Differentials

Antonio Villanacci, Laura Carosi, Pierluigi Benevieri and Andrea Battinelli
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Antonio Villanacci: Università degli Studi di Firenze
Laura Carosi: Università degli Studi di Pisa
Pierluigi Benevieri: Università degli Studi di Firenze
Andrea Battinelli: Università degli Studi di Siena

Chapter Chapter 3 in Differential Topology and General Equilibrium with Complete and Incomplete Markets, 2002, pp 49-78 from Springer

Abstract: Abstract This chapter is devoted to the introduction of a few basic tools making the reader acquainted, we hope, with the development of elementary calculus on manifolds. As we argued in the introduction of Chapter 2, one of the main objects of elementary calculus is the representation of the local behavior of nonlinear functions mapping open subsets of ℝ m into ℝ n by means of their linear and higher order approximations. Similarly, one of the main purposes of elementary calculus on manifolds is the development of appropriate objects allowing the construction of linear and higher order approximations for the local behavior of functions mapping manifolds into manifolds.

Keywords: Open Subset; Tangent Space; Open Neighborhood; Local Parametrization; Tangent Bundle (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4757-3619-9_3

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DOI: 10.1007/978-1-4757-3619-9_3

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