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Main Question or Discussion Point
- Author: Michael Spivak
- Title: Calculus on Manifolds
- Amazon link: https://www.amazon.com/dp/0805390219/?tag=pfamazon01-20
- Prerequisities: Rigorous Calculus
- Level: Undergrad
Table of Contents:
Code:
[LIST]
[*] Foreword
[*] Preface
[*] Functions on Euclidean Space
[LIST]
[*] Norm and Inner Product
[*] Subsets of Euclidean Space
[*] Functions and Continuity
[/LIST]
[*] Differentiation
[LIST]
[*] Basic Definitions
[*] Basic Theorems
[*] Partial Derivatives
[*] Derivatives
[*] Inverse Functions
[*] Implicit Functions
[*] Notation
[/LIST]
[*] Integration
[LIST]
[*] Basic Definitions
[*] Measure Zero and Content Zero
[*] Integrable Functions
[*] Fubini's Theorem
[*] Partitions of Unity
[*] Change of Variable
[/LIST]
[*] Integration on Chains
[LIST]
[*] Algebraic Preliminaries
[*] Fields and Forms
[*] Geometric Preliminaries
[*] The Fundamental Theorem of Calculus
[/LIST]
[*] Integration on Manifolds
[LIST]
[*] Manifolds
[*] Fields and Forms on Manifolds
[*] Stokes' Theorem on Manifolds
[*] The Volume Element
[*] The Classical Theorems
[/LIST]
[*] Bibliography
[*] Index
[/LIST]
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