Real mathematical analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
2002
|
| Series: | Undergraduate texts in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XI, 437 S. graph. Darst. |
| ISBN: | 0387952977 |
Staff View
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV014213590 | ||
| 003 | DE-604 | ||
| 005 | 20170320 | ||
| 007 | t | ||
| 008 | 020322s2002 d||| |||| 00||| eng d | ||
| 020 | |a 0387952977 |9 0-387-95297-7 | ||
| 035 | |a (OCoLC)248842345 | ||
| 035 | |a (DE-599)BVBBV014213590 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-355 |a DE-824 |a DE-703 |a DE-634 |a DE-11 |a DE-20 |a DE-188 | ||
| 050 | 0 | |a QA300 | |
| 082 | 0 | |a 515 | |
| 084 | |a SK 400 |0 (DE-625)143237: |2 rvk | ||
| 084 | |a SK 420 |0 (DE-625)143238: |2 rvk | ||
| 084 | |a 17,1 |2 ssgn | ||
| 100 | 1 | |a Pugh, Charles Chapman |d 1940- |e Verfasser |0 (DE-588)123790255 |4 aut | |
| 245 | 1 | 0 | |a Real mathematical analysis |c Charles Chapman Pugh |
| 264 | 1 | |a New York [u.a.] |b Springer |c 2002 | |
| 300 | |a XI, 437 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Undergraduate texts in mathematics | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Reelle Analysis | |
| 650 | 4 | |a Mathematical analysis | |
| 650 | 0 | 7 | |a Reelle Analysis |0 (DE-588)4627581-2 |2 gnd |9 rswk-swf |
| 655 | 7 | |8 1\p |0 (DE-588)4151278-9 |a Einführung |2 gnd-content | |
| 689 | 0 | 0 | |a Reelle Analysis |0 (DE-588)4627581-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u 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 |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-009745486 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Record in the Search Index
| _version_ | 1804129098271817728 |
|---|---|
| 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
|
| any_adam_object | 1 |
| author | Pugh, Charles Chapman 1940- |
| author_GND | (DE-588)123790255 |
| author_facet | Pugh, Charles Chapman 1940- |
| author_role | aut |
| author_sort | Pugh, Charles Chapman 1940- |
| author_variant | c c p cc ccp |
| building | Verbundindex |
| bvnumber | BV014213590 |
| callnumber-first | Q - Science |
| callnumber-label | QA300 |
| callnumber-raw | QA300 |
| callnumber-search | QA300 |
| callnumber-sort | QA 3300 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 400 SK 420 |
| ctrlnum | (OCoLC)248842345 (DE-599)BVBBV014213590 |
| 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 |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01673nam a2200433 c 4500</leader><controlfield tag="001">BV014213590</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20170320 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">020322s2002 d||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0387952977</subfield><subfield code="9">0-387-95297-7</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)248842345</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV014213590</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-355</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA300</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 400</subfield><subfield code="0">(DE-625)143237:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 420</subfield><subfield code="0">(DE-625)143238:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">17,1</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Pugh, Charles Chapman</subfield><subfield code="d">1940-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)123790255</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Real mathematical analysis</subfield><subfield code="c">Charles Chapman Pugh</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">2002</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XI, 437 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Undergraduate texts in mathematics</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Hier auch später erschienene, unveränderte Nachdrucke</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Reelle Analysis</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematical analysis</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Reelle Analysis</subfield><subfield code="0">(DE-588)4627581-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="8">1\p</subfield><subfield code="0">(DE-588)4151278-9</subfield><subfield code="a">Einführung</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Reelle Analysis</subfield><subfield code="0">(DE-588)4627581-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">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</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-009745486</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| genre | 1\p (DE-588)4151278-9 Einführung gnd-content |
| genre_facet | Einführung |
| id | DE-604.BV014213590 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:59:44Z |
| institution | BVB |
| isbn | 0387952977 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009745486 |
| oclc_num | 248842345 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-824 DE-703 DE-634 DE-11 DE-20 DE-188 |
| owner_facet | DE-355 DE-BY-UBR DE-824 DE-703 DE-634 DE-11 DE-20 DE-188 |
| physical | XI, 437 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Springer |
| record_format | marc |
| series2 | Undergraduate texts in mathematics |
| spelling | Pugh, Charles Chapman 1940- Verfasser (DE-588)123790255 aut Real mathematical analysis Charles Chapman Pugh New York [u.a.] Springer 2002 XI, 437 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in mathematics Hier auch später erschienene, unveränderte Nachdrucke Reelle Analysis Mathematical analysis Reelle Analysis (DE-588)4627581-2 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Reelle Analysis (DE-588)4627581-2 s DE-604 HBZ Datenaustausch application/pdf 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 Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| 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 |
| url | 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 |
| work_keys_str_mv | AT pughcharleschapman realmathematicalanalysis |