| 書目名稱 | Functions of several variables | | 編輯 | B. D. Craven | | 視頻video | http://file.papertrans.cn/350/349907/349907.mp4 | | 圖書封面 |  | | 描述 | This book is aimed at mathematics students, typically in the second year of a university course. The first chapter, however, is suitable for first-year students. Differentiable functions are treated initially from the standpoint of approximating a curved surface locally by a fiat surface. This enables both geometric intuition, and some elementary matrix algebra, to be put to effective use. In Chapter 2, the required theorems - chain rule, inverse and implicit function theorems, etc- are stated, and proved (for n variables), concisely and rigorously. Chapter 3 deals with maxima and minima, including problems with equality and inequality constraints. The chapter includes criteria for discriminating between maxima, minima and saddlepoints for constrained problems; this material is relevant for applications, but most textbooks omit it. In Chapter 4, integration over areas, volumes, curves and surfaces is developed, and both the change-of-variable formula, and the Gauss-Green-Stokes set of theorems are obtained. The integrals are defined with approximative sums (ex- pressed concisely by using step-functions); this preserves some geometrical (and physical) concept of what is happening. C | | 出版日期 | Book 1981 | | 關(guān)鍵詞 | Implicit function; calculus; derivative; extrema; integral; integration; maximum; minimum | | 版次 | 1 | | doi | https://doi.org/10.1007/978-94-010-9347-7 | | isbn_softcover | 978-0-412-23340-1 | | isbn_ebook | 978-94-010-9347-7 | | copyright | B.D. Craven 1981 |
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