Theoretical Numerical Analysis

From the reviews of the third edition: "Overall, the book is clearly written, quite pleasant to read, and contains a lot of important material; and the authors have done an excellent job at balancing theoretical developments, interesting examples and exercises, numerical experiments, and bibliographical references." (SIAM) "This is the third edition, based on a graduate course taught by the authors at the University of Iowa for many years. ... There are tons and tons of well chosen explicit examples. ... it can be used for reading courses in functional analysis for strong senior undergraduates that aren't quite ready for a graduate analysis course, and it can be used as a reference for analysts of all stripes. I got a lot from reading it and so will you." (Andrew Locascio, The Mathematical Association of America, October, 2010)

• Linear Spaces.- Linear Operators on Normed Spaces.- Approximation Theory.- Fourier Analysis and Wavelets.- Nonlinear Equations and Their Solution by Iteration.- Finite Difference Method.- Sobolev Spaces.- Weak Formulations of Elliptic Boundary Value Problems.- The Galerkin Method and Its Variants.- Finite Element Analysis.- Elliptic Variational Inequalities and Their Numerical Approximations.- Numerical Solution of Fredholm Integral Equations of the Second Kind.- Boundary Integral Equations.- Multivariable Polynomial Approximations.