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Analysis and Applications — ISAAC 2001 pp 51–71Cite as

Power Geometry as a New Calculus

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Part of the book series: International Society for Analysis, Applications and Computation ((ISAA,volume 10))

Abstract

Power Geometry develops Differential Calculus and aims at nonlinear problems. The algorithms of Power Geometry allow to simplify equations,to resolve their singularities, to isolate their first approximations, and to find either their solutions or the asymptotics of the solutions. This approach allows to compute also the asymptotic and the local expansions of solutions. Algorithms of Power Geometry are applicable to equations of various types: algebraic, ordinary differential and partial differential, and also to systems of such equations. Power Geometry is an alternative to Algebraic Geometry, Group Analysis, Nonstandard Analysis, Microlocal Analysis etc.

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References

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Author information

Authors and Affiliations

  1. Keldysh Institute of Applied Mathematics, Moscow, 125047, Russia

    Alexander D. Bruno

Authors
  1. Alexander D. Bruno
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Editor information

Editors and Affiliations

  1. Freie Universität Berlin, Berlin, Germany

    Heinrich G. W. Begehr

  2. University of Delaware, Newark, DE, USA

    Robert P. Gilbert

  3. York University, Toronto, Canada

    Man Wah Wong

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© 2003 Springer Science+Business Media Dordrecht

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Bruno, A.D. (2003). Power Geometry as a New Calculus. In: Begehr, H.G.W., Gilbert, R.P., Wong, M.W. (eds) Analysis and Applications — ISAAC 2001. International Society for Analysis, Applications and Computation, vol 10. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3741-7_4

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  • DOI: https://doi.org/10.1007/978-1-4757-3741-7_4

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-5247-9

  • Online ISBN: 978-1-4757-3741-7

  • eBook Packages: Springer Book Archive

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