| 書目名稱 | Introduction to Calculus and Analysis |
| 副標題 | Volume II |
| 編輯 | Richard Courant,Fritz John |
| 視頻video | http://file.papertrans.cn/474/473493/473493.mp4 |
| 圖書封面 |  |
| 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 |
| 關鍵詞 | 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 |
|Archiver|手機版|小黑屋|
派博傳思國際
( 京公網(wǎng)安備110108008328)
GMT+8, 2026-1-22 03:13
發(fā)表于 2025-3-21 19:40:47
