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About The Book

The emphasis on this First Volume is the study of differential forms and de Rham Cohomology Theory. Spivak also covers two ‘bonus’ topics: integral manifolds & foliations and Lie groups.

Table of Contents

Chapter 1: Manifolds

Chapter 2: Differentiable Structures

Chapter 3: The Tangent Bundle

Chapter 4: Tensors

Chapter 5: Vector Fields and Differential Equations

Chapter 6: Integral Manifolds

Chapter 7: Differential Forms

Chapter 8: Integration

Chapter 9: Riemannian Metrics

Chapter 10: Lie Groups

Chapter 11: Excursion in the Realm of Algebraic Topology

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