Numerical Analysis: An Introduction

Revised and updated, this second edition of Walter Gautschi's successful Numerical Analysis explores computational methods for problems arising in the areas of classical analysis, approximation theory, and ordinary differential equations, among others. Topics included in the book are presented with a view toward stressing basic principles and maintaining simplicity and teachability as far as possible, while subjects requiring a higher level of technicality are referenced in detailed bibliographic notes at the end of each chapter. Readers are thus given the guidance and opportunity to pursue advanced modern topics in more depth.

Along with updated references, new biographical notes, and enhanced notational clarity, this second edition includes the expansion of an already large collection of exercises and assignments, both the kind that deal with theoretical and practical aspects of the subject and those requiring machine computation and the use of mathematical software. Perhaps most notably, the edition also comes with a complete solutions manual, carefully developed and polished by the author, which will serve as an exceptionally valuable resource for instructors.

“This is an excellent first graduate text on numerical analysis for the theoretically oriented. It is unusual in deliberately omitting discussion of numerical linear algebra and of the numerical solution of partial differential equations, claiming that, nowadays, these topics are likely to need a course to themselves...Each chapter closes with an extensive set of notes about the material of the chapter, additional reading and extensions to areas of current interest not covered in the text. Brief biographical and historical footnotes are scattered through the textbook. Also, included with each chapter is a large set of theoretical and practical exercises, and a number of computer assignments extending the discussion in the text. There are about 450 bibliographic references to textbooks, research monographs and research papers, and a good subject index. Certainly, this is one of the better books of its type; most of its competitors are listed in the bibliography.”

--Mathematical Reviews

"The book reads like an unfolding story... Topics are motivated with great care and ingenuity that might be given to establishing the drive behind characters in a good novel... Clarity is never sacrificed for elegance. Above all, the pace is always lively and brisk, the writing concise, and the author never lets the exposition bog down... Both the theoretical problems and machine assignments are a great resource... This is a stylish, lucid, and engaging book... [It] successfully conveys the author's interest and experience in the subject to the reader."

--SIAM Review

"An excellent text for a first graduate course in numerical analysis, excluding both linear algebra and PDEs... The book's emphasis is firmly on the analysis of the various problems and methods. The level of this analysis is appropriate for the envisaged course. This is a well written, well-produced, rigorous treatment of approximation, nonlinear equations, numerical differentiation and integration, and ordinary differential equations... Each chapter concludes with a substantial set of exercises covering all the chapter's topics and extending students' understanding with some new material. Some of these exercises are substantial and will challenge the best students... A sound introduction... A one-stop shopping guide to the current state-of-the-art."

--Computing Reviews(P. Turner)

"This book is well written... Every teacher should look at this textbook to see how this material has been presented by a numerical analyst with many years of teaching experience and a high reputation."

--Computing Reviews(D. Hicks)

"...[The book concentrates] on matters related to machine arithmetic and conditioning, computer approximation and interpolation, numerical differentiation and integration, nonlinear equations, initial value problems...and two-point boundary value problems for ODEs. The book contains many exercises, machine problems, a prologue with useful material including listings of major journals and pointers to software resources and relevant literature."

--IEEE CS&E Bookshelf