A rigorous and comprehensive introduction to numerical analysis
Numerical Methods provides a clear and concise exploration of standard numerical analysis topics, as well as nontraditional ones, including mathematical modeling, Monte Carlo methods, Markov chains, and fractals. Filled with appealing examples that will motivate students, the textbook considers modern application areas, such as information retrieval and animation, and classical topics from physics and engineering. Exercises use MATLAB and promote understanding of computational results.
The book gives instructors the flexibility to emphasize different aspects-design, analysis, or computer implementation-of numerical algorithms, depending on the background and interests of students. Designed for upper-division undergraduates in mathematics or computer science classes, the textbook assumes that students have prior knowledge of linear algebra and calculus, although these topics are reviewed in the text. Short discussions of the history of numerical methods are interspersed throughout the chapters. The book also includes polynomial interpolation at Chebyshev points, use of the MATLAB package Chebfun, and a section on the fast Fourier transform. Supplementary materials are available online.
• Clear and concise exposition of standard numerical analysis topics
• Explores nontraditional topics, such as mathematical modeling and Monte Carlo methods
• Covers modern applications, including information retrieval and animation, and classical applications from physics and engineering
• Promotes understanding of computational results through MATLAB exercises
• Provides flexibility so instructors can emphasize mathematical or applied/computational aspects of numerical methods or a combination
• Includes recent results on polynomial interpolation at Chebyshev points and use of the MATLAB package Chebfun
• Short discussions of the history of numerical methods interspersed throughout
• Supplementary materials available online
Anne Greenbaum is professor of applied mathematics at the University of Washington. She is the author of Iterative Methods for Solving Linear Systems. Timothy P. Chartier is associate professor of mathematics at Davidson College. "This is an excellent introduction to the exciting world of numerical analysis. Fulfilling the need for a modern textbook on numerical methods, this volume has a wealth of examples that will keep students interested in the material. The mathematics is completely rigorous and I applaud the authors for doing such a marvelous job."-Michele Benzi, Emory University
"Filled with polished details and a plethora of examples and illustrations, this ambitious and substantial text touches every standard topic of numerical analysis. The authors have done a huge amount of work and produced a major textbook for this subject."-Lloyd N. Trefethen, University of Oxford "Distinguishing features are the inclusion of many recent applications of numerical methods and the extensive discussion of methods based on Chebyshev interpolation. This book would be suitable for use in courses aimed at advanced undergraduate students in mathematics, the sciences, and engineering." "An instructor could assemble several different one-semester courses using this book-numerical linear algebra and interpolation, or numerical solutions of differential equations-or perhaps a two-semester sequence. This is a charming book, well worth consideration for the next numerical analysis course."---William J. Satzer, MAA Focus "[Numerical Methods] is a very pleasant book, where the concepts involved are clearly explained. All chapters begin with motivating examples that give a precise idea of the methods developed. In addition, every chapter ends with an extensive collection of exercises, useful to understand the importance of the results. These are complemented by a series of exercises, designed to be performed
