MARC ayrıntıları
| 000 -LEADER |
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| fixed length control field |
03565nam a2200349 i 4500 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
990505s2000 enka b 001 0 eng |
| 010 ## - LIBRARY OF CONGRESS CONTROL NUMBER |
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| LC control number |
99031354 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
0521497035 |
| Qualifying information |
(hardback) |
|
|---|
| International Standard Book Number |
0521497868 |
| Qualifying information |
(paperback) |
| 040 ## - CATALOGING SOURCE |
|---|
| Original cataloging agency |
DLC |
| Transcribing agency |
DLC |
| Modifying agency |
YDX |
| -- |
BAUN |
| Description conventions |
rda |
| 049 ## - LOCAL HOLDINGS (OCLC) |
|---|
| Holding library |
BAUN_MERKEZ |
| 050 04 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QC20.7.D5 |
| Item number |
H93 2000 |
| 082 00 - DEWEY DECIMAL CLASSIFICATION NUMBER |
|---|
| Edition number |
21 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
|---|
| Personal name |
Hydon, Peter E. |
| Fuller form of name |
(Peter Ellsworth), |
| Dates associated with a name |
1960- |
| 245 10 - TITLE STATEMENT |
|---|
| Title |
Symmetry methods for differential equations : |
| Remainder of title |
a beginner's guide / |
| Statement of responsibility, etc |
Peter E. Hydon |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE |
|---|
| Place of production, publication, distribution, manufacture |
Cambridge ; |
| -- |
New York : |
| Name of producer, publisher, distributor, manufacturer |
Cambridge University Press, |
| Date of production, publication, distribution, manufacture, or copyright notice |
2000. |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
xi, 213 pages : |
| Other physical details |
illustrations ; |
| Dimensions |
24 cm |
| 336 ## - CONTENT TYPE |
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| Content Type Term |
text |
| Content Type Code |
txt |
| Source |
rdacontent |
| 337 ## - MEDIA TYPE |
|---|
| Media Type Term |
unmediated |
| Media Type Code |
unmediated |
| Source |
rdamedia |
| 338 ## - CARRIER TYPE |
|---|
| Carrier Type Term |
volume |
| Carrier Type Code |
volume |
| Source |
rdacarrier |
| 490 1# - SERIES STATEMENT |
|---|
| Series statement |
Cambridge texts in applied mathematics |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
|---|
| Bibliography, etc |
Includes bibliographical references (pages 209-210) and index |
| 505 00 - FORMATTED CONTENTS NOTE |
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| Title |
Preface |
| -- |
Acknowledgements |
| -- |
1 Introduction to Symmetries 1 |
| -- |
1.1 Symmetries of Planar Objects 1 |
| -- |
1.2 Symmetries of the Simplest ODE 5 |
| -- |
1.3 The Symmetry Condition for First-Order ODEs 8 |
| -- |
1.4 Lie Symmetries Solve First-Order ODEs 11 |
| -- |
2 Lie Symmetries of First-Order ODEs 15 |
| -- |
2.1 The Action of Lie Symmetries on the Plane 15 |
| -- |
2.2 Canonical Coordinates 22 |
| -- |
2.3 How to Solve ODEs with Lie Symmetries 26 |
| -- |
2.4 The Linearized Symmetry Condition 30 |
| -- |
2.5 Symmetries and Standard Methods 34 |
| -- |
2.6 The Infinitesimal Generator 38 |
| -- |
3 How to Find Lie Point Symmetries of ODEs 43 |
| -- |
3.1 The Symmetry Condition 43 |
| -- |
3.2 The Determining Equations for Lie Point Symmetries 46 |
| -- |
3.3 Linear ODEs 52 |
| -- |
3.4 Justification of the Symmetry Condition 54 |
| -- |
4 How to Use a One-Parameter Lie Group 58 |
| -- |
4.1 Reduction of Order by Using Canonical Coordinates 58 |
| -- |
4.2 Variational Symmetries 63 |
| -- |
4.3 Invariant Solutions 68 |
| -- |
5 Lie Symmetries with Several Parameters 74 |
| -- |
5.1 Differential Invariants and Reduction of Order 74 |
| -- |
5.2 The Lie Algebra of Point Symmetry Generators 79 |
| -- |
5.3 Stepwise Integration of ODEs 89 |
| -- |
6 Solution of ODEs with Multiparameter Lie Groups 93 |
| -- |
6.1 The Basic Method: Exploiting Solvability 93 |
| -- |
6.2 New Symmetries Obtained During Reduction 99 |
| -- |
6.3 Integration of Third-Order ODEs with sl(2) 101 |
| -- |
7 Techniques Based on First Integrals 108 |
| -- |
7.1 First Integrals Derived from Symmetries 108 |
| -- |
7.2 Contact Symmetries and Dynamical Symmetries 116 |
| -- |
7.3 Integrating Factors 122 |
| -- |
7.4 Systems of ODEs 128 |
| -- |
8 How to Obtain Lie Point Symmetries of PDEs 136 |
| -- |
8.1 Scalar PDEs with Two Dependent Variables 136 |
| -- |
8.2 The Linearized Symmetry Condition for General PDEs 146 |
| -- |
8.3 Finding Symmetries by Computer Algebra 149 |
| -- |
9 Methods for Obtaining Exact Solutions of PDEs 155 |
| -- |
9.1 Group-Invariant Solutions 155 |
| -- |
9.2 New Solutions from Known Ones 162 |
| -- |
9.3 Nonclassical Symmetries 166 |
| -- |
10 Classification of Invariant Solutions 173 |
| -- |
10.1 Equivalence of Invariant Solutions 173 |
| -- |
10.2 How to Classify Symmetry Generators 176 |
| -- |
10.3 Optimal Systems of Invariant Solutions 182 |
| -- |
11 Discrete Symmetries 187 |
| -- |
11.1 Some Uses of Discrete Symmetries 187 |
| -- |
11.2 How to Obtain Discrete Symmetries from Lie Symmetries 188 |
| -- |
11.3 Classification of Discrete Symmetries 191 |
| -- |
11.4 Examples 195 |
| -- |
Hints and Partial Solutions to Some Exercises 201 |
| -- |
Bibliography 209 |
| -- |
Index 211 |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Differential equations |
| General subdivision |
Numerical solutions |
|
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| Topical term or geographic name as entry element |
Symmetry |
|
|---|
| Topical term or geographic name as entry element |
Mathematical physics |
| 710 2# - ADDED ENTRY--CORPORATE NAME |
|---|
| 9 (RLIN) |
72911 |
| Corporate name or jurisdiction name as entry element |
Cambridge University Press. |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE |
|---|
| 9 (RLIN) |
110164 |
| Uniform title |
Cambridge texts in applied mathematics. |
| 900 ## - EQUIVALENCE OR CROSS-REFERENCE-PERSONAL NAME [LOCAL, CANADA] |
|---|
| Personal Name |
25677 |
|
|---|
| Numeration |
satın |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
|---|
| Source of classification or shelving scheme |
Library of Congress Classification |
| Koha item type |
Kitap |
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