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  3. A Practical Guide to the Invariant Calculus
  • Cited by 46
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    • Publisher:
      Cambridge University Press
      Publication date:
      June 2012
      April 2010
      ISBN:
      9780511844621
      9780521857017
      DOI:
      https://doi.org/10.1017/CBO9780511844621
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.55kg, 260 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics, Computational Science, Geometry and Topology
      Series:
      Cambridge Monographs on Applied and Computational Mathematics (26)
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    Subjects:
    Mathematics, Computational Science, Geometry and Topology
    Series:
    Cambridge Monographs on Applied and Computational Mathematics (26)
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    Book description

    This book explains recent results in the theory of moving frames that concern the symbolic manipulation of invariants of Lie group actions. In particular, theorems concerning the calculation of generators of algebras of differential invariants, and the relations they satisfy, are discussed in detail. The author demonstrates how new ideas lead to significant progress in two main applications: the solution of invariant ordinary differential equations and the structure of Euler-Lagrange equations and conservation laws of variational problems. The expository language used here is primarily that of undergraduate calculus rather than differential geometry, making the topic more accessible to a student audience. More sophisticated ideas from differential topology and Lie theory are explained from scratch using illustrative examples and exercises. This book is ideal for graduate students and researchers working in differential equations, symbolic computation, applications of Lie groups and, to a lesser extent, differential geometry.

    Reviews

    'This book is a very good introduction to Cartan's method of moving frames, using primarily undergraduate calculus. …full of good examples.'

    Source: Mathematical Reviews

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