Calculus On Manifolds: A Modern Approach To Classical Theorems Of Advanced Calcu

Description: Calculus On Manifolds by Michael Spivak This book uses elementary versions of modern methods found in sophisticated mathematics to discuss portions of "advanced calculus" in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level. FORMAT Paperback LANGUAGE English CONDITION Brand New Publisher Description This little book is especially concerned with those portions of "advanced calculus" in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level. The approach taken here uses elementary versions of modern methods found in sophisticated mathematics. The formal prerequisites include only a term of linear algebra, a nodding acquaintance with the notation of set theory, and a respectable first-year calculus course (one which at least mentions the least upper bound (sup) and greatest lower bound (inf) of a set of real numbers). Beyond this a certain (perhaps latent) rapport with abstract mathematics will be found almost essential. Author Biography Michael Spivak Table of Contents Functions on Euclidean Space * Norm and inner Product * Subsets of Euclidean Space * Functions and Continuity Differentiation * Basic Definitions * Basic Theorems * Partial Derivatives * Inverse Functions * Implicit Functions * Notation Integration * Basic Definitions * Measure Zero and Content Zero * Integrable Functions * Fubinis Theorem * Partitions of Unity * Change of Variable Integration on Chains * Algebraic Preliminaries * Fields and Forms * Geometric Preliminaries * The Fundamental Theorem of Calculus Integration on Manifolds * Manifolds * Fields and Forms on Manifolds * Stokes Theorem on Manifolds * The Volume Element * The Classical Theorems Long Description This little book is especially concerned with those portions of "advanced calculus" in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level. The approach taken here uses elementary versions of modern methods found in sophisticated mathematics. The formal prerequisites include only a term of linear algebra, a nodding acquaintance with the notation of set theory, and a respectable first-year calculus course (one which at least mentions the least upper bound (sup) and greatest lower bound (inf) of a set of real numbers). Beyond this a certain (perhaps latent) rapport with abstract mathematics will be found almost essential. Details ISBN0805390219 Author Michael Spivak Short Title CALCULUS ON MANIFOLDS Language English ISBN-10 0805390219 ISBN-13 9780805390216 Media Book Format Paperback DEWEY 515 Year 1971 Country of Publication United States Illustrations Ill. Edition 5th Imprint Westview Press Inc Place of Publication Boulder, CO Subtitle A Modern Approach To Classical Theorems Of Advanced Calculus DOI 10.1604/9780805390216 UK Release Date 1971-01-22 AU Release Date 1971-01-22 NZ Release Date 1971-01-22 US Release Date 1971-01-22 Publisher Taylor & Francis Inc Publication Date 1971-01-22 Alternative 9780367091903 Audience Tertiary & Higher Education Pages 162 We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:22722487;

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