 Название: Manifolds, Vector Fields, and Differential Forms: An Introduction to Differential Geometry
Автор: Gal Gross, Eckhard Meinrenken
Издательство: Springer
Серия: Springer Undergraduate Mathematics Series
Год: 2023
Страниц: 348
Язык: английский
Формат: pdf (true), epub
Размер: 22.0 MB
This textbook serves as an introduction to modern differential geometry at a level accessible to advanced undergraduate and master's students. It places special emphasis on motivation and understanding, while developing a solid intuition for the more abstract concepts. In contrast to graduate level references, the text relies on a minimal set of prerequisites: a solid grounding in linear algebra and multivariable calculus, and ideally a course on ordinary differential equations. Manifolds are introduced intrinsically in terms of coordinate patches glued by transition functions. The theory is presented as a natural continuation of multivariable calculus; the role of point-set topology is kept to a minimum.
Contents:
1. Introduction
2. Manifolds
3. Smooth Maps
4. Submanifolds
5. Tangent Spaces
6. Vector Fields
7. Differential Forms
8. Integration
9. Vector Bundles
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Manifolds, Vector Fields, and Differential Forms 
