Calculus on Normed Vector Spaces (Universitext)

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. 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. Rodney Coleman. Includes Bibliographical References (p. 245-246) And Index. 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 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