An Introduction to Numerical Methods and Analysis, 2nd Edition

**Praise for the __First Edition__** ". . . outstandingly appealing with regard to its style, contents, considerations of requirements of practice, choice of examples, and exercises."—__Zentralblatt MATH__ ". . . carefully structured with many detailed worked examples."—__The Mathematical Gazette__ The __Second Edition__ of the highly regarded __An Introduction to Numerical Methods and Analysis__ provides a fully revised guide to numerical approximation. The book continues to be accessible and expertly guides readers through the many available techniques of numerical methods and analysis. __An Introduction to Numerical Methods and Analysis, Second Edition__ reflects the latest trends in the field, includes new material and revised exercises, and offers a unique emphasis on applications. The author clearly explains how to both construct and evaluate approximations for accuracy and performance, which are key skills in a variety of fields. A wide range of higher-level methods and solutions, including new topics such as the roots of polynomials, spectral collocation, finite element ideas, and Clenshaw-Curtis quadrature, are presented from an introductory perspective, and the __Second Edition__ also features: * Chapters and sections that begin with basic, elementary material followed by gradual coverage of more advanced material * Exercises ranging from simple hand computations to challenging derivations and minor proofs to programming exercises * Widespread exposure and utilization of MATLAB * An appendix that contains proofs of various theorems and other material The book is an ideal textbook for students in advanced undergraduate mathematics and engineering courses who are interested in gaining an understanding of numerical methods and numerical analysis. Praise for the First Edition'... outstandingly appealing with regard to its style, contents, considerations of requirements of practice, choice of examples, and exercises.'—Zentralblatt MATH'... carefully structured with many detailed worked examples.'—The Mathematical GazetteThe Second Edition of the highly regarded An Introduction to Numerical Methods and Analysis provides a fully revised guide to numerical approximation. The book continues to be accessible and expertly guides readers through the many available techniques of numerical methods and analysis.An Introduction to Numerical Methods and Analysis, Second Edition reflects the latest trends in the field, includes new material and revised exercises, and offers a unique emphasis on applications. The author clearly explains how to both construct and evaluate approximations for accuracy and performance, which are key skills in a variety of fields. A wide range of higher-level methods and solutions, including new topics such as the roots of polynomials, spectral collocation, finite element ideas, and Clenshaw-Curtis quadrature, are presented from an introductory perspective, and the Second Edition also features:Chapters and sections that begin with basic, elementary material followed by gradual coverage of more advanced materialExercises ranging from simple hand computations to challenging derivations and minor proofs to programming exercisesWidespread exposure and utilization of MATLABAn appendix that contains proofs of various theorems and other materialThe book is an ideal textbook for students in advanced undergraduate mathematics and engineering courses who are interested in gaining an understanding of numerical methods and numerical analysis.JAMES F. EPPERSON, PhD, is Associate Editor of Mathematical Reviews for the American Mathematical Society. He was previously associate professor in the Department of Mathematics at The University of Alabama in Huntsville and assistant professor at the University of Georgia in Athens. He earned his doctorate at Carnegie Mellon University in Pittsburgh and his undergraduate degree from the College of Engineering at the University of Michigan, Ann Arbor. "The objective of this book is for readers to learn where approximation methods come from, why they work, why they sometimes don't work, and when to use which of the many techniques that are available, and to do all this in an environment that emphasizes readability and usefulness to the numerical methods novice. Each chapter and each section begins with the basic, elementary material and gradually builds up to more advanced topics. The text begins with a review of the important calculus results, and why and where these ideas play an important role throughout the book. Some of the concepts required for the study of computational mathematics are introduced, and simple approximations using Taylor's Theorem are treated in some depth. The exposition is intended to be lively and "student friendly". Exercises run the gamut from simple hand computations that might be characterized are "starter exercises", to challenging derivations and minor proofs, to programming exercises. Eleven new exercises have been added throughout including: Basins of Attraction; Roots of Polynomials I; Radial Basis Function Interpolation; Tension Splines; An Introduction to Galerkin/Finite Element Ideas for BVPs; Broyden's Method; Roots of Polynomials, II; Spectral/collocation methods for PDEs; Algebraic Multigrid Method; Trigonometric interpolation/Fourier analysis; and Monte Carlo methods. Various sections have been revised to reflect recent trends and updates in the field"-- Provided by publisher A solutions manual to accompany An Introduction toNumerical Methods and Analysis, Second Edition An Introduction to Numerical Methods and Analysis, SecondEdition reflects the latest trends in the field, includesnew material and revised exercises, and offers a unique emphasis onapplications.