Infinitesimal Analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
2002
|
| Schriftenreihe: | Mathematics and Its Applications
544 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Infinitesimal analysis, once a synonym for calculus, is now viewed as a technique for studying the properties of an arbitrary mathematical object by discriminating between its standard and nonstandard constituents. Resurrected by A. Robinson in the early 1960's with the epithet 'nonstandard', infinitesimal analysis not only has revived the methods of infinitely small and infinitely large quantities, which go back to the very beginning of calculus, but also has suggested many powerful tools for research in every branch of modern mathematics. The book sets forth the basics of the theory, as well as the most recent applications in, for example, functional analysis, optimization, and harmonic analysis. The concentric style of exposition enables this work to serve as an elementary introduction to one of the most promising mathematical technologies, while revealing up-to-date methods of monadology and hyperapproximation. This is a companion volume to the earlier works on nonstandard methods of analysis by A.G. Kusraev and S.S. Kutateladze (1999), ISBN 0-7923-5921-6 and Nonstandard Analysis and Vector Lattices edited by S.S. Kutateladze (2000), ISBN 0-7923-6619-0 |
| Beschreibung: | 1 Online-Ressource (XIV, 422 p) |
| ISBN: | 9789401700634 9789048160709 |
| DOI: | 10.1007/978-94-017-0063-4 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042424184 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s2002 |||| o||u| ||||||eng d | ||
| 020 | |a 9789401700634 |c Online |9 978-94-017-0063-4 | ||
| 020 | |a 9789048160709 |c Print |9 978-90-481-6070-9 | ||
| 024 | 7 | |a 10.1007/978-94-017-0063-4 |2 doi | |
| 035 | |a (OCoLC)1184492091 | ||
| 035 | |a (DE-599)BVBBV042424184 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 515.7 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Gordon, E. I. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Infinitesimal Analysis |c by E. I. Gordon, A. G. Kusraev, S. S. Kutateladze |
| 264 | 1 | |a Dordrecht |b Springer Netherlands |c 2002 | |
| 300 | |a 1 Online-Ressource (XIV, 422 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Mathematics and Its Applications |v 544 | |
| 500 | |a Infinitesimal analysis, once a synonym for calculus, is now viewed as a technique for studying the properties of an arbitrary mathematical object by discriminating between its standard and nonstandard constituents. Resurrected by A. Robinson in the early 1960's with the epithet 'nonstandard', infinitesimal analysis not only has revived the methods of infinitely small and infinitely large quantities, which go back to the very beginning of calculus, but also has suggested many powerful tools for research in every branch of modern mathematics. The book sets forth the basics of the theory, as well as the most recent applications in, for example, functional analysis, optimization, and harmonic analysis. The concentric style of exposition enables this work to serve as an elementary introduction to one of the most promising mathematical technologies, while revealing up-to-date methods of monadology and hyperapproximation. This is a companion volume to the earlier works on nonstandard methods of analysis by A.G. Kusraev and S.S. Kutateladze (1999), ISBN 0-7923-5921-6 and Nonstandard Analysis and Vector Lattices edited by S.S. Kutateladze (2000), ISBN 0-7923-6619-0 | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Functional analysis | |
| 650 | 4 | |a Operator theory | |
| 650 | 4 | |a Logic, Symbolic and mathematical | |
| 650 | 4 | |a Functional Analysis | |
| 650 | 4 | |a Operator Theory | |
| 650 | 4 | |a Measure and Integration | |
| 650 | 4 | |a Mathematical Logic and Foundations | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Infinitesimalanalysis |0 (DE-588)4161657-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Infinitesimalanalysis |0 (DE-588)4161657-1 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 700 | 1 | |a Kusraev, A. G. |e Sonstige |4 oth | |
| 700 | 1 | |a Kutateladze, S. S. |e Sonstige |4 oth | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-94-017-0063-4 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027859601 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804153100828672000 |
|---|---|
| any_adam_object | |
| author | Gordon, E. I. |
| author_facet | Gordon, E. I. |
| author_role | aut |
| author_sort | Gordon, E. I. |
| author_variant | e i g ei eig |
| building | Verbundindex |
| bvnumber | BV042424184 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)1184492091 (DE-599)BVBBV042424184 |
| dewey-full | 515.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.7 |
| dewey-search | 515.7 |
| dewey-sort | 3515.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-017-0063-4 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03014nmm a2200541zcb4500</leader><controlfield tag="001">BV042424184</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s2002 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789401700634</subfield><subfield code="c">Online</subfield><subfield code="9">978-94-017-0063-4</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789048160709</subfield><subfield code="c">Print</subfield><subfield code="9">978-90-481-6070-9</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-94-017-0063-4</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1184492091</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042424184</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515.7</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Gordon, E. I.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Infinitesimal Analysis</subfield><subfield code="c">by E. I. Gordon, A. G. Kusraev, S. S. Kutateladze</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Dordrecht</subfield><subfield code="b">Springer Netherlands</subfield><subfield code="c">2002</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (XIV, 422 p)</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">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Mathematics and Its Applications</subfield><subfield code="v">544</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Infinitesimal analysis, once a synonym for calculus, is now viewed as a technique for studying the properties of an arbitrary mathematical object by discriminating between its standard and nonstandard constituents. Resurrected by A. Robinson in the early 1960's with the epithet 'nonstandard', infinitesimal analysis not only has revived the methods of infinitely small and infinitely large quantities, which go back to the very beginning of calculus, but also has suggested many powerful tools for research in every branch of modern mathematics. The book sets forth the basics of the theory, as well as the most recent applications in, for example, functional analysis, optimization, and harmonic analysis. The concentric style of exposition enables this work to serve as an elementary introduction to one of the most promising mathematical technologies, while revealing up-to-date methods of monadology and hyperapproximation. This is a companion volume to the earlier works on nonstandard methods of analysis by A.G. Kusraev and S.S. Kutateladze (1999), ISBN 0-7923-5921-6 and Nonstandard Analysis and Vector Lattices edited by S.S. Kutateladze (2000), ISBN 0-7923-6619-0</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Functional analysis</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Operator theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Logic, Symbolic and mathematical</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Functional Analysis</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Operator Theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Measure and Integration</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematical Logic and Foundations</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Infinitesimalanalysis</subfield><subfield code="0">(DE-588)4161657-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Infinitesimalanalysis</subfield><subfield code="0">(DE-588)4161657-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Kusraev, A. G.</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Kutateladze, S. S.</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-94-017-0063-4</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027859601</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> |
| id | DE-604.BV042424184 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:15Z |
| institution | BVB |
| isbn | 9789401700634 9789048160709 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027859601 |
| oclc_num | 1184492091 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (XIV, 422 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Springer Netherlands |
| record_format | marc |
| series2 | Mathematics and Its Applications |
| spelling | Gordon, E. I. Verfasser aut Infinitesimal Analysis by E. I. Gordon, A. G. Kusraev, S. S. Kutateladze Dordrecht Springer Netherlands 2002 1 Online-Ressource (XIV, 422 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 544 Infinitesimal analysis, once a synonym for calculus, is now viewed as a technique for studying the properties of an arbitrary mathematical object by discriminating between its standard and nonstandard constituents. Resurrected by A. Robinson in the early 1960's with the epithet 'nonstandard', infinitesimal analysis not only has revived the methods of infinitely small and infinitely large quantities, which go back to the very beginning of calculus, but also has suggested many powerful tools for research in every branch of modern mathematics. The book sets forth the basics of the theory, as well as the most recent applications in, for example, functional analysis, optimization, and harmonic analysis. The concentric style of exposition enables this work to serve as an elementary introduction to one of the most promising mathematical technologies, while revealing up-to-date methods of monadology and hyperapproximation. This is a companion volume to the earlier works on nonstandard methods of analysis by A.G. Kusraev and S.S. Kutateladze (1999), ISBN 0-7923-5921-6 and Nonstandard Analysis and Vector Lattices edited by S.S. Kutateladze (2000), ISBN 0-7923-6619-0 Mathematics Functional analysis Operator theory Logic, Symbolic and mathematical Functional Analysis Operator Theory Measure and Integration Mathematical Logic and Foundations Mathematik Infinitesimalanalysis (DE-588)4161657-1 gnd rswk-swf Infinitesimalanalysis (DE-588)4161657-1 s 1\p DE-604 Kusraev, A. G. Sonstige oth Kutateladze, S. S. Sonstige oth https://doi.org/10.1007/978-94-017-0063-4 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Gordon, E. I. Infinitesimal Analysis Mathematics Functional analysis Operator theory Logic, Symbolic and mathematical Functional Analysis Operator Theory Measure and Integration Mathematical Logic and Foundations Mathematik Infinitesimalanalysis (DE-588)4161657-1 gnd |
| subject_GND | (DE-588)4161657-1 |
| title | Infinitesimal Analysis |
| title_auth | Infinitesimal Analysis |
| title_exact_search | Infinitesimal Analysis |
| title_full | Infinitesimal Analysis by E. I. Gordon, A. G. Kusraev, S. S. Kutateladze |
| title_fullStr | Infinitesimal Analysis by E. I. Gordon, A. G. Kusraev, S. S. Kutateladze |
| title_full_unstemmed | Infinitesimal Analysis by E. I. Gordon, A. G. Kusraev, S. S. Kutateladze |
| title_short | Infinitesimal Analysis |
| title_sort | infinitesimal analysis |
| topic | Mathematics Functional analysis Operator theory Logic, Symbolic and mathematical Functional Analysis Operator Theory Measure and Integration Mathematical Logic and Foundations Mathematik Infinitesimalanalysis (DE-588)4161657-1 gnd |
| topic_facet | Mathematics Functional analysis Operator theory Logic, Symbolic and mathematical Functional Analysis Operator Theory Measure and Integration Mathematical Logic and Foundations Mathematik Infinitesimalanalysis |
| url | https://doi.org/10.1007/978-94-017-0063-4 |
| work_keys_str_mv | AT gordonei infinitesimalanalysis AT kusraevag infinitesimalanalysis AT kutateladzess infinitesimalanalysis |