Differential calculus in normed linear spaces (Q5907041)

This book is written for students possessing some background in analysis and linear algebra. In chapters 1 and 2, the author gives an introduction to linear and multilinear algebra, using also some methods of category theory. Chapter 3 covers basic material on the topology of normed spaces and metric spaces, including the principle of irrelevance of algebraic inequalities. \newline Chapters 4 and 5 constitute the main part of this textbook. In chapter 4, the author develops the differential calculus in Banach spaces and gives some features concerning finite dimensional (Hilbert) spaces. Chapter 5 shows the connections with Banach's fixed point theorem, ordinary differential equations, the inverse function theorem, the fundamental theorem of algebra, and the implicit function theorem. Chapter 6 is devoted to very remarkable applications of Lagrange's method of undetermined multipliers and the calculus of variations, including the spectral theorem and geodesics of the hyperbolic plane. Expecially this chapter makes this textbook recommendable in spite of various misprints and some, albeit few mathematical mistakes.