- 188 pages
- English
- ePUB (mobile friendly)
- Available on iOS & Android
eBook - ePub
A First Course in Differential Geometry
About this book
This book proposes a new approach which is designed to serve as an introductory course in differential geometry for advanced undergraduate students. It is based on lectures given by the author at several universities, and discusses calculus, topology, and linear algebra.
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Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app.
Yes, you can access A First Course in Differential Geometry by Izu Vaisman in PDF and/or ePUB format, as well as other popular books in Mathematics & Geometry. We have over one million books available in our catalogue for you to explore.
Information
Table of contents
- Cover
- Half Title
- Series Page
- Title Page
- Copyright Page
- Preface
- Contents
- 1. DIFFERENTIABLE MANIFOLDS IN IRn
- 1.1 The Space IRn
- 1.2 Differentiable Functions
- 1.3 Differentiable Manifolds in IRn
- 1.4 Parameterizations and Maps
- 1.5 The Tangent Space of a Manifold
- 1.6 Differentiable Mappings of Manifolds
- 1.7 Orientable and Nonorientable Manifolds
- 1.8 Tensors and Tensor Fields on Manifolds
- 2. CURVES IN E2 AND E3
- 2.1 The Natural Parameterization
- 2.2 Local Euclidean Invariants
- 2.3 Computation Formulas: Comments and Applications
- 2.4 Global Theorems for Embedded Curves
- 2.5 Plane Curves
- 3. SURFACES IN E3
- 3.1 The Fundamental Tensors
- 3.2 Geometry of the Second Fundamental Form
- 3.3 The Covariant Derivative and the Fundamental Theorem
- 3.4 Curves on Surfaces: Geodesic Lines
- 3.5 Some Particular Classes of Surfaces
- 3.6 The Gauss-Bonnet Formula. Compact Surfaces
- REFERENCES AND SUGGESTED READINGS
- INDEX