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Power Geometry as a New Calculus

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Part of the International Society for Analysis, Applications and Computation book series (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.

Keywords

  • Normal Cone
  • Differential Calculus
  • Nonstandard Analysis
  • Power Expansion
  • Newton Polyhedron

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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