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Differential algebra. --- Functional analysis. --- Ideals (Algebra). --- Differentiable functions.

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Geometry, Algebraic. --- Global analysis (Mathematics) --- Functional analysis. --- Analyse globale (mathématiques) --- Analyse fonctionnelle. --- Géométrie algébrique --- Differentiable functions. --- Differentiable functions --- Functions, Differentiable --- Functions of real variables

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Functional analysis --- Differentiable functions --- Interval functions --- Functions, Interval --- Set functions --- Functions, Differentiable --- Functions of real variables --- Fonctions différentiables --- Fonctions différentiables.

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This self-contained book brings together the important results of a rapidly growing area.As a starting point it presents the classic results of the theory. The book covers such results as: the extension of Wells' theorem and Aron's theorem for the fine topology of order m; extension of Bernstein's and Weierstrass' theorems for infinite dimensional Banach spaces; extension of Nachbin's and Whitney's theorem for infinite dimensional Banach spaces; automatic continuity of homomorphisms in algebras of continuously differentiable functions, etc.

Mathematical analysis --- Differentiable functions. --- Approximation theory. --- Banach spaces. --- Functions of complex variables --- Generalized spaces --- Topology --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Functions, Differentiable --- Functions of real variables

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This brief provides an elementary introduction to the theory of piecewise differentiable functions with an emphasis on differentiable equations.  In the first chapter, two sample problems are used to motivate the study of this theory. The presentation is then developed using two basic tools for the analysis of piecewise differentiable functions: the Bouligand derivative as the nonsmooth analogue of the classical derivative concept and the theory of piecewise affine functions as the combinatorial tool for the study of this approximation function. In the end, the results are combined to develop inverse and implicit function theorems for piecewise differentiable equations.  This Introduction to Piecewise Differentiable Equations will serve graduate students and researchers alike. The reader is assumed to be familiar with basic mathematical analysis and to have some familiarity with polyhedral theory.

Differentiable functions. --- Functions of complex variables. --- Global analysis (Mathematics). --- Mathematics. --- Differentiable functions --- Engineering & Applied Sciences --- Applied Mathematics --- Functions of real variables. --- Real variables --- Functions, Differentiable --- Mathematical analysis. --- Analysis (Mathematics). --- Calculus of variations. --- Analysis. --- Functions of a Complex Variable. --- Calculus of Variations and Optimal Control; Optimization. --- Functions of complex variables --- Functions of real variables --- Mathematical optimization. --- Analysis, Global (Mathematics) --- Differential topology --- Geometry, Algebraic --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Complex variables --- Elliptic functions --- Isoperimetrical problems --- Variations, Calculus of --- 517.1 Mathematical analysis