A first course in real analysis:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York u.a.
Springer
1991
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Undergraduate texts in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Spätere Ausg. u.d.T.: Berberian, Sterling T.: A first course in real analysis |
| Beschreibung: | XVIII, 534 S. graph. Darst. |
| ISBN: | 3540974377 0387974377 |
Internformat
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| 245 | 1 | 0 | |a A first course in real analysis |c Murray H. Protter ; Charles B. Morrey |
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Datensatz im Suchindex
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| adam_text | MURRAY H. PROTTER CHARLES B. MORREY, JR. A FIRST COURSE IN REAL ANALYSIS
SECOND EDITION WITH 143 ILLUSTRATIONS SPRINGER CONTENTS PREFACE TO THE
SECOND EDITION VII PREFACE TO THE FIRST EDITION XI CHAPTER L THE REAL
NUMBER SYSTEM 1 1.1 AXIOMS FOR A FIELD 1 1.2 NATURAL NUMBERS AND
SEQUENCES 9 1.3 INEQUALITIES 15 1.4 MATHEMATICAL INDUCTION 25 CHAPTER 2
CONTINUITY AND LIMITS 30 2.1 CONTINUITY 30 2.2 LIMITS 35 2.3 ONE-SIDED
LIMITS 42 2.4 LIMITS AT INFINITY; INFINITE LIMITS 48 2.5 LIMITS OF
SEQUENCES 55 CHAPTER 3 BASIC PROPERTIES OF FUNCTIONS ON U 1 59 3.1 THE
INTERMEDIATE-VALUE THEOREM 59 3.2 LEAST UPPER BOUND; GREATEST LOWER
BOUND 62 3.3 THE BOLZANO-WEIERSTRASS THEOREM 68 3.4 THE BOUNDEDNESS AND
EXTREME-VALUE THEOREMS 70 3.5 UNIFORM CONTINUITY 72 3.6 THE CAUCHY
CRITERION 75 3.7 THE HEINE-BOREL AND LEBESGUE THEOREMS 77 XV XVI
CONTENTS CHAPTER 4 ELEMENTARY THEORY OF DIFFERENTIATION 83 4.1 THE
DERIVATIVE IN R 1 83 4.2 INVERSE FUNCTIONS IN R 1 94 CHAPTER 5
ELEMENTARY THEORY OF INTEGRATION 98 5.1 THE DARBOUX INTEGRAL FOR
FUNCTIONS ON R 1 98 5.2 THE RIEMANN INTEGRAL 111 5.3 THE LOGARITHM AND
EXPONENTIAL FUNCTIONS 117 5.4 JORDAN CONTENT AND AREA 122 CHAPTER 6
ELEMENTARY THEORY OF METRIC SPACES 130 6.1 THE SCHWARZ AND TRIANGLE
INEQUALITIES; METRIC SPACES 130 6.2 ELEMENTS OF POINT SET TOPOLOGY 136
6.3 COUNTABLE AND UNCOUNTABLE SETS 145 6.4 COMPACT SETS AND THE
HEINE-BOREL THEOREM 150 6.5 FUNCTIONS ON COMPACT SETS 157 6.6 CONNECTED
SETS 161 6.7 MAPPINGS FROM ONE METRIC SPACE TO ANOTHER 164 CHAPTER 7
DIFFERENTIATION IN IR 173 7.1 PARTIAL DERIVATIVES AND THE CHAIN RULE
173 7.2 TAYLOR S THEOREM; MAXIMA AND MINIMA 178 7.3 THE DERIVATIVE IN W
188 CHAPTER 8 INTEGRATION IN W 194 8.1 VOLUME IN R* 194 8.2 THE DARBOUX
INTEGRAL IN R 197 8.3 THE RIEMANN INTEGRAL IN U N 203 CHAPTER 9
INFINITE SEQUENCES AND INFINITE SERIES 211 9.1 TESTS FOR CONVERGENCE AND
DIVERGENCE 211 9.2 SERIES OF POSITIVE AND NEGATIVE TERMS; POWER SERIES
216 9.3 UNIFORM CONVERGENCE OF SEQUENCES 222 9.4 UNIFORM CONVERGENCE OF
SERIES; POWER SERIES 230 9.5 UNORDERED SUMS 241 9.6 THE COMPARISON TEST
FOR UNORDERED SUMS; UNIFORM CONVERGENCE 250 9.7 MULTIPLE SEQUENCES AND
SERIES 254 CONTENTS XVII CHAPTER 10 FOURIER SERIES 263 10.1 EXPANSIONS
OF PERIODIC FUNCTIONS 263 10.2 SINE SERIES AND COSINE SERIES; CHANGE OF
INTERVAL 270 10.3 CONVERGENCE THEOREMS 275 CHAPTER 11 FUNCTIONS DEFINED
BY INTEGRALS; IMPROPER INTEGRALS 285 11.1 THE DERIVATIVE OF A FUNCTION
DEFINED BY AN INTEGRAL; THE LEIBNIZ RULE 285 11.2 CONVERGENCE AND
DIVERGENCE OF IMPROPER INTEGRALS 290 11.3 THE DERIVATIVE OF FUNCTIONS
DEFINED BY IMPROPER INTEGRALS; THE GAMMA FUNCTION 295 CHAPTER 12 THE
RIEMANN-STIELTJES INTEGRAL AND FUNCTIONS OF BOUNDED VARIATION 305 12.1
FUNCTIONS OF BOUNDED VARIATION 305 12.2 THE RIEMANN-STIELTJES INTEGRAL
316 CHAPTER 13 CONTRACTION MAPPINGS, NEWTON S METHOD, AND DIFFERENTIAL
EQUATIONS 329 13.1 A FIXED POINT THEOREM AND NEWTON S METHOD 329 13.2
APPLICATION OF THE FIXED POINT THEOREM TO DIFFERENTIAL EQUATIONS 335
CHAPTER 14 IMPLICIT FUNCTION THEOREMS AND LAGRANGE MULTIPLIERS 341 14.1
THE IMPLICIT FUNCTION THEOREM FOR A SINGLE EQUATION 341 14.2 THE
IMPLICIT FUNCTION THEOREM FOR SYSTEMS 348 14.3 CHANGE OF VARIABLES IN A
MULTIPLE INTEGRAL 359 14.4 THE LAGRANGE MULTIPLIER RULE 369 CHAPTER 15
FUNCTIONS ON METRIC SPACES; APPROXIMATION 374 15.1 COMPLETE METRIC
SPACES 374 15.2 CONVEX SETS AND CONVEX FUNCTIONS 381 15.3 ARZELA S
THEOREM; THE TIETZE EXTENSION THEOREM 393 15.4 APPROXIMATIONS AND THE
STONE-WEIERSTRASS THEOREM 403 CHAPTER 16 VECTOR FIELD THEORY; THE
THEOREMS OF GREEN AND STOKES 413 16.1 VECTOR FUNCTIONS ON R 1 413 16.2
VECTOR FUNCTIONS AND FIELDS ON U 423 XVIII CONTENTS 16.3 LINE INTEGRALS
IN U N 434 16.4 GREEN S THEOREM IN THE PLANE 445 16.5 SURFACES IN R 3 ;
PARAMETRIC REPRESENTATION 455 16.6 AREA OF A SURFACE IN R 3 ; SURFACE
INTEGRALS 461 16.7 ORIENTABLE SURFACES 471 16.8 THE STOKES THEOREM 477
16.9 THE DIVERGENCE THEOREM 486 APPENDIXES 495 APPENDIX 1 ABSOLUTE VALUE
495 APPENDIX 2 SOLUTION OF ALGEBRAIC INEQUALITIES 499 APPENDIX 3
EXPANSIONS OF REAL NUMBERS IN ANY BASE 503 APPENDIX 4 VECTORS IN E N 507
ANSWERS TO ODD-NUMBERED PROBLEMS 515 INDEX 529
|
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| author | Protter, Murray H. 1918-2008 Morrey, Charles B. 1907-1984 |
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| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| dewey-search | 515 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T16:15:47Z |
| institution | BVB |
| isbn | 3540974377 0387974377 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002865752 |
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| physical | XVIII, 534 S. graph. Darst. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Springer |
| record_format | marc |
| series2 | Undergraduate texts in mathematics |
| spelling | Protter, Murray H. 1918-2008 Verfasser (DE-588)1102930148 aut A first course in real analysis Murray H. Protter ; Charles B. Morrey 2. ed. New York u.a. Springer 1991 XVIII, 534 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in mathematics Spätere Ausg. u.d.T.: Berberian, Sterling T.: A first course in real analysis Analyse mathématique ram Mathematical analysis Analysis (DE-588)4001865-9 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Analysis (DE-588)4001865-9 s DE-604 Morrey, Charles B. 1907-1984 Verfasser (DE-588)172264332 aut HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002865752&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Protter, Murray H. 1918-2008 Morrey, Charles B. 1907-1984 A first course in real analysis Analyse mathématique ram Mathematical analysis Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4001865-9 (DE-588)4151278-9 |
| title | A first course in real analysis |
| title_auth | A first course in real analysis |
| title_exact_search | A first course in real analysis |
| title_full | A first course in real analysis Murray H. Protter ; Charles B. Morrey |
| title_fullStr | A first course in real analysis Murray H. Protter ; Charles B. Morrey |
| title_full_unstemmed | A first course in real analysis Murray H. Protter ; Charles B. Morrey |
| title_short | A first course in real analysis |
| title_sort | a first course in real analysis |
| topic | Analyse mathématique ram Mathematical analysis Analysis (DE-588)4001865-9 gnd |
| topic_facet | Analyse mathématique Mathematical analysis Analysis Einführung |
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