A first course in analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2018
|
| Schriftenreihe: | Cambridge mathematical textbooks
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xv, 340 Seiten |
| ISBN: | 9781107173149 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV044537252 | ||
| 003 | DE-604 | ||
| 005 | 20180928 | ||
| 007 | t | ||
| 008 | 171013s2018 |||| 00||| eng d | ||
| 020 | |a 9781107173149 |c Hardcover |9 978-1-107-17314-9 | ||
| 035 | |a (OCoLC)1007788009 | ||
| 035 | |a (DE-599)BVBBV044537252 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-19 |a DE-20 |a DE-739 |a DE-634 | ||
| 084 | |a SK 400 |0 (DE-625)143237: |2 rvk | ||
| 100 | 1 | |a Conway, John B. |d 1939- |e Verfasser |0 (DE-588)110699882 |4 aut | |
| 245 | 1 | 0 | |a A first course in analysis |c John B. Conway, The George Washington University, Washington, DC, USA |
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 2018 | |
| 300 | |a xv, 340 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Cambridge mathematical textbooks | |
| 650 | 0 | 7 | |a Analysis |0 (DE-588)4001865-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Analysis |0 (DE-588)4001865-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-316-77981-1 |
| 856 | 4 | 2 | |m Digitalisierung UB Passau - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029936393&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-029936393 | ||
Datensatz im Suchindex
| _version_ | 1804177893222252544 |
|---|---|
| adam_text | Contents
;■ - i ; ;; ;• ■: :■ ■■ r •;
Preface page xi
1 The Real Numbers 1
1.1 Sets and Functions 1
1.2 The Real Numbers 6
1.3 Convergence 16
1.4 Series 24
1.5 Countable and Uncountable Sets 29
1.6 Open Sets and Closed Sets 33
1.7 Continuous Functions 37
1.8 Trigonometric Functions 45
2 Differentiation 47
2.1 Limits 47
2.2 The Derivative 52
2.3 The Sign of the Derivative 57
2.4 Critical Points 62
2.5 Some Applications 65
3 Integration 71
3.1 The Riemann Integral 71
3.2 The Fundamental Theorem of Calculus 78
3.3 The Logarithm and Exponential Functions 81
3.4 Improper Integrals 85
3.5 Sets of Measure Zero and Integrability 89
3.6 The Riemann-Stieltjes Integral 93
4 Sequences of Functions 103
4.1 Uniform Convergence 103
4.2 Power Series 107
5 Metric and Euclidean Spaces 115
5.1 Definitions and Examples 115
5.2 Sequences and Completeness 119
5.3 Open and Closed Sets 121
5.4 Continuity 128
5.5 Compactness 133
X
Contents
5.6 Connectedness 140
5.7 The Space of Continuous Functions 146
6 Differentiation in Higher Dimensions 155
6.1 Vector-valued Functions 155
6.2 Differentiable Functions, Part 1 158
6.3 Orthogonality 168
6.4 Linear Transformations 173
6.5 Differentiable Functions, Part 2 188
6.6 Critical Points 192
6.7 Tangent Planes 197
6.8 Inverse Function Theorem 201
6.9 Implicit Function Theorem 207
6.10 Lagrange Multipliers 212
7 Integration in Higher Dimensions 219
7.1 Integration of Vector-valued Functions 219
7.2 The Riemann Integral 223
7.3 Iterated Integration 233
7.4 Change of Variables 239
7.5 Differentiation under the Integral Sign 250
8 Curves and Surfaces 257
8.1 Curves 257
8.2 Green s Theorem 263
8.3 Surfaces 269
8.4 Integration on Surfaces 275
8.5 The Theorems of Gauss and Stokes 284
9 Differential Forms 293
9.1 Introduction 293
9.2 Change of Variables for Forms 304
9.3 Simplexes and Chains 309
9.4 Oriented Boundaries 317
9.5 Stokes s Theorem 320
9.6 Closed and Exact Forms 323
9.7 Denouement 327
Bibliography 331
Index of Terms 333
Index of Symbols 339
|
| any_adam_object | 1 |
| author | Conway, John B. 1939- |
| author_GND | (DE-588)110699882 |
| author_facet | Conway, John B. 1939- |
| author_role | aut |
| author_sort | Conway, John B. 1939- |
| author_variant | j b c jb jbc |
| building | Verbundindex |
| bvnumber | BV044537252 |
| classification_rvk | SK 400 |
| ctrlnum | (OCoLC)1007788009 (DE-599)BVBBV044537252 |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01396nam a2200337 c 4500</leader><controlfield tag="001">BV044537252</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20180928 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">171013s2018 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781107173149</subfield><subfield code="c">Hardcover</subfield><subfield code="9">978-1-107-17314-9</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1007788009</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV044537252</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-19</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-634</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="100" ind1="1" ind2=" "><subfield code="a">Conway, John B.</subfield><subfield code="d">1939-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)110699882</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">A first course in analysis</subfield><subfield code="c">John B. Conway, The George Washington University, Washington, DC, USA</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge</subfield><subfield code="b">Cambridge University Press</subfield><subfield code="c">2018</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">xv, 340 Seiten</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">Cambridge mathematical textbooks</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Analysis</subfield><subfield code="0">(DE-588)4001865-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Analysis</subfield><subfield code="0">(DE-588)4001865-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-1-316-77981-1</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Passau - ADAM Catalogue Enrichment</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=029936393&sequence=000001&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:BVB01-029936393</subfield></datafield></record></collection> |
| id | DE-604.BV044537252 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:55:18Z |
| institution | BVB |
| isbn | 9781107173149 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029936393 |
| oclc_num | 1007788009 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-20 DE-739 DE-634 |
| owner_facet | DE-19 DE-BY-UBM DE-20 DE-739 DE-634 |
| physical | xv, 340 Seiten |
| publishDate | 2018 |
| publishDateSearch | 2018 |
| publishDateSort | 2018 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Cambridge mathematical textbooks |
| spelling | Conway, John B. 1939- Verfasser (DE-588)110699882 aut A first course in analysis John B. Conway, The George Washington University, Washington, DC, USA Cambridge Cambridge University Press 2018 xv, 340 Seiten txt rdacontent n rdamedia nc rdacarrier Cambridge mathematical textbooks Analysis (DE-588)4001865-9 gnd rswk-swf Analysis (DE-588)4001865-9 s DE-604 Erscheint auch als Online-Ausgabe 978-1-316-77981-1 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029936393&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Conway, John B. 1939- A first course in analysis Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4001865-9 |
| title | A first course in analysis |
| title_auth | A first course in analysis |
| title_exact_search | A first course in analysis |
| title_full | A first course in analysis John B. Conway, The George Washington University, Washington, DC, USA |
| title_fullStr | A first course in analysis John B. Conway, The George Washington University, Washington, DC, USA |
| title_full_unstemmed | A first course in analysis John B. Conway, The George Washington University, Washington, DC, USA |
| title_short | A first course in analysis |
| title_sort | a first course in analysis |
| topic | Analysis (DE-588)4001865-9 gnd |
| topic_facet | Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029936393&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT conwayjohnb afirstcourseinanalysis |