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

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CRC Press, 2018/05/04 - 162 ページ
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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.
 

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目次

Functions on Euclidean Space
1
FUNCTIONS AND continuity
11
BASIC THEOREMs
19
PARTIAL DERIVATIVES
25
INVERSE FUNCTIONs
34
IMPLICIT FUNCTIONs
40
Contents
46
Integration on Chains
75
Integration on Manifolds
109
Bibliography
139
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