Download E-books Manifolds, Tensor Analysis, and Applications (Applied Mathematical Sciences) (v. 75) PDF

By Ralph Abraham

The aim of this publication is to supply middle fabric in nonlinear research for mathematicians, physicists, engineers, and mathematical biologists. the most objective is to supply a operating wisdom of manifolds, dynamical structures, tensors, and differential types. a few purposes to Hamiltonian mechanics, fluid meĀ­ chanics, electromagnetism, plasma dynamics and keep watch over thcory arc given in bankruptcy eight, utilizing either invariant and index notation. the present variation of the booklet doesn't care for Riemannian geometry in a lot aspect, and it doesn't deal with Lie teams, crucial bundles, or Morse conception. a few of this can be deliberate for a next variation. in the meantime, the authors will make to be had to readers supplementary chapters on Lie teams and Differential Topology and invite reviews at the book's contents and improvement. in the course of the textual content supplementary themes are given, marked with the symbols ~ and {l:;J. This equipment permits the reader to bypass numerous themes with out demanding the most movement of the textual content. a few of these offer extra heritage fabric meant for completeness, to reduce the need of consulting too many outdoors references. We deal with finite and infinite-dimensional manifolds at the same time. this is often in part for potency of exposition. with no complicated functions, utilizing manifolds of mappings, the learn of infinite-dimensional manifolds may be tough to encourage.

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