000			03565nam a2200349 i 4500
008			990505s2000 enka b 001 0 eng
010			_a99031354
020			_a0521497035 _q(hardback)
020			_a0521497868 _q(paperback)
040			_aDLC _cDLC _dYDX _dBAUN _erda
049			_aBAUN_MERKEZ
050	0	4	_aQC20.7.D5 _bH93 2000
082	0	0	_221
100	1		_aHydon, Peter E. _q(Peter Ellsworth), _d1960-
245	1	0	_aSymmetry methods for differential equations : _ba beginner's guide / _cPeter E. Hydon
264		1	_aCambridge ; _aNew York : _bCambridge University Press, _c2000.
300			_axi, 213 pages : _billustrations ; _c24 cm
336			_atext _btxt _2rdacontent
337			_aunmediated _bn _2rdamedia
338			_avolume _bnc _2rdacarrier
490	1		_aCambridge texts in applied mathematics
504			_aIncludes bibliographical references (pages 209-210) and index
505	0	0	_tPreface _t Acknowledgements _t1 Introduction to Symmetries 1 _t 1.1 Symmetries of Planar Objects 1 _t 1.2 Symmetries of the Simplest ODE 5 _t 1.3 The Symmetry Condition for First-Order ODEs 8 _t 1.4 Lie Symmetries Solve First-Order ODEs 11 _t2 Lie Symmetries of First-Order ODEs 15 _t 2.1 The Action of Lie Symmetries on the Plane 15 _t 2.2 Canonical Coordinates 22 _t 2.3 How to Solve ODEs with Lie Symmetries 26 _t 2.4 The Linearized Symmetry Condition 30 _t 2.5 Symmetries and Standard Methods 34 _t 2.6 The Infinitesimal Generator 38 _t3 How to Find Lie Point Symmetries of ODEs 43 _t 3.1 The Symmetry Condition 43 _t 3.2 The Determining Equations for Lie Point Symmetries 46 _t 3.3 Linear ODEs 52 _t 3.4 Justification of the Symmetry Condition 54 _t4 How to Use a One-Parameter Lie Group 58 _t 4.1 Reduction of Order by Using Canonical Coordinates 58 _t 4.2 Variational Symmetries 63 _t 4.3 Invariant Solutions 68 _t5 Lie Symmetries with Several Parameters 74 _t 5.1 Differential Invariants and Reduction of Order 74 _t 5.2 The Lie Algebra of Point Symmetry Generators 79 _t 5.3 Stepwise Integration of ODEs 89 _t6 Solution of ODEs with Multiparameter Lie Groups 93 _t 6.1 The Basic Method: Exploiting Solvability 93 _t 6.2 New Symmetries Obtained During Reduction 99 _t 6.3 Integration of Third-Order ODEs with sl(2) 101 _t7 Techniques Based on First Integrals 108 _t 7.1 First Integrals Derived from Symmetries 108 _t 7.2 Contact Symmetries and Dynamical Symmetries 116 _t 7.3 Integrating Factors 122 _t 7.4 Systems of ODEs 128 _t8 How to Obtain Lie Point Symmetries of PDEs 136 _t 8.1 Scalar PDEs with Two Dependent Variables 136 _t 8.2 The Linearized Symmetry Condition for General PDEs 146 _t 8.3 Finding Symmetries by Computer Algebra 149 _t9 Methods for Obtaining Exact Solutions of PDEs 155 _t 9.1 Group-Invariant Solutions 155 _t 9.2 New Solutions from Known Ones 162 _t 9.3 Nonclassical Symmetries 166 _t10 Classification of Invariant Solutions 173 _t 10.1 Equivalence of Invariant Solutions 173 _t 10.2 How to Classify Symmetry Generators 176 _t 10.3 Optimal Systems of Invariant Solutions 182 _t11 Discrete Symmetries 187 _t 11.1 Some Uses of Discrete Symmetries 187 _t 11.2 How to Obtain Discrete Symmetries from Lie Symmetries 188 _t 11.3 Classification of Discrete Symmetries 191 _t 11.4 Examples 195 _t Hints and Partial Solutions to Some Exercises 201 _t Bibliography 209 _t Index 211
650		0	_aDifferential equations _xNumerical solutions
650		0	_aSymmetry
650		0	_aMathematical physics
710	2		_972911 _aCambridge University Press.
830		0	_9110164 _aCambridge texts in applied mathematics.
900			_a25677
900			_bsatın
942			_2lcc _cKT
999			_c21044 _d21044