| 書目名稱 | Functions of Several Variables | | 編輯 | Wendell Fleming | | 視頻video | http://file.papertrans.cn/350/349905/349905.mp4 | | 叢書名稱 | Undergraduate Texts in Mathematics | | 圖書封面 |  | | 描述 | The purpose of this book is to give a systematic development of differential and integral calculus for functions of several variables. The traditional topics from advanced calculus are included: maxima and minima, chain rule, implicit function theorem, multiple integrals, divergence and Stokes‘s theorems, and so on. However, the treatment differs in several important respects from the traditional one. Vector notation is used throughout, and the distinction is maintained between n-dimensional euclidean space En and its dual. The elements of the Lebesgue theory of integrals are given. In place of the traditional vector analysis in ￡3, we introduce exterior algebra and the calculus of exterior differential forms. The formulas of vector analysis then become special cases of formulas about differential forms and integrals over manifolds lying in P. The book is suitable for a one-year course at the advanced undergraduate level. By omitting certain chapters, a one semester course can be based on it. For instance, if the students already have a good knowledge of partial differentiation and the elementary topology of P, then substantial parts of Chapters 4, 5, 7, and 8 can be covered in a s | | 出版日期 | Textbook 1977Latest edition | | 關鍵詞 | Algebra; Differentialform; Differentialrechnung; Functions; Integralrechnung; Manifold; Topology; Variable; | | 版次 | 2 | | doi | https://doi.org/10.1007/978-1-4684-9461-7 | | isbn_softcover | 978-1-4684-9463-1 | | isbn_ebook | 978-1-4684-9461-7Series ISSN 0172-6056 Series E-ISSN 2197-5604 | | issn_series | 0172-6056 | | copyright | Springer Science+Business Media New York 1977 |
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