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Calculus On Manifolds : a Modern Approach To Classical Theorems Of Advanced Calculus

Author: Michael Spivak
Publisher: Boca Raton, FL : CRC Press, 2018.
Edition/Format:   eBook : Document : English : First editionView all editions and formats
Summary:
"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  Read more...
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Genre/Form: Electronic books
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Michael Spivak
ISBN: 9780429501906 0429501900 9780429970450 0429970455
OCLC Number: 1029237047
Description: 1 online resource : text file, PDF
Contents: Cover; Half Title; Title; Copyright; Editors' Foreword; Preface; Contents; 1. Functions on Euclidean Space; NORM AND INNER PRODUCT; SUBSETS OF EUCLIDEAN SPACE; FUNCTIONS AND CONTINUITY; 2. Differentiation; BASIC DEFINITIONS; BASIC THEOREMS; PARTIAL DERIVATIVES; DERIVATIVES; INVERSE FUNCTIONS; IMPLICIT FUNCTIONS; NOTATION; 3. Integration; BASIC DEFINITIONS; MEASURE ZERO AND CONTENT ZERO; INTEGRABLE FUNCTIONS; FUBINI'S THEOREM; PARTITIONS OF UNITY; CHANGE OF VARIABLE; 4. Integration on Chains; ALGEBRAIC PRELIMINARIES; FIELDS AND FORMS; GEOMETRIC PRELIMINARIES THE FUNDAMENTAL THEOREM OF CALCULUS5. Integration on Manifolds; MANIFOLDS; FIELDS AND FORMS ON MANIFOLDS; STOKES' THEOREM ON MANIFOLDS; THE VOLUME ELEMENT; THE CLASSICAL THEOREMS; Bibliography; Index; Addenda
Responsibility: Michael Spivak.

Abstract:

"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."--Provided by publisher.

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