Contact geometry and non-linear differential equations:
Methods from contact and symplectic geometry can be used to solve highly non-trivial nonlinear partial and ordinary differential equations without resorting to approximate numerical methods or algebraic computing software. This book explains how it's done. It combines the clarity and accessibil...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2007
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications
volume 101 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 URL des Erstveröffentlichers |
| Zusammenfassung: | Methods from contact and symplectic geometry can be used to solve highly non-trivial nonlinear partial and ordinary differential equations without resorting to approximate numerical methods or algebraic computing software. This book explains how it's done. It combines the clarity and accessibility of an advanced textbook with the completeness of an encyclopedia. The basic ideas that Lie and Cartan developed at the end of the nineteenth century to transform solving a differential equation into a problem in geometry or algebra are here reworked in a novel and modern way. Differential equations are considered as a part of contact and symplectic geometry, so that all the machinery of Hodge-deRham calculus can be applied. In this way a wide class of equations can be tackled, including quasi-linear equations and Monge-Ampere equations (which play an important role in modern theoretical physics and meteorology) |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xxi, 496 pages) |
| ISBN: | 9780511735141 |
| DOI: | 10.1017/CBO9780511735141 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV043942165 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 161206s2007 |||| o||u| ||||||eng d | ||
| 020 | |a 9780511735141 |c Online |9 978-0-511-73514-1 | ||
| 024 | 7 | |a 10.1017/CBO9780511735141 |2 doi | |
| 035 | |a (ZDB-20-CBO)CR9780511735141 | ||
| 035 | |a (OCoLC)850420492 | ||
| 035 | |a (DE-599)BVBBV043942165 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-92 | ||
| 082 | 0 | |a 516.36 |2 22 | |
| 084 | |a SK 920 |0 (DE-625)143272: |2 rvk | ||
| 100 | 1 | |a Kushner, Alexei |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Contact geometry and non-linear differential equations |c Alexei Kushner, Valentin Lychagin, and Vladimir Rubtsov |
| 246 | 1 | 3 | |a Contact Geometry & Nonlinear Differential Equations |
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 2007 | |
| 300 | |a 1 online resource (xxi, 496 pages) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Encyclopedia of mathematics and its applications |v volume 101 | |
| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 505 | 8 | |a Symmetries and integrals -- Distributions -- Ordinary differential equations -- Model differential equations and the lie superposition principle -- Symplectic algebra -- Linear algebra of symplectic vector spaces -- Exterior algebra on symplectic vector spaces -- A symplectic classification of exterior 2-forms in dimension 4 -- Symplectic classification of exterior 2-forms -- Classification of exterior 3-forms on a six-dimensional symplectic space -- Monge-Ampère equations -- Symplectic manifolds -- Contact manifolds -- Monge-Ampère equations -- Symmetries and contact transformations of Monge-Ampère equations -- Conservation laws -- Monge-Ampère equations on two-dimensional manifolds and geometric structures -- Systems of first-order partial differential equations on two-dimensional manifolds -- Applications -- Non-linear acoustics -- Non-linear thermal conductivity -- Meteorology applications -- Classification of Monge-Ampère equations -- Classification of symplectic MAOs on two-dimensional manifolds -- Classification of symplectic MAEs on two-dimensional manifolds -- Contact classification of MAEs on two-dimensional manifolds -- Symplectic classification of MAEs on three-dimensional manifolds | |
| 520 | |a Methods from contact and symplectic geometry can be used to solve highly non-trivial nonlinear partial and ordinary differential equations without resorting to approximate numerical methods or algebraic computing software. This book explains how it's done. It combines the clarity and accessibility of an advanced textbook with the completeness of an encyclopedia. The basic ideas that Lie and Cartan developed at the end of the nineteenth century to transform solving a differential equation into a problem in geometry or algebra are here reworked in a novel and modern way. Differential equations are considered as a part of contact and symplectic geometry, so that all the machinery of Hodge-deRham calculus can be applied. In this way a wide class of equations can be tackled, including quasi-linear equations and Monge-Ampere equations (which play an important role in modern theoretical physics and meteorology) | ||
| 650 | 4 | |a Contact manifolds | |
| 650 | 4 | |a Differential equations, Nonlinear | |
| 700 | 1 | |a Lychagin, V. V. |e Sonstige |4 oth | |
| 700 | 1 | |a Rubtsov, Vladimir |d 1952- |e Sonstige |4 oth | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druckausgabe |z 978-0-521-82476-7 |
| 856 | 4 | 0 | |u https://doi.org/10.1017/CBO9780511735141 |x Verlag |z URL des Erstveröffentlichers |3 Volltext |
| 912 | |a ZDB-20-CBO | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-029351134 | ||
| 966 | e | |u https://doi.org/10.1017/CBO9780511735141 |l BSB01 |p ZDB-20-CBO |q BSB_PDA_CBO |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1017/CBO9780511735141 |l FHN01 |p ZDB-20-CBO |q FHN_PDA_CBO |x Verlag |3 Volltext | |
Datensatz im Suchindex
| _version_ | 1804176884669349888 |
|---|---|
| any_adam_object | |
| author | Kushner, Alexei |
| author_facet | Kushner, Alexei |
| author_role | aut |
| author_sort | Kushner, Alexei |
| author_variant | a k ak |
| building | Verbundindex |
| bvnumber | BV043942165 |
| classification_rvk | SK 920 |
| collection | ZDB-20-CBO |
| contents | Symmetries and integrals -- Distributions -- Ordinary differential equations -- Model differential equations and the lie superposition principle -- Symplectic algebra -- Linear algebra of symplectic vector spaces -- Exterior algebra on symplectic vector spaces -- A symplectic classification of exterior 2-forms in dimension 4 -- Symplectic classification of exterior 2-forms -- Classification of exterior 3-forms on a six-dimensional symplectic space -- Monge-Ampère equations -- Symplectic manifolds -- Contact manifolds -- Monge-Ampère equations -- Symmetries and contact transformations of Monge-Ampère equations -- Conservation laws -- Monge-Ampère equations on two-dimensional manifolds and geometric structures -- Systems of first-order partial differential equations on two-dimensional manifolds -- Applications -- Non-linear acoustics -- Non-linear thermal conductivity -- Meteorology applications -- Classification of Monge-Ampère equations -- Classification of symplectic MAOs on two-dimensional manifolds -- Classification of symplectic MAEs on two-dimensional manifolds -- Contact classification of MAEs on two-dimensional manifolds -- Symplectic classification of MAEs on three-dimensional manifolds |
| ctrlnum | (ZDB-20-CBO)CR9780511735141 (OCoLC)850420492 (DE-599)BVBBV043942165 |
| dewey-full | 516.36 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.36 |
| dewey-search | 516.36 |
| dewey-sort | 3516.36 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511735141 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03982nmm a2200469zcb4500</leader><controlfield tag="001">BV043942165</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">161206s2007 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780511735141</subfield><subfield code="c">Online</subfield><subfield code="9">978-0-511-73514-1</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1017/CBO9780511735141</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ZDB-20-CBO)CR9780511735141</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)850420492</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV043942165</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-12</subfield><subfield code="a">DE-92</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">516.36</subfield><subfield code="2">22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 920</subfield><subfield code="0">(DE-625)143272:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Kushner, Alexei</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Contact geometry and non-linear differential equations</subfield><subfield code="c">Alexei Kushner, Valentin Lychagin, and Vladimir Rubtsov</subfield></datafield><datafield tag="246" ind1="1" ind2="3"><subfield code="a">Contact Geometry & Nonlinear Differential Equations</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge</subfield><subfield code="b">Cambridge University Press</subfield><subfield code="c">2007</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (xxi, 496 pages)</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">Encyclopedia of mathematics and its applications</subfield><subfield code="v">volume 101</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Title from publisher's bibliographic system (viewed on 05 Oct 2015)</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">Symmetries and integrals -- Distributions -- Ordinary differential equations -- Model differential equations and the lie superposition principle -- Symplectic algebra -- Linear algebra of symplectic vector spaces -- Exterior algebra on symplectic vector spaces -- A symplectic classification of exterior 2-forms in dimension 4 -- Symplectic classification of exterior 2-forms -- Classification of exterior 3-forms on a six-dimensional symplectic space -- Monge-Ampère equations -- Symplectic manifolds -- Contact manifolds -- Monge-Ampère equations -- Symmetries and contact transformations of Monge-Ampère equations -- Conservation laws -- Monge-Ampère equations on two-dimensional manifolds and geometric structures -- Systems of first-order partial differential equations on two-dimensional manifolds -- Applications -- Non-linear acoustics -- Non-linear thermal conductivity -- Meteorology applications -- Classification of Monge-Ampère equations -- Classification of symplectic MAOs on two-dimensional manifolds -- Classification of symplectic MAEs on two-dimensional manifolds -- Contact classification of MAEs on two-dimensional manifolds -- Symplectic classification of MAEs on three-dimensional manifolds</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Methods from contact and symplectic geometry can be used to solve highly non-trivial nonlinear partial and ordinary differential equations without resorting to approximate numerical methods or algebraic computing software. This book explains how it's done. It combines the clarity and accessibility of an advanced textbook with the completeness of an encyclopedia. The basic ideas that Lie and Cartan developed at the end of the nineteenth century to transform solving a differential equation into a problem in geometry or algebra are here reworked in a novel and modern way. Differential equations are considered as a part of contact and symplectic geometry, so that all the machinery of Hodge-deRham calculus can be applied. In this way a wide class of equations can be tackled, including quasi-linear equations and Monge-Ampere equations (which play an important role in modern theoretical physics and meteorology)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Contact manifolds</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Differential equations, Nonlinear</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Lychagin, V. V.</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Rubtsov, Vladimir</subfield><subfield code="d">1952-</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druckausgabe</subfield><subfield code="z">978-0-521-82476-7</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1017/CBO9780511735141</subfield><subfield code="x">Verlag</subfield><subfield code="z">URL des Erstveröffentlichers</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-20-CBO</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-029351134</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9780511735141</subfield><subfield code="l">BSB01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">BSB_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9780511735141</subfield><subfield code="l">FHN01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">FHN_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV043942165 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:17Z |
| institution | BVB |
| isbn | 9780511735141 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029351134 |
| oclc_num | 850420492 |
| open_access_boolean | |
| owner | DE-12 DE-92 |
| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (xxi, 496 pages) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Encyclopedia of mathematics and its applications |
| spelling | Kushner, Alexei Verfasser aut Contact geometry and non-linear differential equations Alexei Kushner, Valentin Lychagin, and Vladimir Rubtsov Contact Geometry & Nonlinear Differential Equations Cambridge Cambridge University Press 2007 1 online resource (xxi, 496 pages) txt rdacontent c rdamedia cr rdacarrier Encyclopedia of mathematics and its applications volume 101 Title from publisher's bibliographic system (viewed on 05 Oct 2015) Symmetries and integrals -- Distributions -- Ordinary differential equations -- Model differential equations and the lie superposition principle -- Symplectic algebra -- Linear algebra of symplectic vector spaces -- Exterior algebra on symplectic vector spaces -- A symplectic classification of exterior 2-forms in dimension 4 -- Symplectic classification of exterior 2-forms -- Classification of exterior 3-forms on a six-dimensional symplectic space -- Monge-Ampère equations -- Symplectic manifolds -- Contact manifolds -- Monge-Ampère equations -- Symmetries and contact transformations of Monge-Ampère equations -- Conservation laws -- Monge-Ampère equations on two-dimensional manifolds and geometric structures -- Systems of first-order partial differential equations on two-dimensional manifolds -- Applications -- Non-linear acoustics -- Non-linear thermal conductivity -- Meteorology applications -- Classification of Monge-Ampère equations -- Classification of symplectic MAOs on two-dimensional manifolds -- Classification of symplectic MAEs on two-dimensional manifolds -- Contact classification of MAEs on two-dimensional manifolds -- Symplectic classification of MAEs on three-dimensional manifolds Methods from contact and symplectic geometry can be used to solve highly non-trivial nonlinear partial and ordinary differential equations without resorting to approximate numerical methods or algebraic computing software. This book explains how it's done. It combines the clarity and accessibility of an advanced textbook with the completeness of an encyclopedia. The basic ideas that Lie and Cartan developed at the end of the nineteenth century to transform solving a differential equation into a problem in geometry or algebra are here reworked in a novel and modern way. Differential equations are considered as a part of contact and symplectic geometry, so that all the machinery of Hodge-deRham calculus can be applied. In this way a wide class of equations can be tackled, including quasi-linear equations and Monge-Ampere equations (which play an important role in modern theoretical physics and meteorology) Contact manifolds Differential equations, Nonlinear Lychagin, V. V. Sonstige oth Rubtsov, Vladimir 1952- Sonstige oth Erscheint auch als Druckausgabe 978-0-521-82476-7 https://doi.org/10.1017/CBO9780511735141 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Kushner, Alexei Contact geometry and non-linear differential equations Symmetries and integrals -- Distributions -- Ordinary differential equations -- Model differential equations and the lie superposition principle -- Symplectic algebra -- Linear algebra of symplectic vector spaces -- Exterior algebra on symplectic vector spaces -- A symplectic classification of exterior 2-forms in dimension 4 -- Symplectic classification of exterior 2-forms -- Classification of exterior 3-forms on a six-dimensional symplectic space -- Monge-Ampère equations -- Symplectic manifolds -- Contact manifolds -- Monge-Ampère equations -- Symmetries and contact transformations of Monge-Ampère equations -- Conservation laws -- Monge-Ampère equations on two-dimensional manifolds and geometric structures -- Systems of first-order partial differential equations on two-dimensional manifolds -- Applications -- Non-linear acoustics -- Non-linear thermal conductivity -- Meteorology applications -- Classification of Monge-Ampère equations -- Classification of symplectic MAOs on two-dimensional manifolds -- Classification of symplectic MAEs on two-dimensional manifolds -- Contact classification of MAEs on two-dimensional manifolds -- Symplectic classification of MAEs on three-dimensional manifolds Contact manifolds Differential equations, Nonlinear |
| title | Contact geometry and non-linear differential equations |
| title_alt | Contact Geometry & Nonlinear Differential Equations |
| title_auth | Contact geometry and non-linear differential equations |
| title_exact_search | Contact geometry and non-linear differential equations |
| title_full | Contact geometry and non-linear differential equations Alexei Kushner, Valentin Lychagin, and Vladimir Rubtsov |
| title_fullStr | Contact geometry and non-linear differential equations Alexei Kushner, Valentin Lychagin, and Vladimir Rubtsov |
| title_full_unstemmed | Contact geometry and non-linear differential equations Alexei Kushner, Valentin Lychagin, and Vladimir Rubtsov |
| title_short | Contact geometry and non-linear differential equations |
| title_sort | contact geometry and non linear differential equations |
| topic | Contact manifolds Differential equations, Nonlinear |
| topic_facet | Contact manifolds Differential equations, Nonlinear |
| url | https://doi.org/10.1017/CBO9780511735141 |
| work_keys_str_mv | AT kushneralexei contactgeometryandnonlineardifferentialequations AT lychaginvv contactgeometryandnonlineardifferentialequations AT rubtsovvladimir contactgeometryandnonlineardifferentialequations AT kushneralexei contactgeometrynonlineardifferentialequations AT lychaginvv contactgeometrynonlineardifferentialequations AT rubtsovvladimir contactgeometrynonlineardifferentialequations |