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Differentials

In: Differential Topology and General Equilibrium with Complete and Incomplete Markets

Author

Listed:
  • 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)

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.

Suggested Citation

  • Antonio Villanacci & Laura Carosi & Pierluigi Benevieri & Andrea Battinelli, 2002. "Differentials," Springer Books, in: Differential Topology and General Equilibrium with Complete and Incomplete Markets, chapter 0, pages 49-78, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4757-3619-9_3
    DOI: 10.1007/978-1-4757-3619-9_3
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