Lectures On The Geometry Of Manifolds (2nd Edition)

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  • Engels
  • Hardcover
  • 9789812708533
  • 01 oktober 2007
  • 608 pagina's
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Samenvatting

The goal of this book is to introduce the reader to some of the most frequently used techniques in modern global geometry. Suited to the beginning graduate student willing to specialize in this very challenging field, the necessary prerequisite is a good knowledge of several variables calculus, linear algebra and point-set topology.The book's guiding philosophy is, in the words of Newton, that in learning the sciences examples are of more use than precepts . We support all the new concepts by examples and, whenever possible, we tried to present several facets of the same issue.While we present most of the local aspects of classical differential geometry, the book has a global and analytical bias . We develop many algebraic-topological techniques in the special context of smooth manifolds such as Poincare duality, Thom isomorphism, intersection theory, characteristic classes and the Gauss-Bonnet theorem.We devoted quite a substantial part of the book to describing the analytic techniques which have played an increasingly important role during the past decades. Thus, the last part of the book discusses elliptic equations, including elliptic Lpand Hoelder estimates, Fredholm theory, spectral theory, Hodge theory, and applications of these. The last chapter is an in-depth investigation of a very special, but fundamental class of elliptic operators, namely, the Dirac type operators.The second edition has many new examples and exercises, and an entirely new chapter on classical integral geometry where we describe some mathematical gems which, undeservedly, seem to have disappeared from the contemporary mathematical limelight.

Productspecificaties

Inhoud

Taal
en
Bindwijze
Hardcover
Oorspronkelijke releasedatum
01 oktober 2007
Aantal pagina's
608
Illustraties
Nee

Betrokkenen

Hoofdauteur
Liviu I Nicolaescu

Overige kenmerken

Editie
2
Extra groot lettertype
Nee
Product breedte
165 mm
Product hoogte
32 mm
Product lengte
267 mm
Studieboek
Ja
Verpakking breedte
166 mm
Verpakking hoogte
39 mm
Verpakking lengte
258 mm
Verpakkingsgewicht
1252 g

EAN

EAN
9789812708533

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