Elementary real and complex analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Dover Publications
1996
|
| Ausgabe: | Revised English ed. |
| Schriftenreihe: | Dover books on mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | Originally published in English: Cambridge, Mass. : MIT Press, 1973. - Literaturangaben |
| Beschreibung: | XI, 516 S. graph. Darst. 22 cm |
| ISBN: | 0486689220 |
Internformat
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| 245 | 1 | 0 | |a Elementary real and complex analysis |c Georgi E. Shilov. Translated and ed. by Richard A. Silverman |
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Datensatz im Suchindex
| _version_ | 1804143683677716480 |
|---|---|
| adam_text | IMAGE 1
ELEMENTARY REAL AND
COMPLEX ANALYSIS
GEORGI E. SHILOV TRANSLATED AND EDITED BY RICHARD A. SILVERMAN
REVISED ENGLISH EDITION
DOVER PUBLICATIONS, INC.
NEW YORK
IMAGE 2
CONTENTS
PREFACE IX
1 REAL N U M B E RS
1.1. SET-THEORETIC PRELIMINARIES 1
1.2. AXIOMS FOR THE REAL NUMBER SYSTEM 3
1.3. CONSEQUENCES OF THE ADDITION AXIOMS 4
1.4. CONSEQUENCES OF THE MULTIPLICATION AXIOMS 5
1.5. CONSEQUENCES OF THE ORDER AXIOMS 9
1.6. CONSEQUENCES OF THE LEAST UPPER BOUND AXIOM 12
1.7. THE PRINCIPLE OF ARCHIMEDES AND ITS CONSEQUENCES 16 1.8. THE
PRINCIPLE OF NESTED INTERVALS 21
1.9. THE EXTENDED REAL NUMBER SYSTEM 22
PROBLEMS 24
2 SETS
2.1. OPERATIONS ON SETS 27
2.2. EQUIVALENCE OF SETS 29
2.3. COUNTABLE SETS 31
2.4. UNCOUNTABLE SETS 33
2.5. MATHEMATICAL STRUCTURES 35
2.6. N-DIMENSIONAL SPACE 39
2.7. COMPLEX NUMBERS 43
2.8. FUNCTIONS AND GRAPHS 48
PROBLEMS 50
3 METRIC SPACES
3.1. DEFINITIONS AND EXAMPLES 53
3.2. OPEN SETS 61
3.3. CONVERGENT SEQUENCES AND HOMEOMORPHISMS 63
3.4. LIMIT POINTS 73
3.5. CLOSED SETS 76
3.6. DENSE SETS AND CLOSURES 78
3.7. COMPLETE METRIC SPACES 80
3.8. COMPLETION OF A METRIC SPACE 87
3.9. COMPACTNESS 91
PROBLEMS 97
IMAGE 3
VI CONTENTS
4 LIMITS
4.1. BASIC CONCEPTS 99
4.2. SOME GENERAL THEOREMS 107
4.3. LIMITS OF NUMERICAL FUNCTIONS 108
4.4. UPPER AND LOWER LIMITS 117
4.5. NONDECREASING AND NONINCREASING FUNCTIONS 119
4.6. LIMITS OF NUMERICAL SEQUENCES 123
4.7. LIMITS OF VECTOR FUNCTIONS 126
PROBLEMS 129
5 CONTINUOUS FUNCTIONS
5.1. CONTINUOUS FUNCTIONS ON A METRIC SPACE 132
5.2. CONTINUOUS NUMERICAL FUNCTIONS ON THE REAL LINE 139 5.3. MONO TONIC
FUNCTIONS 142
5.4. THE LOGARITHM 145
5.5. THE EXPONENTIAL 149
5.6. TRIGONOMETRIC FUNCTIONS 157
5.7. APPLICATIONS OF TRIGONOMETRIC FUNCTIONS 165
5.8. CONTINUOUS VECTOR FUNCTIONS OF A VECTOR VARIABLE 172 5.9. SEQUENCES
OF FUNCTIONS 179
PROBLEMS 183
6 SERIES
6.1. NUMERICAL SERIES 186
6.2. ABSOLUTE AND CONDITIONAL CONVERGENCE 194
6.3. OPERATIONS ON SERIES 196
6.4. SERIES OF VECTORS 203
6.5. SERIES OF FUNCTIONS 211
6.6. POWER SERIES 213
PROBLEMS 218
7 THE DERIVATIVE
7.1. DEFINITIONS AND EXAMPLES 223
7.2. PROPERTIES OF DIFFERENTIABLE FUNCTIONS 233
IMAGE 4
CONTENTS VII
7.3. THE DIFFERENTIAL 235
7.4. MEAN VALUE THEOREMS 237
7.5. CONCAVITY AND INFLECTION POINTS 240
7.6. L HOSPITAL S RULES 243
PROBLEMS 245
8 HIGHER DERIVATIVES
8.1. DEFINITIONS AND EXAMPLES 249
8.2. TAYLOR S FORMULA 251
8.3. MORE ON CONCAVITY AND INFLECTION POINTS 255
8.4. ANOTHER VERSION OF TAYLOR S FORMULA 257
8.5. TAYLOR SERIES 259
8.6. COMPLEX EXPONENTIALS AND TRIGONOMETRIC FUNCTIONS 262 8.7.
HYPERBOLIC FUNCTIONS 267
PROBLEMS 270
9 THE INTEGRAL
9.1. DEFINITIONS AND BASIC PROPERTIES 274
9.2. AREA AND ARC LENGTH 287
9.3. ANTIDERIVATIVES AND INDEFINITE INTEGRALS 291
9.4. TECHNIQUE OF INDEFINITE INTEGRATION 296
9.5. EVALUATION OF DEFINITE INTEGRALS 308
9.6. MORE ON AREA 317
9.7. MORE ON ARC LENGTH 328
9.8. AREA OF A SURFACE OF REVOLUTION 335
9.9. FURTHER APPLICATIONS OF INTEGRATION 342
9.10. INTEGRATION OF SEQUENCES OF FUNCTIONS 349
9.11. PARAMETER-DEPENDENT INTEGRALS 355
9.12. LINE INTEGRALS 361
PROBLEMS 370
10 ANALYTIC FUNCTIONS
10.1. BASIC CONCEPTS 373
10.2. LINE INTEGRALS OF COMPLEX FUNCTIONS 381
10.3. CAUCHY S THEOREM AND ITS CONSEQUENCES 389
IMAGE 5
VIII CONTENTS
10.4. RESIDUES AND ISOLATED SINGULAR POINTS 404
10.5. MAPPINGS AND ELEMENTARY FUNCTIONS 416
PROBLEMS 427
11 IMPROPER INTEGRALS
11.1. IMPROPER INTEGRALS OF THE FIRST KIND 431
11.2. CONVERGENCE OF IMPROPER INTEGRALS 438
11.3. IMPROPER INTEGRALS OF THE SECOND AND THIRD KINDS 443 11.4.
EVALUATION OF IMPROPER INTEGRALS BY RESIDUES 447
11.5. PARAMETER-DEPENDENT IMPROPER INTEGRALS 457
11.6. THE GAMMA AND BETA FUNCTIONS 467
PROBLEMS 479
APPENDIX A ELEMENTARY SYMBOLIC LOGIC 482
APPENDIX B MEASURE AND INTEGRATION ON A COMPACT METRIC SPACE 484
SELECTED HINTS AND ANSWERS 489
INDEX 505
|
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| author | Šilov, Georgij E. 1917-1975 |
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| author_variant | g e š ge geš |
| building | Verbundindex |
| bvnumber | BV036959190 |
| classification_rvk | SK 400 |
| classification_tum | MAT 260f |
| ctrlnum | (OCoLC)635632725 (DE-599)GBV187803102 |
| discipline | Mathematik |
| edition | Revised English ed. |
| format | Book |
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| isbn | 0486689220 |
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| physical | XI, 516 S. graph. Darst. 22 cm |
| publishDate | 1996 |
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| publisher | Dover Publications |
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| spelling | Šilov, Georgij E. 1917-1975 Verfasser (DE-588)133801780 aut Matematičeskij analiz Elementary real and complex analysis Georgi E. Shilov. Translated and ed. by Richard A. Silverman Revised English ed. New York, NY Dover Publications 1996 XI, 516 S. graph. Darst. 22 cm txt rdacontent n rdamedia nc rdacarrier Dover books on mathematics Originally published in English: Cambridge, Mass. : MIT Press, 1973. - Literaturangaben Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Analysis (DE-588)4001865-9 s DE-604 Lineare Algebra (DE-588)4035811-2 s 2\p DE-604 Funktionalanalysis (DE-588)4018916-8 s 3\p DE-604 DE-601 pdf/application http://www.zentralblatt-math.org/zmath/en/search/?an=0866.26001 Zentralblatt MATH kostenfrei Inhaltstext GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020874102&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 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Šilov, Georgij E. 1917-1975 Elementary real and complex analysis Lineare Algebra (DE-588)4035811-2 gnd Analysis (DE-588)4001865-9 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4035811-2 (DE-588)4001865-9 (DE-588)4018916-8 (DE-588)4151278-9 |
| title | Elementary real and complex analysis |
| title_alt | Matematičeskij analiz |
| title_auth | Elementary real and complex analysis |
| title_exact_search | Elementary real and complex analysis |
| title_full | Elementary real and complex analysis Georgi E. Shilov. Translated and ed. by Richard A. Silverman |
| title_fullStr | Elementary real and complex analysis Georgi E. Shilov. Translated and ed. by Richard A. Silverman |
| title_full_unstemmed | Elementary real and complex analysis Georgi E. Shilov. Translated and ed. by Richard A. Silverman |
| title_short | Elementary real and complex analysis |
| title_sort | elementary real and complex analysis |
| topic | Lineare Algebra (DE-588)4035811-2 gnd Analysis (DE-588)4001865-9 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Lineare Algebra Analysis Funktionalanalysis Einführung |
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