Differential Calculus

Serge Lang
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Serge Lang: Yale University, Department of Mathematics

Chapter Chapter I in Differential Manifolds, 1985, pp 1-19 from Springer

Abstract: Abstract We shall recall briefly the notion of derivative and some of its useful properties. As mentioned in the foreword, Chapter VIII of Dieudonné’s book or my Real Analysis give a self-contained and complete treatment for Banach spaces. We summarize certain facts concerning their properties as topological vector spaces, and then we summarize differential calculus. The reader can actually skip this chapter and start immediately with Chapter II if he is accustomed to thinking about the derivative of a map as a linear transformation. (In the finite dimensional case, when bases have been selected, the entries in the matrix of this transformation are the partial derivatives of the map.) We have repeated the proofs for the more important theorems, for the ease of the reader.

Keywords: Banach Space; Vector Bundle; Open Subset; Topological Vector Space; Differential Calculus (search for similar items in EconPapers)
Date: 1985
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DOI: 10.1007/978-1-4684-0265-0_1

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