Numerical Mathematics
Authors: Quarteroni, Alfio, Sacco, Riccardo, Saleri, Fausto
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 About this Textbook

Numerical mathematics is the branch of mathematics that proposes, develops, analyzes and applies methods from scientific computing to several fields including analysis, linear algebra, geometry, approximation theory, functional equations, optimization and differential equations. Other disciplines, such as physics, the natural and biological sciences, engineering, and economics and the financial sciences frequently give rise to problems that need scientific computing for their solutions. As such, numerical mathematics is the crossroad of several disciplines of great relevance in modern applied sciences, and can become a crucial tool for their qualitative and quantitative analysis.
One of the purposes of this book is to provide the mathematical foundations of numerical methods, to analyze their basic theoretical properties (stability, accuracy, computational complexity) and demonstrate their performance on examples and counterexamples which outline their pros and cons. This is done using the MATLABTM software environment which is userfriendly and widely adopted. Within any specific class of problems, the most appropriate scientific computing algorithms are reviewed, their theoretical analyses are carried out and the expected results are verified on a MATLABTM computer implementation. Every chapter is supplied with examples, exercises and applications of the discussed theory to the solution of reallife problems.
This book is addressed to senior undergraduate and graduate students with particular focus on degree courses in engineering, mathematics, physics and computer sciences. The attention which is paid to the applications and the related development of software makes it valuable also for researchers and users of scientific computing in a large variety of professional fields.
In this second edition, the readability of pictures, tables and program headings has been improved. Several changes in the chapters on iterative methods and on polynomial approximation have also been added.
From the reviews of the first edition:
"This is an excellent and modern textbook in numerical mathematics! It is primarily addressed to undergraduate students in mathematics, physics, computer science and engineering. But you will need a weekly 4 hour lecture for 3 terms lecture to teach all topics treated in this book! Well known methods as well as very new algorithms are given. The methods and their performances are demonstrated by illustrative examples and computer examples. Exercises shall help the reader to understand the theory and to apply it. MATLABsoftware satisfies the need of userfriendliness. [....] In the reviewers opinion, the presented book is the best textbook in numerical mathematics edited in the last ten years."
Zentralblatt für Mathematik 2001, 991.38387
 About the authors

Alfio Quarteroni (see http://www.cirstm.org/researchers/researchers.php?id=319):
Author of a huge amount of books
Professor and Chair of Modelling and Scientific Computing (CMCS) at the Institute of Analysis and Scientific Computing of EPFL, Lausanne (Switzerland), since 1998.
Professor of Numerical Analysis at the Politecnico di Milano (Italy) since 1989 and Scientific Director of MOX, since 2002.
Research Interests :His current research involves computational fluid dynamics, modelling and simulation of haemodynamics, numerical analysis of domain decomposition methods with application to multiphysics problems.
Awards and Honors : NASA Group Achievement Award for the pioneering work in Computational Fluid Dynamics as a member of the ICASE numerical analysis and algorithms group, 1992.
Member of the Lombard Academy of Science (Istituto Lombardo di Scienze e Lettere) (since 1995).  Chairman of the Mathematics and Computer Science RTN evaluation panel of the E.U., 1999.
 Cochairman (with P.L.Lions) of the AMIF research programme of the European Science Foundation (19962001).
 Recipient of the Galileian Chair, Scuola Normale Superiore, Pisa, Italy (2001).
Premio Agrumello 2003.  Laurea Honoris Causa in Naval Engineering , University of Trieste, Italy, October 2003.
 Recipient of one of the SIAM Outstanding Paper Prize 2004 (for a paper in collaboration with A. Veneziani and P. Zunino).
 IACM (International Association for Computational Mechanics), Fellow Award, 2004.
 Member of Accademia Nazionale dei Lincei, (Italian National Academy of Sciences) 2004.
 President of the Evaluation Panel "Mathematics and Computer Sciences" of CIVR, 2005.
 NASA Group Achievement Award for the pioneering work in Computational Fluid Dynamics as a member of the ICASE numerical analysis and algorithms group, 1992.
 Reviews

From the reviews of the first edition:
SIAM REVIEW
"I found many of the examples to be quite interesting. I find no fault with any of the theoretical portions of the text. The authors are quite thorough in their discussion of the theory underlying each of the topics…This text uses MATLAB for programming the numerical codes. This is a very good choice…It contains a lot of interesting and useful information for experienced users of numerical methods…"
ZENTRALBLATT MATH
"This is an excellent and modern textbook in numerical mathematics! It is primarily addressed to undergraduate students in mathematics, physics, computer science and engineering. But you will need a weekly 4 hour lecture for 3 terms lecture to teach all topics treated in this book! Well known methods as well as very new algorithms are given. The methods and their performances are demonstrated by illustrative examples and computer examples. Exercises shall help the reader to understand the theory and to apply it. MATLABsoftware satisfies the need of userfriendliness. he spread of numerical software presents an enrichment for the scientific community. However, the user has to make the correct choice of the method which best suits at hand. As a matter of fact, no blackbox methods or algorithms exist that can effectively and accurately solve all kinds of problems.' All MATLABprograms are available by internet. ... There are a lot of numerical examples and impressing figures and very useful applications, as for instance: Regularization of a triangular grid, analysis of an electric network and of a nonlinear electrical circuit, finite difference analysis of beam bending, analysis of the buckling of a beam, free dynamic vibration of a bridge, analysis of the state equation for a real gas, solution of a nonlinear system arising from semiconductor device simulation, finite element analysis of a clamped beam, geometric reconstruction based on computer tomographies, computation of the wind action on a sailboat mast, numerical solution of blackbody radiation, compliance of arterial walls, lubrication of a slider, heat conduction in a bar, a hyperbolic model for blood flow interaction with arterial walls. It is a joy to read the book, it is carefully written and well printed. ..... In the reviewers opinion, the presented book is the best textbook in numerical mathematics edited in the last ten years."
W.H.Schmidt, Zentralblatt für Mathematik 991.38387
 Table of contents (13 chapters)


Foundations of Matrix Analysis
Pages 331

Principles of Numerical Mathematics
Pages 3356

Direct Methods for the Solution of Linear Systems
Pages 59124

Iterative Methods for Solving Linear Systems
Pages 125182

Approximation of Eigenvalues and Eigenvectors
Pages 183244

Table of contents (13 chapters)
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Bibliographic Information
 Bibliographic Information

 Book Title
 Numerical Mathematics
 Authors

 Alfio Quarteroni
 Riccardo Sacco
 Fausto Saleri
 Series Title
 Texts in Applied Mathematics
 Series Volume
 37
 Copyright
 2007
 Publisher
 SpringerVerlag Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
 eBook ISBN
 9783540498094
 DOI
 10.1007/b98885
 Hardcover ISBN
 9783540346586
 Softcover ISBN
 9783642071010
 Series ISSN
 09392475
 Edition Number
 2
 Number of Pages
 XVIII, 657
 Number of Illustrations
 135 b/w illustrations
 Topics