Elements of Concave Analysis and Applications

Description

Concave analysis deals mainly with concave and quasi-concave functions, although convex and quasi-convex functions are considered because of their mutual inherent relationship. The aim of Elements of Concave Analysis and Applications is to provide a basic and self‐contained introduction to concepts and 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

1. Preface
2. Matrix Algebra
3. Differential Calculus
4. Concave and Convex Functions
5. Concave Programming
6. Convex Programming
7. Quasi-Concave Functions
8. Quasi-Convex Functions
9. Log-concave Functions
10. Quadratic Programming
11. Optimal Control Theory
12. Demands
13. Black-Scholes Equation
14. Appendices:
    1. A Probability Topics
    2. B Differentiation of Operators
    3. C Distributions
    4. D Laplace Transforms
    5. E Implicit Function Theorem
    6. F Locally Nonsatiated Function

Author Biography

Prem K. Kythe is a Professor Emeritus of Mathematics at the University of New Orleans. He is the author/co-author of 11 books and author of 46 research papers. His research interests encompass the fields of complex analysis, continuum mechanics, and wave theory, including boundary element methods, finite element methods, conformal mappings, PDEs and boundary value problems, linear integral equations, computation integration, fundamental solutions of differential operators, Green’s functions, and coding theory.