Applications du calcul différentiel / Paul Ver Eecke

The present book constitutes volume II to the textbook: "Fondements du calcul différentiel" (1983; Zbl 0517.26002) by the same author and provides a successful synthesis between the common classical approach (real-valued functions of several independent variables) and elementary parts of contemporary nonlinear functional analysis. Appropriate assumptions on linear topological spaces and mappings do not make the theory enormously difficult. The book consists of three chapters. Chapter IV discusses the implicit function theory (differentiability, existence questions, functional dependence, immersion, submersion, subimmersion). Chapter V is devoted to ordinary differential equations (existence, uniqueness, continuity and smooth dependence of initial data, Frobenius theorem, classical finite- dimensional case, especially linear systems with constant coefficients). Chapter VI is concerned with elementary parts of the calculus of variations of functionals on submanifolds of a linear topological space (Lagrange multipliers for the finite codimension, Euler-Lagrange system, transversality). One third of the book is devoted to extensive bibliography with very interesting comments. The exposition is clear and thorough even if the proofs are of technical character and usually are omitted in other current textbooks on the same subject. (Zentralblatt)

Notes bibliogr. . Index