Calculus on Normed Vector Spaces

• Main Author: Coleman, Rodney (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York : Imprint: Springer, 2012.
• Series: Universitext,
• Subjects: Mathematics.; Functional analysis.; Mathematical optimization.; Functional Analysis.; Optimization.

This book serves as an introduction to calculus on normed vector spaces at a higher undergraduate or beginning graduate level. The prerequisites include basic calculus and linear algebra, as well as a certain mathematical maturity. All the important topology and functional analysis topics are introd...

Table of Contents:

• Preface
• 1 Normed Vector Spaces
• 2 Differentiation
• 3 Mean value theorems
• 4 Higher derivatives and differentials
• 5 Taylor theorems and applications
• 6 Hilbert spaces
• 7 Convex functions
• 8 The inverse and implicit mapping theorems
• 9 Vector fields
• 10 The flow of a vector field
• 11 The calculus of variations: an introduction
• Bibliography
• Index.