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 introduced where necessary.
In its attempt to show how calculus on normed vector spaces extends the basic calculus of functions of several variables, this book is one of the few textbooks to bridge the gap between the available elementary texts and high level texts. The inclusion of many non-trivial applications of the theory and interesting exercises provides motivation for the reader.
Author(s): Rodney Coleman (auth.)
Series: Universitext
Edition: 1
Publisher: Springer-Verlag New York
Year: 2012
Language: English
Pages: 249
Tags: Functional Analysis; Optimization
Front Matter....Pages i-xi
Normed Vector Spaces....Pages 1-33
Differentiation....Pages 35-60
Mean Value Theorems....Pages 61-78
Higher Derivatives and Differentials....Pages 79-105
Taylor Theorems and Applications....Pages 107-124
Hilbert Spaces....Pages 125-140
Convex Functions....Pages 141-159
The Inverse and Implicit Mapping Theorems....Pages 161-188
Vector Fields....Pages 189-212
The Flow of a Vector Field....Pages 213-227
The Calculus of Variations: An Introduction....Pages 229-244
Back Matter....Pages 245-249
