Asymptotics of Linear Differential Equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
2001
|
| Schriftenreihe: | Mathematics and Its Applications
533 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The asymptotic theory deals with the problem of determining the behaviour of a function in a neighborhood of its singular point. The function is replaced by another known function ( named the asymptotic function) close (in a sense) to the function under consideration. Many problems of mathematics, physics, and other divisions of natural science bring out the necessity of solving such problems. At the present time asymptotic theory has become an important and independent branch of mathematical analysis. The present consideration is mainly based on the theory of asymptotic spaces. Each asymptotic space is a collection of asymptotics united by an associated real function which determines their growth near the given point and (perhaps) some other analytic properties. The main contents of this book is the asymptotic theory of ordinary linear differential equations with variable coefficients. The equations with power order growth coefficients are considered in detail. As the application of the theory of differential asymptotic fields, we also consider the following asymptotic problems: the behaviour of explicit and implicit functions, improper integrals, integrals dependent on a large parameter, linear differential and difference equations, etc .. The obtained results have an independent meaning. The reader is assumed to be familiar with a comprehensive course of the mathematical analysis studied, for instance at mathematical departments of universities. Further necessary information is given in this book in summarized form with proofs of the main aspects |
| Beschreibung: | 1 Online-Ressource (IX, 441 p) |
| ISBN: | 9789401597975 9789048157730 |
| DOI: | 10.1007/978-94-015-9797-5 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042424167 | ||
| 003 | DE-604 | ||
| 005 | 20170912 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s2001 |||| o||u| ||||||eng d | ||
| 020 | |a 9789401597975 |c Online |9 978-94-015-9797-5 | ||
| 020 | |a 9789048157730 |c Print |9 978-90-481-5773-0 | ||
| 024 | 7 | |a 10.1007/978-94-015-9797-5 |2 doi | |
| 035 | |a (OCoLC)879622935 | ||
| 035 | |a (DE-599)BVBBV042424167 | ||
| 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 515.352 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Lantsman, M. H. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Asymptotics of Linear Differential Equations |c by M. H. Lantsman |
| 264 | 1 | |a Dordrecht |b Springer Netherlands |c 2001 | |
| 300 | |a 1 Online-Ressource (IX, 441 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and Its Applications |v 533 | |
| 500 | |a The asymptotic theory deals with the problem of determining the behaviour of a function in a neighborhood of its singular point. The function is replaced by another known function ( named the asymptotic function) close (in a sense) to the function under consideration. Many problems of mathematics, physics, and other divisions of natural science bring out the necessity of solving such problems. At the present time asymptotic theory has become an important and independent branch of mathematical analysis. The present consideration is mainly based on the theory of asymptotic spaces. Each asymptotic space is a collection of asymptotics united by an associated real function which determines their growth near the given point and (perhaps) some other analytic properties. The main contents of this book is the asymptotic theory of ordinary linear differential equations with variable coefficients. The equations with power order growth coefficients are considered in detail. As the application of the theory of differential asymptotic fields, we also consider the following asymptotic problems: the behaviour of explicit and implicit functions, improper integrals, integrals dependent on a large parameter, linear differential and difference equations, etc .. The obtained results have an independent meaning. The reader is assumed to be familiar with a comprehensive course of the mathematical analysis studied, for instance at mathematical departments of universities. Further necessary information is given in this book in summarized form with proofs of the main aspects | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Harmonic analysis | |
| 650 | 4 | |a Functional equations | |
| 650 | 4 | |a Operator theory | |
| 650 | 4 | |a Differential Equations | |
| 650 | 4 | |a Sequences (Mathematics) | |
| 650 | 4 | |a Ordinary Differential Equations | |
| 650 | 4 | |a Difference and Functional Equations | |
| 650 | 4 | |a Operator Theory | |
| 650 | 4 | |a Abstract Harmonic Analysis | |
| 650 | 4 | |a Sequences, Series, Summability | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Lineare gewöhnliche Differentialgleichung |0 (DE-588)4353441-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Asymptotik |0 (DE-588)4126634-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Lineare gewöhnliche Differentialgleichung |0 (DE-588)4353441-7 |D s |
| 689 | 0 | 1 | |a Asymptotik |0 (DE-588)4126634-1 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 830 | 0 | |a Mathematics and Its Applications |v 533 |w (DE-604)BV008163334 |9 533 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-94-015-9797-5 |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:BVB01-027859584 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804153100793020416 |
|---|---|
| any_adam_object | |
| author | Lantsman, M. H. |
| author_facet | Lantsman, M. H. |
| author_role | aut |
| author_sort | Lantsman, M. H. |
| author_variant | m h l mh mhl |
| building | Verbundindex |
| bvnumber | BV042424167 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)879622935 (DE-599)BVBBV042424167 |
| dewey-full | 515.352 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.352 |
| dewey-search | 515.352 |
| dewey-sort | 3515.352 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-015-9797-5 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03671nmm a2200589zcb4500</leader><controlfield tag="001">BV042424167</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20170912 </controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s2001 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789401597975</subfield><subfield code="c">Online</subfield><subfield code="9">978-94-015-9797-5</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789048157730</subfield><subfield code="c">Print</subfield><subfield code="9">978-90-481-5773-0</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-94-015-9797-5</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)879622935</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042424167</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">515.352</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">Lantsman, M. H.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Asymptotics of Linear Differential Equations</subfield><subfield code="c">by M. H. Lantsman</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Dordrecht</subfield><subfield code="b">Springer Netherlands</subfield><subfield code="c">2001</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (IX, 441 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="1" ind2=" "><subfield code="a">Mathematics and Its Applications</subfield><subfield code="v">533</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">The asymptotic theory deals with the problem of determining the behaviour of a function in a neighborhood of its singular point. The function is replaced by another known function ( named the asymptotic function) close (in a sense) to the function under consideration. Many problems of mathematics, physics, and other divisions of natural science bring out the necessity of solving such problems. At the present time asymptotic theory has become an important and independent branch of mathematical analysis. The present consideration is mainly based on the theory of asymptotic spaces. Each asymptotic space is a collection of asymptotics united by an associated real function which determines their growth near the given point and (perhaps) some other analytic properties. The main contents of this book is the asymptotic theory of ordinary linear differential equations with variable coefficients. The equations with power order growth coefficients are considered in detail. As the application of the theory of differential asymptotic fields, we also consider the following asymptotic problems: the behaviour of explicit and implicit functions, improper integrals, integrals dependent on a large parameter, linear differential and difference equations, etc .. The obtained results have an independent meaning. The reader is assumed to be familiar with a comprehensive course of the mathematical analysis studied, for instance at mathematical departments of universities. Further necessary information is given in this book in summarized form with proofs of the main aspects</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Harmonic analysis</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Functional equations</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Operator theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Differential Equations</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Sequences (Mathematics)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Ordinary Differential Equations</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Difference and Functional Equations</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Operator Theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Abstract Harmonic Analysis</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Sequences, Series, Summability</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Lineare gewöhnliche Differentialgleichung</subfield><subfield code="0">(DE-588)4353441-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Asymptotik</subfield><subfield code="0">(DE-588)4126634-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Lineare gewöhnliche Differentialgleichung</subfield><subfield code="0">(DE-588)4353441-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Asymptotik</subfield><subfield code="0">(DE-588)4126634-1</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="830" ind1=" " ind2="0"><subfield code="a">Mathematics and Its Applications</subfield><subfield code="v">533</subfield><subfield code="w">(DE-604)BV008163334</subfield><subfield code="9">533</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-94-015-9797-5</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:BVB01-027859584</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.BV042424167 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:15Z |
| institution | BVB |
| isbn | 9789401597975 9789048157730 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027859584 |
| oclc_num | 879622935 |
| 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 (IX, 441 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Springer Netherlands |
| record_format | marc |
| series | Mathematics and Its Applications |
| series2 | Mathematics and Its Applications |
| spelling | Lantsman, M. H. Verfasser aut Asymptotics of Linear Differential Equations by M. H. Lantsman Dordrecht Springer Netherlands 2001 1 Online-Ressource (IX, 441 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 533 The asymptotic theory deals with the problem of determining the behaviour of a function in a neighborhood of its singular point. The function is replaced by another known function ( named the asymptotic function) close (in a sense) to the function under consideration. Many problems of mathematics, physics, and other divisions of natural science bring out the necessity of solving such problems. At the present time asymptotic theory has become an important and independent branch of mathematical analysis. The present consideration is mainly based on the theory of asymptotic spaces. Each asymptotic space is a collection of asymptotics united by an associated real function which determines their growth near the given point and (perhaps) some other analytic properties. The main contents of this book is the asymptotic theory of ordinary linear differential equations with variable coefficients. The equations with power order growth coefficients are considered in detail. As the application of the theory of differential asymptotic fields, we also consider the following asymptotic problems: the behaviour of explicit and implicit functions, improper integrals, integrals dependent on a large parameter, linear differential and difference equations, etc .. The obtained results have an independent meaning. The reader is assumed to be familiar with a comprehensive course of the mathematical analysis studied, for instance at mathematical departments of universities. Further necessary information is given in this book in summarized form with proofs of the main aspects Mathematics Harmonic analysis Functional equations Operator theory Differential Equations Sequences (Mathematics) Ordinary Differential Equations Difference and Functional Equations Operator Theory Abstract Harmonic Analysis Sequences, Series, Summability Mathematik Lineare gewöhnliche Differentialgleichung (DE-588)4353441-7 gnd rswk-swf Asymptotik (DE-588)4126634-1 gnd rswk-swf Lineare gewöhnliche Differentialgleichung (DE-588)4353441-7 s Asymptotik (DE-588)4126634-1 s 1\p DE-604 Mathematics and Its Applications 533 (DE-604)BV008163334 533 https://doi.org/10.1007/978-94-015-9797-5 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lantsman, M. H. Asymptotics of Linear Differential Equations Mathematics and Its Applications Mathematics Harmonic analysis Functional equations Operator theory Differential Equations Sequences (Mathematics) Ordinary Differential Equations Difference and Functional Equations Operator Theory Abstract Harmonic Analysis Sequences, Series, Summability Mathematik Lineare gewöhnliche Differentialgleichung (DE-588)4353441-7 gnd Asymptotik (DE-588)4126634-1 gnd |
| subject_GND | (DE-588)4353441-7 (DE-588)4126634-1 |
| title | Asymptotics of Linear Differential Equations |
| title_auth | Asymptotics of Linear Differential Equations |
| title_exact_search | Asymptotics of Linear Differential Equations |
| title_full | Asymptotics of Linear Differential Equations by M. H. Lantsman |
| title_fullStr | Asymptotics of Linear Differential Equations by M. H. Lantsman |
| title_full_unstemmed | Asymptotics of Linear Differential Equations by M. H. Lantsman |
| title_short | Asymptotics of Linear Differential Equations |
| title_sort | asymptotics of linear differential equations |
| topic | Mathematics Harmonic analysis Functional equations Operator theory Differential Equations Sequences (Mathematics) Ordinary Differential Equations Difference and Functional Equations Operator Theory Abstract Harmonic Analysis Sequences, Series, Summability Mathematik Lineare gewöhnliche Differentialgleichung (DE-588)4353441-7 gnd Asymptotik (DE-588)4126634-1 gnd |
| topic_facet | Mathematics Harmonic analysis Functional equations Operator theory Differential Equations Sequences (Mathematics) Ordinary Differential Equations Difference and Functional Equations Operator Theory Abstract Harmonic Analysis Sequences, Series, Summability Mathematik Lineare gewöhnliche Differentialgleichung Asymptotik |
| url | https://doi.org/10.1007/978-94-015-9797-5 |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT lantsmanmh asymptoticsoflineardifferentialequations |