Numerical analysis - Gautschi, Walter (Springer, 2012)
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.