Calculus On Manifolds : a Modern Approach To Classical Theorems Of Advanced Calculus / Michael Spivak.
| Author/creator | Spivak, Michael author. |
| Format | Electronic |
| Edition | First edition. |
| Publication | Boca Raton, FL : CRC Press, 2018. |
| Description | 1 online resource : text file, PDF |
| Supplemental Content | Taylor & Francis |
| Subjects |
| 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 |
| Contents | THE FUNDAMENTAL THEOREM OF CALCULUS; 5. Integration on Manifolds; MANIFOLDS; FIELDS AND FORMS ON MANIFOLDS; STOKES' THEOREM ON MANIFOLDS; THE VOLUME ELEMENT; THE CLASSICAL THEOREMS; Bibliography; Index; Addenda |
| Scope and content | "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. |
| Issued in other form | 9780429970450 9780429981531 |
| Genre/form | Electronic books. |
| ISBN | 9780429501906 (e-book) |
| ISBN | 0429501900 |
| ISBN | 9780429970450 (e-book ; PDF) |
| ISBN | 0429970455 |
| Stock number | 9780429970450 Ingram Content Group |
Availability
| Library | Location | Call Number | Status | Item Actions |
|---|---|---|---|---|
| Electronic Resources | Access Content Online | ✔ Available |