Calculus On Manifolds: A Modern Approach To Classical Theorems Of Advanced Calculus (Paperback)

Michael Spivak

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商品描述

This little book is especially concerned with those portions of ”advanced calculus” in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level. The approach taken here uses elementary versions of modern methods found in sophisticated mathematics. The formal prerequisites include only a term of linear algebra, a nodding acquaintance with the notation of set theory, and a respectable first-year calculus course (one which at least mentions the least upper bound (sup) and greatest lower bound (inf) of a set of real numbers). Beyond this a certain (perhaps latent) rapport with abstract mathematics will be found almost essential.

商品描述(中文翻譯)

這本小書特別關注「高等微積分」中那些概念和方法的微妙之處,這些概念和方法在初級水平上很難達到嚴謹性。這裡所採用的方法使用了現代數學中的基本版本。正式的先備知識只需要線性代數的一個學期、對集合論符號的略知一二,以及一個可觀的第一年微積分課程(至少提到了實數集合的上界(sup)和下界(inf))。除此之外,對抽象數學的某種(或許是潛在的)理解幾乎是必不可少的。