Functional Analysis, Approximation Theory And Numerical Analysis

This book is an introduction to one of the important as­ pects of Numerical Analysis, namely the approximate solution of functional equations. We intend to show, by a few brief examples, the different theoretical and practical problems related to the numerical approximation of boundary value problems. We have chosen for this the approximate solution of certain linear elliptic partial differential equations (the first two parts of the book) and the approximate solution of a nonlinear elliptic differential equation.

Functional analysis studies linear spaces provided with suitable topo- logical structures and (continuous) linear transformations between such spaces. It has far reaching applications in several disciplines. For in- stance, the modern theory of (partial) differential equations and the numerical approximation of their solutions rely a lot on functional ana- lytic techniques. Functional analysis is now an integral part of the curriculum in any post graduate course in Mathematics. Ideally it should be taught after having covered courses in linear algebra, real and complex analysis, and topology.

This book is a contribution to the fast and broad Density Functional Theory (DFT) applications of the last few years. Each chapter presents a specific subject contributing to a vision of the great potential of the quantum/DFT simulations in high pressure, chemical reactivity, ionic liquid, chemoinformatic, molecular docking, and non-equilibrium state.

This book develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis.

This book develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis.

This book develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis.