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

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Michael Spivak

Calculus On Manifolds

A Modern Approach To Classical Theorems Of Advanced Calculus

Michael Spivak

$105

Paperback

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English

Perseus Books
22 January 1971

Mathematics & Sciences; Mathematics; Calculus

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.

By: Michael Spivak
Imprint: Perseus Books
Country of Publication: United States
Dimensions: Height: 216mm, Width: 138mm, Spine: 13mm
Weight: 60g
ISBN: 9780805390216
ISBN 10: 0805390219
Pages: 160
Publication Date: 22 January 1971
Audience: College/higher education , Professional and scholarly , Professional & Vocational , Primary , Undergraduate
Replaced By: 9780201501735
Format: Paperback
Publisher's Status: Active

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