Book:Michael Spivak/Calculus on Manifolds

Michael Spivak: Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus

Published $\text {1965}$, Addison-Wesley

ISBN 0-8053-9021-9

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