Books by Prem K. (University of New Orleans Kythe

Due to the growing need of introduction of numerical methods in engineering to solve boundary value problems, many engineering and mathematics graduate curricula now include courses in both finite and boundary element methods. Traditionally numerical methods have always been mathematically oriented.

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.

This self-contained text provides a sufficient theoretical basis to understand Green¿s function method, which is used to solve initial and boundary value problems involving linear ODEs and PDEs. It presents a variety of approaches, including classical and general variations of parameters, Wronskian method, Bernoulli¿s separation method, integral transform method, method of images, conformal mapping method, and interpolation method. The text also covers applications of Green¿s functions and contains numerous examples and exercises from diverse areas of mathematics, applied science, and engineering.

Incorporates the fourth version of the software package Mathematica (4.x). This title includes a section of Mathematica projects in each chapter, a chapter on Green's functions, a chapter on boundary value problems, and material on inverse operators, Legendre functions, and Bessel functions.

Many engineering and mathematics graduate curricula include a course in boundary element methods. Such a course must cover numerical methods, basic methodology to real problems, and interactive computer usage. This textbook provides both theory and applications, necessary for applied courses.