Book:Michael Spivak/Calculus on Manifolds

Subject Matter

 * Calculus

Contents

 * Editor's Foreword
 * Preface


 * 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 Calculus


 * 5. Integration on Manifolds
 * Manifolds
 * Fields and Forms on Manifolds
 * Stokes' Theorem on Manifolds
 * The Volume Element
 * The Classical Theorems


 * Bibliography
 * Index