Calculus on manifolds : a modern approach to classical theorems of advanced calculus
著者
書誌事項
Calculus on manifolds : a modern approach to classical theorems of advanced calculus
（Mathematics monograph series）（Advanced book program）
CRC Press, 2019
- : hbk.
- タイトル別名
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Calculus on manifolds
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注記
First published 1965 by Westview Press -- T.p.verso
First issued in hardback 2019 -- T.p.verso
Includes bibliographical references (p. 139-140) and index
内容説明・目次
内容説明
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.
目次
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
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