This text covers the basics of functional analysis and also some additional topics in numerical analysis. It is suitable for graduate courses in numerical analysis in mathematics, engineering, physics, chemistry, and related departments and is useful for researchers in these areas. It is especially for graduate students in mathematics who wish to work in theoretical numerical analysis and seek a background in the "tools of the trade" covered in this text.

Klappentext

This book gives an introduction to functional analysis in a way that is tailored to fit the needs of the researcher or student. The book explains the basic results of functional analysis as well as relevant topics in numerical analysis. Applications of functional analysis are given by considering numerical methods for solving partial differential equations and integral equations. The material is especially useful for researchers and students who wish to work in theoretical numerical analysis and seek a background in the "tools of the trade" covered in this book.

Inhalt

Preface * 1 Linear Spaces * 2 Linear Operators on Normed Spaces * 3 Approximation Theory * 4 Nonlinear Equations and Their Solution by Iteration * 5 Finite Difference Method * 6 Sobolev Spaces * 7 Variational Formulations of Elliptic Boundary Value Problems * 8 The Galerkin Method and Its Variants * 9 Finite Element Analysis * 10 Elliptic Variational Inequalities and Their Numerical Approximations * 11 Numerical Solution of Fredholm Integral Equations of the Second Kind * 12 Boundary Integral Equations * References * Index