALS 183
CHAPTER 10 THE RIEMANN-STIELTJES INTEGRAL 190 10.1 FUNCTIONS OF BOUNDED
VARIATION 190 10.2 THE RIEMANN-STIELTJES INTEGRAL 195 CHAPTER 11 THE
IMPLICIT FUNCTION THEOREM. LAGRANGE MULTIPLIERS 205 11.1 THE IMPLICIT
FUNCTION THEOREM 205 11.2 LAGRANGE MULTIPLIERS * 210 CONTENTS XI CHAPTER
12 VECTOR FUNCTIONS ON R N ; THE THEOREMS OF GREEN AND STOKES 214 12.1
VECTOR FUNCTIONS ON R N 214 12.2 LINE INTEGRALS IN R N 225 12.3 GREEN S
THEOREM IN THE PLANE 232 12.4 AREA OF A SURFACE IN R 3 239 12.5 THE
STOKES THEOREM 244 12.6 THE DIVERGENCE THEOREM 253 ANSWERS TO
ODD-NUMBERED PROBLEMS 261 INDEX 269
|
| any_adam_object | 1 |
| author | Protter, Murray H. 1918-2008 |
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| classification_rvk | SK 400 |
| ctrlnum | (OCoLC)246169862 (DE-599)BVBBV012338659 |
| 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 |
| format | Book |
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| genre_facet | Lehrbuch - Infinitesimalrechnung - Mehrere Variable |
| id | DE-604.BV012338659 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:25:51Z |
| institution | BVB |
| isbn | 9780387984797 0387984798 9780387227498 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008366964 |
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| physical | xl, 273 Seiten Diagramme |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Springer |
| record_format | marc |
| series2 | Undergraduate texts in mathematics |
| spelling | Protter, Murray H. 1918-2008 (DE-588)1102930148 aut Basic elements of real analysis Murray H. Protter New York ; Berlin ; Heidelberg ; Barcelona ; Budapest ; Hong Kong ; London ; Milan ; Paris ; Singapore ; Tokyo Springer [1998] © 1998 xl, 273 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in mathematics Analysis Mathematical analysis Analysis (DE-588)4001865-9 gnd rswk-swf Lehrbuch - Infinitesimalrechnung - Mehrere Variable Analysis (DE-588)4001865-9 s DE-604 Erscheint auch als Online-Ausgabe 978-0-387-22749-8 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008366964&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Protter, Murray H. 1918-2008 Basic elements of real analysis Analysis Mathematical analysis Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4001865-9 |
| title | Basic elements of real analysis |
| title_auth | Basic elements of real analysis |
| title_exact_search | Basic elements of real analysis |
| title_full | Basic elements of real analysis Murray H. Protter |
| title_fullStr | Basic elements of real analysis Murray H. Protter |
| title_full_unstemmed | Basic elements of real analysis Murray H. Protter |
| title_short | Basic elements of real analysis |
| title_sort | basic elements of real analysis |
| topic | Analysis Mathematical analysis Analysis (DE-588)4001865-9 gnd |
| topic_facet | Analysis Mathematical analysis Lehrbuch - Infinitesimalrechnung - Mehrere Variable |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008366964&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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