Continuous symmetries, Lie algebras, differential equations and computer algebra

Willi-Hans Steeb

This textbook comprehensively introduces students and researchers to the application of continuous symmetries and their Lie algebras to ordinary and partial differential equations. Covering all the modern techniques in detail, it relates applications to cutting-edge research fields such as Yang-Mills theory and string theory. Aimed at readers in applied mathematics and physics rather than pure mathematics, the material is ideally suited to students and researchers whose main interest lies in finding solutions to differential equations and invariants of maps.A large number of worked examples and challenging exercises help readers to work independently of teachers, and by including SymbolicC++ implementations of the techniques in each chapter, the book takes full advantage of the advancements in algebraic computation. Twelve new sections have been added in this edition, including: Haar measure, Sato's theory and sigma functions, universal algebra, anti-self dual Yang-Mills equation, and discrete Painleve equations.

「Nielsen BookData」より

[目次]

  • Groups
  • Lie Groups and Lie Transformation Groups
  • Infinitesimal Transformations
  • Lie Algebras
  • Introductory Examples
  • Differential Forms and Tensor Fields
  • Lie Derivative and Invariance
  • Invariance of Differential Equations
  • Lie-Backlund Vector Fields
  • Differential Equation for a Given Lie Algebra
  • A List of Lie Symmetry Vector Fields
  • Recursion Operators
  • Backlund Transformations
  • Lax Representations
  • Conservation Laws
  • Symmetries and Painleve Test
  • Lie Algebra Valued Differential Forms
  • Bose Operators and Lie Algebras
  • Maps and Invariants
  • Computer Algebra
  • Differential Manifolds.

「Nielsen BookData」より

この本の情報

書名 Continuous symmetries, Lie algebras, differential equations and computer algebra
著作者等 Steeb, W.-H.
Steeb Willi-Hans
出版元 World Scientific
刊行年月 c2007
版表示 2nd ed
ページ数 xiv, 457 p.
大きさ 24 cm
ISBN 9789812708090
NCID BA83561450
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言語 英語
出版国 アメリカ合衆国
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