This book provides a thorough and careful introduction to the theory and practice of scientific computing at an elementary, yet rigorous, level, from theory via examples and algorithms to computer programs. The original FORTRAN programs have been rewritten in MATLAB and now appear in a new appendix and online, offering a modernized version of this classic reference for basic numerical algorithms.
Offering a clear, precise, and accessible presentation, complete with MATLAB programs, this new Third Edition of Elementary Numerical Analysis gives students the support they need to master basic numerical analysis and scientific computing. Now updated and revised, this significant revision features reorganized and rewritten content, as well as some new additional examples and problems.The text introduces core areas of numerical analysis and scientific computing along with basic themes of numerical analysis such as the approximation of problems by simpler methods, the construction of algorithms, iteration methods, error analysis, stability, asymptotic error formulas, and the effects of machine arithmetic.· Taylor Polynomials · Error and Computer Arithmetic · Rootfinding · Interpolation and Approximation · Numerical Integration and Differentiation · Solution of Systems of Linear Equations · Numerical Linear Algebra: Advanced Topics · Ordinary Differential Equations · Finite Difference Method for PDEs
Author: James Edward Miller,David G. Moursund,Charles S. Duris
Publisher: Courier Corporation
This updated introduction to modern numerical analysis is a complete revision of a classic text originally written in Fortran but now featuring the programming language C++. It focuses on a relatively small number of basic concepts and techniques. Many exercises appear throughout the text, most with solutions. An extensive tutorial explains how to solve problems with C++.
Dieses Numerik-Lehrbuch entwickelte sich seit der 1. Auflage zum Standardwerk. In zahlreichen Lehrveranstaltungen wird es als Begleittext verwendet. Der Erfolg dieses Lehrbuchs ist begründet. Es präsentiert, streng analytisch, grundlegende Prinzipien der Numerischen Mathematik, verknüpft diese aber zugleich mit der praktischen Anwendung, indem es fundamentale algorithmische Werkzeuge bereitstellt und diskutiert. Neue Methodologien und daraus resultierende numerische Verfahren der vergangenen Jahre sind in die 10. Neuauflage integriert: aktualisierte Grundlagen, neue algorithmische Techniken, die kritische Beurteilung existenter Methoden.
Design, Analysis, and Computer Implementation of Algorithms
Author: Anne Greenbaum,Timothy P. Chartier
Publisher: Princeton University Press
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
This book explains how precise numerical analysis is constructed with C++. Included is a CD-ROM which contains executable Windows 95 programs for the PC and which demonstrates how these programs can be used to solvetypical problems of elementary numerical analysis with precision. The book also provides exercises which illustrate points from the text and references for the methods presented. . Ordinary differential equation solver demos . Numerical integration demos . Polynomial root finder demos . Complete demo C++text files . Book explains all methods demos use This book is an excellent choice as a text for a course in numerical analysis for advanced undergraduate or graduate students. It is also an invaluable reference for anyone concerned with precise numerical solutions to common engineering problems.