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  • Cited by 141
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    • Publisher:
      Cambridge University Press
      Publication date:
      05 July 2011
      26 January 1990
      ISBN:
      9780511599941
      9780521366892
      DOI:
      https://doi.org/10.1017/CBO9780511599941
      Dimensions:
      Weight & Pages:
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.41kg, 276 Pages
      • Subjects:
      Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory, Physics and Astronomy, Theoretical Physics and Mathematical Physics
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    • Selected: Digital
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    Subjects:
    Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory, Physics and Astronomy, Theoretical Physics and Mathematical Physics
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    Book description

    This book provides an introduction to the theory and application of the solution of differential equations using symmetries, a technique of great value in mathematics and the physical sciences. In many branches of physics, mathematics, and engineering, solving a problem means a set of ordinary or partial differential equations. Nearly all methods of constructing closed form solutions rely on symmetries. The theory and application of such methods have therefore attracted increasing attention in the last two decades. In this text the emphasis is on how to find and use the symmetries in different cases. Many examples are discussed, and the book includes more than 100 exercises. This book will form an introduction accessible to beginning graduate students in physics, applied mathematics, and engineering. Advanced graduate students and researchers in these disciplines will find the book an invaluable reference.

    Reviews

    "...as an account of classical general relativity, this well produced and excellently translated book has many virtues." Physics Bulletin

    "A nice introduction to the theory and practice of finding and using symmetries to solve differential equations." American Mathematical Monthly

    "...Stephani's book does a good job of motivating the study of Lie group methods for differential equations from an elementary standpoint." SIAM Reviews

    "The author, who has an easy-to-read practical style, consistently keeps the emphasis on applications. Thus, most physicists will be able to get useful information about ordinary differential equations (ODE's) and partial differential equations (PDE's), without being bogged down in cumbersome mathematical formalism....well worth reading if one is at all interested in sophisticated and powerful symmetry techniques for handling differential equations and if one wishes to have the most straightforward approach to the topic." D. E. Vincent, Physics in Canada

    "...Stephani...has built a book that tries to guide its readers toward a sure knowledge of this very important tool for finding solutions of (nonlinear) differential equations. In the early sections, the derivations presented are the most clear and detailed ones that this writer has ever seen....Students new to this area will find reading or studying the current book an altogether enjoyable occupation, without any of the intimidation that sometimes is caused by similar books." J.D. Finley, Foundations of Physics

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