Numerical Analysis

A Mathematical Introduction
Erscheinungsjahr 2002
ISBN: 978-0-19-850852-6
Verlag: OUP Oxford

Buch, Englisch, 518 Seiten, Format (B × H): 156 mm x 234 mm, Gewicht: 778 g

Numerical analysis explains why numerical computations work, or fail. This book is divided into four parts. Part I starts Part I starts with a guided tour of floating number systems and machine arithmetic. The exponential and the logarithm are constructed from scratch to present a new point of view on questions well-known to the reader, and the needed knowledge of linear algebra is summarized. Part II starts with polynomial approximation (polynomial interpolation,
mean-square approximation, splines). It then deals with Fourier series, providing the trigonometric version of least square approximations, and one of the most important numerical algorithms, the fast Fourier transform. Any scientific computation program spends most of its time solving linear systems
or approximating the solution of linear systems, even when trying to solve non-linear systems. Part III is therefore about numerical linear algebra, while Part IV treats a selection of non-linear or complex problems: resolution of linear equations and systems, ordinary differential equations, single step and multi-step schemes, and an introduction to partial differential equations. The book has been written having in mind the advanced undergraduate students in mathematics who are interested
in the spice and spirit of numerical analysis. The book does not assume previous knowledge of numerical methods. It will also be useful to scientists and engineers wishing to learn what mathematics has to say about the reason why their numerical methods work - or fail.

Autoren/Hrsg.

Schatzman, Michelle

Schatzman, M.

Taylor, John

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Moderne Anwendungen der Analysis
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Mathematik | Informatik Mathematik Algebra Homologische Algebra

Über Autor(innen)

Professor Michelle Schatzman, MAPLY, 21 Avenue Claude Bernard, UCBL, F-69622 Villeurbanne Cedex, Tel: [phone], Fax: [phone], Email: [e-mail]