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Numerical Mathematics / Edition 2

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Overview

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 user-friendly 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 real-life 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. MATLAB-software satisfies the need of user-friendliness. [....] 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

"...provides the mathematical foundations of numerical methods, analyzes their basic theoretical properties & demonstrates their performance on examples & counter examples which outline their pros & cons."

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Editorial Reviews

From the Publisher
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. MATLAB-software satisfies the need of user-friendliness. 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 black-box methods or algorithms exist that can effectively and accurately solve all kinds of problems.' All MATLAB-programs 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

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Product Details

  • ISBN-13: 9783642071010
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 11/25/2010
  • Series: Texts in Applied Mathematics Series , #37
  • Edition description: Softcover reprint of hardcover 2nd ed. 2007
  • Edition number: 2
  • Pages: 657
  • Product dimensions: 6.14 (w) x 9.21 (h) x 1.36 (d)

Meet the Author

Alfio Quarteroni:

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 multi-physics 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.
• Co-chairman (with P.L.Lions) of the AMIF research programme of the European Science Foundation (1996-2001).
• 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.

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Table of Contents

Series Preface.- Preface.- I Getting Started.- 1. Foundations of Matrix Analysis.- 2 Principles of Numerical Mathematics.- II Numerical Linear Algebra.- 3 Direct Methods for the Solution of Linear Systems.- 4 Iterative Methods for Solving Linear Systems.- 5 Approximation of Eigenvalues and Eigenvectors.- III Around Functions and Functionals.- 6 Rootfinding for Nonlinear Equations.- 7 Nonlinear Systems and Numerical Optimization.- 8 Polynomial Interpolation.- 9 Numerical Integration.- IV Transforms, Differentiation and Problem Discretization.- 10 Orthogonal Polynomials in Approximation Theory.- 11 Numerical Solution of Ordinary Differential Equations.- 12 Two-Point Boundary Value Problems.- 13 Parabolic and Hyperbolic Initial Boundary Value Problems.- References.- Index of MATLAB Programs.- Index.

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