Contact geometry and non-linear differential equations / (Record no. 518364)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 03650nam a22003978i 4500 |
| 001 - CONTROL NUMBER | |
| control field | CR9780511735141 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | UkCbUP |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20200124160239.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS--GENERAL INFORMATION | |
| fixed length control field | m|||||o||d|||||||| |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr|||||||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 100325s2007||||enk o ||1 0|eng|d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9780511735141 (ebook) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Cancelled/invalid ISBN | 9780521824767 (hardback) |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | UkCbUP |
| Language of cataloging | eng |
| Description conventions | rda |
| Transcribing agency | UkCbUP |
| 050 00 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA614.3 |
| Item number | .K87 2007 |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 516.36 |
| Edition number | 22 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Kushner, Alexei, |
| Relator term | author. |
| 245 10 - TITLE STATEMENT | |
| Title | Contact geometry and non-linear differential equations / |
| Statement of responsibility, etc | Alexei Kushner, Valentin Lychagin, and Vladimir Rubtsov. |
| 246 3# - VARYING FORM OF TITLE | |
| Title proper/short title | Contact Geometry & Nonlinear Differential Equations |
| 264 #1 - Production, Publication, Distribution, Manufacture, and Copyright Notice (R) | |
| Place of production, publication, distribution, manufacture (R) | Cambridge : |
| Name of producer, publisher, distributor, manufacturer (R) | Cambridge University Press, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2007. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (xxi, 496 pages) : |
| Other physical details | digital, PDF file(s). |
| 336 ## - Content Type (R) | |
| Content type term (R) | text |
| Content type code (R) | txt |
| Source (NR) | rdacontent |
| 337 ## - Media Type (R) | |
| Media type term (R) | computer |
| Media type code (R) | c |
| Source (NR) | rdamedia |
| 338 ## - Carrier Type (R) | |
| Carrier type term (R) | online resource |
| Carrier type code (R) | cr |
| Source (NR) | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| სერიის ცნობა | Encyclopedia of mathematics and its applications ; |
| Volume number/sequential designation | volume 101 |
| 500 ## - GENERAL NOTE | |
| General note | Title from publisher's bibliographic system (viewed on 05 Oct 2015). |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 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 ## - SUMMARY, ETC. | |
| Summary, etc | 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 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Contact manifolds. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Differential equations, Nonlinear. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Lychagin, V. V. |
| Fuller form of name | (Valentin Vasilʹevich), |
| Relator term | author. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Rubtsov, Vladimir, |
| Dates associated with a name | 1952- |
| Relator term | author. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Display text | Print version: |
| International Standard Book Number | 9780521824767 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Encyclopedia of mathematics and its applications ; |
| Volume number/sequential designation | v. 101. |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://doi.org/10.1017/CBO9780511735141">https://doi.org/10.1017/CBO9780511735141</a> |
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