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 ℝm into ℝn 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.
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© 2002 Springer Science+Business Media Dordrecht
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Villanacci, A., Carosi, L., Benevieri, P., Battinelli, A. (2002). Differentials. In: Differential Topology and General Equilibrium with Complete and Incomplete Markets. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3619-9_3
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DOI: https://doi.org/10.1007/978-1-4757-3619-9_3
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-5306-3
Online ISBN: 978-1-4757-3619-9
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