Lectures On The Geometry Of Manifolds 2nd Edition Ebook

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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 topologyThe books 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 issueWhile 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 Poincar duality Thom isomorphism intersection theory characteristic classes and the Gauss-Bonnet theoremWe 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 Hlder 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 operatorsThe 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 limelightLectures On The Geometry Of Manifolds 2nd Edition EbookBy Nicolaescu Liviu I Publisher World Scientific Print ISBN 9789812708533 9812708537 eText ISBN 9789812770295 9812770291 Edition 2nd Format PDF Available from 27000 USD SKU 9789812770295

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9789812708533

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 topologyThe books 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 issueWhile 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 Poincar duality Thom isomorphism intersection theory characteristic classes and the Gauss-Bonnet theoremWe 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 Hlder 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 operatorsThe 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 limelightLectures On The Geometry Of Manifolds 2nd Edition EbookBy Nicolaescu Liviu I Publisher World Scientific Print ISBN 9789812708533 9812708537 eText ISBN 9789812770295 9812770291 Edition 2nd Format PDF Available from 27000 USD SKU 9789812770295