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Calculus on Manifolds : A Modern Approach to Classical Theorems of Advanced Calculus by Michael Spivak (1971, Trade Paperback)

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About this product

Product Identifiers

PublisherCRC Press LLC

ISBN-100805390219

ISBN-139780805390216

eBay Product ID (ePID)639620

Product Key Features

Number of Pages161 Pages

LanguageEnglish

Publication NameCalculus on Manifolds : a Modern Approach to Classical Theorems of Advanced Calculus

SubjectGeneral, Calculus, Topology

Publication Year1971

TypeTextbook

AuthorMichael Spivak

Subject AreaMathematics

FormatTrade Paperback

Dimensions

Item Height0.4 in

Item Weight7.9 Oz

Item Length8.2 in

Item Width5.5 in

Additional Product Features

Intended AudienceCollege Audience

IllustratedYes

Dewey Decimal517.34

Table Of ContentFunctions 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

SynopsisThis 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., 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., 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.

LC Classification NumberQA612