Differential Calculus In Normed Linear Spaces, 2Nd Edition (Text And Readings In Mathematics, Volume 26)

Mukherjee Kalyan

ISBN 10: 8185931763 / ISBN 13: 9788185931760

Edité par Hindustan, 2007

A propos de cet article

ISBN:9788185931760.

N° de réf. du vendeur 2296121

Détails bibliographiques

• Titre: Differential Calculus In Normed Linear Spaces, 2Nd Edition (Text And Readings In Mathematics, Volume 26)
• Éditeur: Hindustan
• Date de parution: 2007
• Langue: anglais
• ISBN à 10 chiffres: 8185931763
• ISBN à 13 chiffres: 9788185931760
• Reliure: Soft cover
• Édition: 2ème Édition
• État de l'article: New

A propos de ce titre

Synopsis

This book presents Advanced Calculus from a geometric point of view: instead of dealing with partial derivatives of functions of several variables, the derivative of the function is treated as a linear transformation between normed linear spaces. Not only does this lead to a simplified and transparent exposition of "difficult" results like the Inverse and Implicit Function Theorems but also permits, without any extra effort, a discussion of the Differential Calculus of functions defined on infinite dimensional Hilbert or Banach spaces.The prerequisites demanded of the reader are modest: a sound understanding of convergence of sequences and series of real numbers, the continuity and differentiability properties of functions of a real variable and a little Linear Algebra should provide adequate background for understanding the book. The first two chapters cover much of the more advanced background material on Linear Algebra (like dual spaces, multilinear functions and tensor products.) Chapter 3 gives an ab initio exposition of the basic results concerning the topology of metric spaces, particularly of normed linear spaces.The last chapter deals with miscellaneous applications of the Differential Calculus including an introduction to the Calculus of Variations. As a corollary to this, there is a brief discussion of geodesics in Euclidean and hyperbolic planes and non-Euclidean geometry.