Real mathematical analysis:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
New York [u.a.]
Springer
2002
|
| Schriftenreihe: | Undergraduate texts in mathematics
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009745486&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Umfang: | XI, 437 S. graph. Darst. |
| ISBN: | 0387952977 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1819327186962743296 |
|---|---|
| adam_text | Contents
1 Real Numbers 1
1 Preliminaries 1
2 Cuts 10
3 Euclidean Space 21
4 Cardinality 28
5* Comparing Cardinalities 34
6* The Skeleton of Calculus 36
Exercises 40
2 A Taste of Topology 51
1 Metric Space Concepts 51
2 Compactness 76
3 Connectedness 82
4 Coverings 88
5 Cantor Sets 95
6* Cantor Set Lore 99
7* Completion 108
Exercises 115
x Contents
3 Functions of a Real Variable 139
1 Differentiation 139
2 Riemann Integration 154
3 Series 179
Exercises 186
4 Function Spaces 201
1 Uniform Convergence and C°[a, b] 201
2 Power Series 211
3 Compactness and Equicontinuity in C° 213
4 Uniform Approximation in C° 217
5 Contractions and ODE s 228
6* Analytic Functions 235
7* Nowhere Differentiable Continuous Functions 240
8* Spaces of Unbounded Functions 248
Exercises 251
5 Multivariable Calculus 267
1 Linear Algebra 267
2 Derivatives 271
3 Higher derivatives 279
4 Smoothness Classes 284
5 Implicit and Inverse Functions 286
6* The Rank Theorem 290
7* Lagrange Multipliers 296
8 Multiple Integrals 300
9 Differential Forms 313
10 The General Stokes Formula 325
11 * The Brouwer Fixed Point Theorem 334
Appendix A: Perorations of Dieudonne 337
Appendix B: The History of Cavalieri s Principle 338
Appendix C: A Short Excursion into
the Complex Field 339
Appendix D: Polar Form 340
Appendix E: Determinants 342
Exercises 345
Contents xi
6 Lebesgue Theory 363
1 Outer measure 363
2 Measurability 367
3 Regularity 371
4 Lebesgue integrals 376
5 Lebesgue integrals as limits 383
6 Italian Measure Theory 387
7 Vitali coverings and density points 391
8 Lebesgue s Fundamental Theorem of Calculus 396
9 Lebesgue s Last Theorem 401
Appendix A: Translations and Nonmeasurable sets 407
Appendix B: The Banach Tarski Paradox 409
Appendix C: Riemann integrals as undergraphs 409
Appendix D: Littlewood s Three Principles 411
Appendix E: Roundness 412
Appendix F: Money 413
Suggested Reading 414
Bibliography 415
Exercises 417
Index 431
|
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| indexdate | 2024-12-20T11:01:22Z |
| institution | BVB |
| isbn | 0387952977 |
| language | English |
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| physical | XI, 437 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Springer |
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| series2 | Undergraduate texts in mathematics |
| spellingShingle | Pugh, Charles Chapman 1940- Real mathematical analysis Reelle Analysis Mathematical analysis Reelle Analysis (DE-588)4627581-2 gnd |
| subject_GND | (DE-588)4627581-2 (DE-588)4151278-9 |
| title | Real mathematical analysis |
| title_auth | Real mathematical analysis |
| title_exact_search | Real mathematical analysis |
| title_full | Real mathematical analysis Charles Chapman Pugh |
| title_fullStr | Real mathematical analysis Charles Chapman Pugh |
| title_full_unstemmed | Real mathematical analysis Charles Chapman Pugh |
| title_short | Real mathematical analysis |
| title_sort | real mathematical analysis |
| topic | Reelle Analysis Mathematical analysis Reelle Analysis (DE-588)4627581-2 gnd |
| topic_facet | Reelle Analysis Mathematical analysis Einführung |
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