MARC details
| 000 -LEADER |
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| fixed length control field |
03215cam a2200253 a 4500 |
| 001 - CONTROL NUMBER |
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| control field |
vtls000001710 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
VRT |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20250102223524.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
081109s2001 riu |b 001 0 eng |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
0821820567 (alk. paper) |
| 039 #9 - LEVEL OF BIBLIOGRAPHIC CONTROL AND CODING DETAIL [OBSOLETE] |
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| Level of rules in bibliographic description |
201402040058 |
| Level of effort used to assign nonsubject heading access points |
VLOAD |
| Level of effort used to assign subject headings |
201007271141 |
| Level of effort used to assign classification |
malmash |
| Level of effort used to assign subject headings |
200811101314 |
| Level of effort used to assign classification |
venkatrajand |
| Level of effort used to assign subject headings |
200811091038 |
| Level of effort used to assign classification |
Noora |
| -- |
200811091037 |
| -- |
Noora |
| 050 00 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA649 |
| Item number |
.B47 2001 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Berndt, Rolf, |
| Dates associated with a name |
1940- |
| 9 (RLIN) |
25086 |
| 240 10 - UNIFORM TITLE |
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| Uniform title |
English |
| 245 13 - TITLE STATEMENT |
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| Title |
An Introduction to Symplectic Geometry / |
| Statement of responsibility, etc. |
Rolf Berndt ; translated by Michael Klucznik. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. |
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| Place of publication, distribution, etc. |
Providence, R.I. : |
| Name of publisher, distributor, etc. |
American Mathematical Society, |
| Date of publication, distribution, etc. |
c2001. |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
xvi, 195 p. ; |
| Dimensions |
26 cm. |
| 440 #0 - SERIES STATEMENT/ADDED ENTRY--TITLE |
|---|
| Title |
Graduate studies in mathematics, |
| Volume/sequential designation |
v. 26 |
| 9 (RLIN) |
10389 |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
|---|
| Bibliography, etc. note |
Includes bibliographical references (p. 185-187) and index. |
| 505 ## - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
Some aspects of theoretical mechanics Symplectic algebra Symplectic manifolds Hamiltonian vectorfields and the Poisson bracket The moment map Quantization Differentiable manifolds and vector bundles Lie groups and Lie algebras A little cohomology theory Representations of groups Bibliography Index Symbols. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc. |
Symplectic geometry is a central topic of current research in mathematics. Indeed, symplectic methods are key ingredients in the study of dynamical systems, differential equations, algebraic geometry, topology, mathematical physics and representations of Lie groups. This book is a true introduction to symplectic geometry, assuming only a general background in analysis and familiarity with linear algebra. It starts with the basics of the geometry of symplectic vector spaces. Then, symplectic manifolds are defined and explored. In addition to the essential classic results, such as Darboux's theorem, more recent results and ideas are also included here, such as symplectic capacity and pseudoholomorphic curves. These ideas have revolutionized the subject. The main examples of symplectic manifolds are given, including the cotangent bundle, Kahler manifolds, and coadjoint orbits.Further principal ideas are carefully examined, such as Hamiltonian vector fields, the Poisson bracket, and connections with contact manifolds. Berndt describes some of the close connections between symplectic geometry and mathematical physics in the last two chapters of the book. In particular, the moment map is defined and explored, both mathematically and in its relation to physics. He also introduces symplectic reduction, which is an important tool for reducing the number of variables in a physical system and for constructing new symplectic manifolds from old. The final chapter is on quantization, which uses symplectic methods to take classical mechanics to quantum mechanics.This section includes a discussion of the Heisenberg group and the Weil (or metaplectic) representation of the symplectic group. Several appendices provide background material on vector bundles, on cohomology, and on Lie groups and Lie algebras and their representations. Berndt's presentation of symplectic geometry is a clear and concise introduction to the major methods and applications of the subject, and requires only |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Symplectic geometry. |
| 9 (RLIN) |
25087 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
|---|
| Source of classification or shelving scheme |
Library of Congress Classification |
| Suppress in OPAC |
No |
| Koha item type |
Books |
