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

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Características del artículo

Estado
En buen estado: Libro que se ha leído pero que está en buen estado. Daños mínimos en la tapa, ...
Book Title
Calculus On Manifolds: A Modern Approach To Classical Theorems Of
ISBN
9780805390216
Categoría

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Product Identifiers

Publisher
CRC Press LLC
ISBN-10
0805390219
ISBN-13
9780805390216
eBay Product ID (ePID)
639620

Product Key Features

Number of Pages
161 Pages
Language
English
Publication Name
Calculus on Manifolds : a Modern Approach to Classical Theorems of Advanced Calculus
Subject
General, Calculus, Topology
Publication Year
1971
Type
Textbook
Author
Michael Spivak
Subject Area
Mathematics
Format
Trade Paperback

Dimensions

Item Height
0.4 in
Item Weight
7.9 Oz
Item Length
8.2 in
Item Width
5.5 in

Additional Product Features

Intended Audience
College Audience
Illustrated
Yes
Dewey Decimal
517.34
Table Of Content
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
Synopsis
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 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 Number
QA612

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