Numerical Analysis

ISBN-13: 9780817682583 / Angielski / Twarda / 2011 / 588 str.

Walter Gautschi

Opis

Revised andupdated, this second edition of Walter Gautschi's successful Numerical Analysisexplorescomputational methodsfor 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 editionincludes the expansion of an alreadylarge 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."

Recenzje

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... [The book] successfully conveys the author's interest and experience in the subject to the reader. -SIAM, review of the First Edition

From the reviews of the second edition:

"This is the second updated edition of the 1997 version. It's a classical book on numerical analysis that can be used as course notes. ... The second edition has updated references and notes ... . The major change is however that now solutions to all exercises and computer assignments are available. ... Conclusion: one of the better handbooks on the market today, based on several decades of teaching experience of the author. It is an excellent tool for teaching a classical numerical analysis course." (A. Bultheel, The European Mathematical Society, February, 2012)

Spis treści

Preface to the Second Edition.- Preface.- Prologue.- Chapter 1. Machine Arithmetic and Related Matters.- Chapter 2. Approximation and Interpolation.- Chapter 3. Numerical Differentiation and Integration.- Chapter 4. Nonlinear Equations.- Chapter 5. Initial Value Problems for ODEs --- One-Step Methods.- Chapter 6. Initial Value Problems for ODEs --- Multi-Step Methods.- Chapter 7. Two-Point Boundary Value Problems for ODEs.- References.- Subject Index.

O autorze

Walter Gautschi holds a Ph.D. in mathematics from the University of Basel, and completed postdoctoral work as a Janggen-Pöhn Research Fellow at the Istituto Nazionale per le Applicazioni del Calcolo in Rome and at the Harvard Computation Laboratory. His professional experience included positions at the National Bureau of Standards, the American University in Washington D.C., and the Oak Ridge National Laboratory, after which he spent his entire career at Purdue University. In addition to his previous edition of this title, Dr. Gautschi has authored a book on orthogonal polynomials and over 150 papers, many on the subject of numerical analysis.

Blurb

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... [The book] successfully conveys the author's interest and experience in the subject to the reader. —SIAM Review (on the First Edition)

Revised and updated, this second edition of Walter Gautschi's successful Numerical Analysis textbook explores computational methods for problems arising in areas such as classical analysis, approximation theory, nonlinear equations, and ordinary differential equations. 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 author has carefully developed and polished a complete solutions manual for this edition, which is available through the publisher and will serve as an exceptionally valuable resource for instructors.

The text is geared to a one- or two-semester graduate course in numerical analysis for students who have a good background in calculus and advanced calculus and some knowledge of linear algebra, complex analysis, and differential equations. Previous exposure to numerical methods in an undergraduate class is desirable but not absolutely necessary.