ISBN 9781138705289
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Concave analysis deals mainly with concave and quasi-concave functions, although convex and quasi-convex functions are considered because of their mutual inherent relationship. Elements of Concave Analysis and Applications aim to provide a basic and self-contained introduction to concepts and a detailed study of concave and convex functions. It is written in the style of a textbook, designed for courses in mathematical economics, finance, and manufacturing design. The suggested prerequisites are multivariate calculus, ordinary and elementary PDEs, and elementary probability theory. Table of Contents Preface 1 Matrix Algebra 2 Differential Calculus 3 Concave and Convex Functions 4 Concave Programming 5 Convex Programming 6 Quasi-Concave Functions 7 Quasi-Convex Functions 8 Log-concave Functions 9 Quadratic Programming 10 Optimal Control Theory 11 Demands 12 Black-Scholes Equation Appendices: A Probability Topics B Differentiation of Operators C Distributions D Laplace Transforms E Impl