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CALCULUS ON MANIFOLDS : a modern approach to classical theorems of advanced calculus.

Author: MICHAEL SPIVAK
Publisher: [Place of publication not identified] CRC Press, 2019.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

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  Read more...

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Document Type: Book
All Authors / Contributors: MICHAEL SPIVAK
ISBN: 0367091909 9780367091903
OCLC Number: 1105935721
Description: 1 volume ; 22 cm
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

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