Infinitesimal analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Dordrecht
Kluwer Academic Publishers
2002
|
| Series: | Mathematics and its applications
544 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. [385]-413) and indexes |
| Physical Description: | xiii, 422 p. ill. : 25 cm |
| ISBN: | 1402007388 |
Staff View
MARC
| LEADER | 00000nam a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV014629994 | ||
| 003 | DE-604 | ||
| 005 | 20050202 | ||
| 007 | t | ||
| 008 | 020731s2002 ne a||| |||| 00||| eng d | ||
| 010 | |a 2002074109 | ||
| 020 | |a 1402007388 |9 1-4020-0738-8 | ||
| 035 | |a (OCoLC)50252091 | ||
| 035 | |a (DE-599)BVBBV014629994 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 1 | |a eng |h rus | |
| 044 | |a ne |c NL | ||
| 049 | |a DE-703 | ||
| 050 | 0 | |a QA299.82 | |
| 082 | 0 | |a 519.4 |2 21 | |
| 084 | |a SK 400 |0 (DE-625)143237: |2 rvk | ||
| 100 | 1 | |a Gordon, Evgenij I. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Infinitesimal analysis |c by E.I. Gordon, A.G. Kusraev, and S.S. Kutateladze |
| 264 | 1 | |a Dordrecht |b Kluwer Academic Publishers |c 2002 | |
| 300 | |a xiii, 422 p. |b ill. : 25 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications |v 544 | |
| 500 | |a Includes bibliographical references (p. [385]-413) and indexes | ||
| 650 | 4 | |a Nonstandard mathematical analysis | |
| 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 | |5 DE-604 | |
| 700 | 1 | |a Kusraev, A. G. |e Sonstige |4 oth | |
| 700 | 1 | |a Kutateladze, Semen S. |d 1945- |e Sonstige |0 (DE-588)123299268 |4 oth | |
| 830 | 0 | |a Mathematics and its applications |v 544 |w (DE-604)BV008163334 |9 544 | |
| 856 | 4 | 2 | |m HEBIS Datenaustausch Darmstadt |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009940626&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-009940626 | ||
Record in the Search Index
| _version_ | 1804129402063159296 |
|---|---|
| adam_text | INFINITESIMAL ANALYSIS BY E.I. GORDON EASTERN ILLINOIS UNIVERSITY,
CHARLESTON, ILLINOIS, U.S.A. A.G. KUSRAEV VLADIKAVKAZ STATE UNIVERSITY,
VLADIKAVKAZ, RUSSIA AND S.S. KUTATELADZE SOBOLEV INSTITUTE OF
MATHEMATICS, SIBERIAN DIVISION OF THE RUSSIAN ACADEMY OF SCIENCES,
NOVOSIBIRSK, RUSSIA KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON /
LONDON CONTENTS FOREWORD IX CHAPTER 1. EXCURSUS INTO THE HISTORY OF
CALCULUS 1 § 1.1. G. W. LEIBNIZ AND I. NEWTON 2 § 1.2. L. EULER 5 § 1.3.
G. BERKELEY 5 § 1.4. J. D ALEMBERT AND L. CARNOT 6 § 1.5. B. BOLZANO, A.
CAUCHY, AND K. WEIERSTRASS 7 § 1.6. N. N. LUZIN 7 § 1.7. A. ROBINSON 9
CHAPTER 2. NAIVE FOUNDATIONS OF INFINITESIMAL ANALYSIS 10 § 2.1. THE
CONCEPT OF SET IN INFINITESIMAL ANALYSIS 10 § 2.2. PRELIMINARIES ON
STANDARD AND NONSTANDARD REALS 16 § 2.3. BASICS OF CALCULUS ON THE REAL
AXIS 23 CHAPTER 3. SET-THEORETIC FORMALISMS OF INFINITESIMAL ANALYSIS 35
§ 3.1. THE LANGUAGE OF SET THEORY 37 § 3.2. ZERMELO-FRAENKEL SET THEORY
47 § 3.3. NELSON INTERNAL SET THEORY 64 5 3.4. EXTERNAL SET THEORIES ..
. . 72 VI CONTENTS § 3.5. CREDENDA OF INFINITESIMAL ANALYSIS 80 § 3.6.
VON NEUMANN-GODEL-BERNAYS THEORY 85 § 3.7. NONSTANDARD CLASS THEORY 94 §
3.8. CONSISTENCY OF NCT 101 § 3.9. RELATIVE INTERNAL SET THEORY 106
CHAPTER 4. MONADS IN GENERAL TOPOLOGY 116 § 4.1. MONADS AND FILTERS 116
§ 4.2. MONADS AND TOPOLOGICAL SPACES 123 § 4.3. NEARSTANDARDNESS AND
COMPACTNESS 126 § 4.4. INFINITE PROXIMITY IN UNIFORM SPACE 129 § 4.5.
PRENEARSTANDARDNESS, COMPACTNESS, AND TOTAL BOUNDEDNESS .. 133 § 4.6.
RELATIVE MONADS 140 § 4.7. COMPACTNESS AND SUBCONTINUITY 148 § 4.8.
CYCLIC AND EXTENSIONAL FILTERS 151 § 4.9. ESSENTIAL AND PROIDEAL POINTS
OF CYCLIC MONADS 156 § 4.10. DESCENDING COMPACT AND PRECOMPACT SPACES
159 § 4.11. PROULTRAFILTERS AND EXTENSIONAL FILTERS 160 CHAPTER 5.
INFINITESIMALS AND SUB DIFFERENTIALS 166 § 5.1. VECTOR TOPOLOGY 166 §
5.2. CLASSICAL APPROXIMATING AND REGULARIZING CONES 170 § 5.3.
KURATOWSKI AND ROCKAFELLAR LIMITS 180 § 5.4. APPROXIMATION GIVEN A SET
OF INFINITESIMALS 189 § 5.5. APPROXIMATION TO COMPOSITES 199, § 5.6.
INFINITESIMAL SUBDIFFERENTIALS 204 § 5.7. INFINITESIMAL OPTIMALITY 219
CONTENTS VII CHAPTER 6. TECHNIQUE OF HYPERAPPROXIMATION 223 § 6.1.
NONSTANDARD HULLS 224 § 6.2. DISCRETE APPROXIMATION IN BANACH SPACE 233
§ 6.3. LOEB MEASURE 242 § 6.4. HYPERAPPROXIMATION OF MEASURE SPACE 252 §
6.5. HYPERAPPROXIMATION OF INTEGRAL OPERATORS 262 § 6.6. PSEUDOINTEGRAL
OPERATORS AND RANDOM LOEB MEASURES 272 CHAPTER 7. INFINITESIMALS IN
HARMONIC ANALYSIS 281 § 7.1. HYPERAPPROXIMATION OF THE FOURIER TRANSFORM
ON THE REALS ... 281 § 7.2. A NONSTANDARD HULL OF A HYPERFINITE GROUP
294 § 7.3. THE CASE OF A COMPACT NONSTANDARD HULL 307 § 7.4.
HYPERAPPROXIMATION OF LOCALLY COMPACT ABELIAN GROUPS .... 316 § 7.5.
EXAMPLES OF HYPERAPPROXIMATION 327 § 7.6. DISCRETE APPROXIMATION OF
FUNCTION SPACES ON A LOCALLY COMPACT ABELIAN GROUP 340 § 7.7.
HYPERAPPROXIMATION OF PSEUDODIFFERENTIAL OPERATORS 355 CHAPTER 8.
EXERCISES AND UNSOLVED PROBLEMS 367 § 8.1. NONSTANDARD HULLS AND LOEB
MEASURES 367 § 8.2. HYPERAPPROXIMATION AND SPECTRAL THEORY 369 § 8.3.
COMBINING NONSTANDARD METHODS 371 § 8.4. CONVEX ANALYSIS AND EXTREMAL
PROBLEMS 374 § 8.5. MISCELLANY 376 APPENDIX , 380 REFERENCES 385
NOTATION INDEX 414 SUBJECT INDEX 417
|
| any_adam_object | 1 |
| author | Gordon, Evgenij I. |
| author_GND | (DE-588)123299268 |
| author_facet | Gordon, Evgenij I. |
| author_role | aut |
| author_sort | Gordon, Evgenij I. |
| author_variant | e i g ei eig |
| building | Verbundindex |
| bvnumber | BV014629994 |
| callnumber-first | Q - Science |
| callnumber-label | QA299 |
| callnumber-raw | QA299.82 |
| callnumber-search | QA299.82 |
| callnumber-sort | QA 3299.82 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 400 |
| ctrlnum | (OCoLC)50252091 (DE-599)BVBBV014629994 |
| dewey-full | 519.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.4 |
| dewey-search | 519.4 |
| dewey-sort | 3519.4 |
| 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>01695nam a2200433zcb4500</leader><controlfield tag="001">BV014629994</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20050202 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">020731s2002 ne a||| |||| 00||| eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">2002074109</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1402007388</subfield><subfield code="9">1-4020-0738-8</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)50252091</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV014629994</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="1" ind2=" "><subfield code="a">eng</subfield><subfield code="h">rus</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">ne</subfield><subfield code="c">NL</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-703</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA299.82</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519.4</subfield><subfield code="2">21</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">Gordon, Evgenij 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, and S.S. Kutateladze</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Dordrecht</subfield><subfield code="b">Kluwer Academic Publishers</subfield><subfield code="c">2002</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">xiii, 422 p.</subfield><subfield code="b">ill. : 25 cm</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="1" ind2=" "><subfield code="a">Mathematics and its applications</subfield><subfield code="v">544</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references (p. [385]-413) and indexes</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Nonstandard mathematical analysis</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="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, Semen S.</subfield><subfield code="d">1945-</subfield><subfield code="e">Sonstige</subfield><subfield code="0">(DE-588)123299268</subfield><subfield code="4">oth</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Mathematics and its applications</subfield><subfield code="v">544</subfield><subfield code="w">(DE-604)BV008163334</subfield><subfield code="9">544</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HEBIS Datenaustausch Darmstadt</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=009940626&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:BVB01-009940626</subfield></datafield></record></collection> |
| id | DE-604.BV014629994 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:04:34Z |
| institution | BVB |
| isbn | 1402007388 |
| language | English Russian |
| lccn | 2002074109 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009940626 |
| oclc_num | 50252091 |
| open_access_boolean | |
| owner | DE-703 |
| owner_facet | DE-703 |
| physical | xiii, 422 p. ill. : 25 cm |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Kluwer Academic Publishers |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Gordon, Evgenij I. Verfasser aut Infinitesimal analysis by E.I. Gordon, A.G. Kusraev, and S.S. Kutateladze Dordrecht Kluwer Academic Publishers 2002 xiii, 422 p. ill. : 25 cm txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 544 Includes bibliographical references (p. [385]-413) and indexes Nonstandard mathematical analysis Infinitesimalanalysis (DE-588)4161657-1 gnd rswk-swf Infinitesimalanalysis (DE-588)4161657-1 s DE-604 Kusraev, A. G. Sonstige oth Kutateladze, Semen S. 1945- Sonstige (DE-588)123299268 oth Mathematics and its applications 544 (DE-604)BV008163334 544 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009940626&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gordon, Evgenij I. Infinitesimal analysis Mathematics and its applications Nonstandard mathematical analysis 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, and S.S. Kutateladze |
| title_fullStr | Infinitesimal analysis by E.I. Gordon, A.G. Kusraev, and S.S. Kutateladze |
| title_full_unstemmed | Infinitesimal analysis by E.I. Gordon, A.G. Kusraev, and S.S. Kutateladze |
| title_short | Infinitesimal analysis |
| title_sort | infinitesimal analysis |
| topic | Nonstandard mathematical analysis Infinitesimalanalysis (DE-588)4161657-1 gnd |
| topic_facet | Nonstandard mathematical analysis Infinitesimalanalysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009940626&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT gordonevgeniji infinitesimalanalysis AT kusraevag infinitesimalanalysis AT kutateladzesemens infinitesimalanalysis |