Calculus on normed vector spaces /
Rodney Coleman.
- New York, NY : Springer, c2012
- xi, 249 pages : illustrations ; 24 cm.
Includes bibliographical references and index.
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.
Annotation This volume bridges a gap between introductory and high-level textbooks, showing how calculus on normed vector spaces extends the basic calculus of functions of several variables. It includes many non-trivial applications of the theory and interesting exercises.