Advertisement

Differentials

  • Antonio Villanacci
  • Laura Carosi
  • Pierluigi Benevieri
  • Andrea Battinelli
Chapter

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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • Antonio Villanacci
    • 1
  • Laura Carosi
    • 2
  • Pierluigi Benevieri
    • 1
  • Andrea Battinelli
    • 3
  1. 1.Università degli Studi di FirenzeItaly
  2. 2.Università degli Studi di PisaItaly
  3. 3.Università degli Studi di SienaItaly

Personalised recommendations