| 书目名称 | Introduction to Calculus and Analysis |
| 副标题 | Volume II |
| 编辑 | Richard Courant,Fritz John |
| 视频video | |
| 图书封面 |  |
| 描述 | The new Chapter 1 contains all the fundamental properties of linear differential forms and their integrals. These prepare the reader for the introduction to higher-order exterior differential forms added to Chapter 3. Also found now in Chapter 3 are a new proof of the implicit function theorem by successive approximations and a discus sion of numbers of critical points and of indices of vector fields in two dimensions. Extensive additions were made to the fundamental properties of multiple integrals in Chapters 4 and 5. Here one is faced with a familiar difficulty: integrals over a manifold M, defined easily enough by subdividing M into convenient pieces, must be shown to be inde pendent of the particular subdivision. This is resolved by the sys tematic use of the family of Jordan measurable sets with its finite intersection property and of partitions of unity. In order to minimize topological complications, only manifolds imbedded smoothly into Euclidean space are considered. The notion of "orientation" of a manifold is studied in the detail needed for the discussion of integrals of exterior differential forms and of their additivity properties. On this basis, proofs are given |
| 出版日期 | Textbook Dec 2013Latest edition |
| 关键词 | Implicit function; integral; manifold |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-1-4613-8958-3 |
| copyright | Springer-Verlag New York, Inc. 1989 |
发表于 2025-3-21 19:40:47
