Coleman R. Calculus on Normed Vector Spaces

Springer Science+Business Media, New York, 2012. — 263 p. — (UTX) — ISBN10: 1461438934This 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.Normed Vector Spaces
Differentiation
Mean Value Theorems
Higher Derivatives and Differentials
Taylor Theorems and Applications
Hilbert Spaces
Convex Functions
The Inverse and Implicit Mapping Theorems
Vector Fields
The Flow of a Vector Field
The Calculus of Variations: An Introduction