Numerical Analysis

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Springer Science & Business Media, Dec 7, 2011 - Mathematics - 588 pages
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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.

 

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Contents

Chapter 1 Machine Arithmetic and Related Matters
1
Chapter 2 Approximation and Interpolation
55
Chapter 3 Numerical Differentiation and Integration
159
Chapter 4 Nonlinear Equations
253
Chapter 5 Initial Value Problems for ODEs OneStep Methods
325
Chapter 6 Initial Value Problems for ODEs Multistep Methods
399
Chapter 7 TwoPoint Boundary Value Problems for ODEs
471
References
543
Index
571
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About the author (2011)

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.