Symmetry Methods for Differential Equations: A Beginner's GuideCambridge University Press, 28.01.2000 - 213 Seiten This book is a straightforward introduction to the subject of symmetry methods for solving differential equations, and is aimed at applied mathematicians, physicists, and engineers. The presentation is informal, using many worked examples to illustrate the main symmetry methods. It is written at a level suitable for postgraduates and advanced undergraduates, and is designed to enable the reader to master the main techniques quickly and easily.The book contains some methods that have not previously appeared in a text. These include methods for obtaining discrete symmetries and integrating factors. |
Inhalt
Lie Symmetries of FirstOrder ODEs | 15 |
How to Find Lie Point Symmetries of ODEs | 43 |
How to Use a OneParameter Lie Group | 58 |
Lie Symmetries with Several Parameters | 74 |
Solution of ODES with Multiparameter Lie Groups | 93 |
Techniques Based on First Integrals | 108 |
How to Obtain Lie Point Symmetries of PDEs | 136 |
Methods for Obtaining Exact Solutions of PDEs | 155 |
Classification of Invariant Solutions | 173 |
Discrete Symmetries | 187 |
Hints and Partial Solutions to Some Exercises | 201 |
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Symmetry Methods for Differential Equations: A Beginner's Guide Peter E. Hydon Keine Leseprobe verfügbar - 2000 |
Häufige Begriffe und Wortgruppen
algebra of point arbitrary constants basis X1 c₁ calculate canonical coordinates characteristic commutator computer algebra contact transformation derivatives determining equations diffeomorphism differential equations discrete point symmetries discrete symmetries dynamical symmetries equivalent Euler-Lagrange equation Example first-order ODE fundamental differential invariants Gröbner basis group of symmetries heat equation Hence independent variables infinitesimal integrating factor invariant solutions invariant surface condition Lie algebra Lie point symmetries Lie symmetries linearized symmetry condition mapped matrix nonclassical symmetries nonlinear nontrivial obtain ODE of order one-parameter group one-parameter Lie group optimal system original ODE packages parameter PDEs point transformation problem quadrature r₁ reduced ODE restrict attention result rotations satisfies solution curve solve the ODE subalgebra symmetry group symmetry methods system of ODEs tangent vector third-order ODE u₁ v₁ vector field X₁ xəx zero