Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition (Paperback)

Manfredo P. do Carmo

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商品描述

One of the most widely used texts in its field, this volume introduces the differential geometry of curves and surfaces in both local and global aspects. The presentation departs from the traditional approach with its more extensive use of elementary linear algebra and its emphasis on basic geometrical facts rather than machinery or random details. Many examples and exercises enhance the clear, well-written exposition, along with hints and answers to some of the problems.
The treatment begins with a chapter on curves, followed by explorations of regular surfaces, the geometry of the Gauss map, the intrinsic geometry of surfaces, and global differential geometry. Suitable for advanced undergraduates and graduate students of mathematics, this text's prerequisites include an undergraduate course in linear algebra and some familiarity with the calculus of several variables. For this second edition, the author has corrected, revised, and updated the entire volume.

商品描述(中文翻譯)

這本書是該領域中最廣泛使用的教材之一,介紹了曲線和曲面的微分幾何,包括局部和全局的觀點。該書的呈現方式不同於傳統方法,更廣泛地使用了基礎線性代數,並強調基本的幾何事實,而不是機械或隨機的細節。許多例子和練習增強了清晰、寫作流暢的敘述,並提供了一些問題的提示和答案。

該書的內容從曲線的章節開始,接著探討了正則曲面、高斯映射的幾何、曲面的內在幾何以及全局微分幾何。適合數學高年級本科生和研究生使用,先修課程包括線性代數本科課程和對多變數微積分有一定熟悉程度。在第二版中,作者對整本書進行了修正、修訂和更新。