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Numerical Mathematics de Alfio Quarteroni

Numerical Mathematics: Texts in Applied Mathematics, cartea 37

Autor Alfio Quarteroni, Riccardo Sacco, Fausto Saleri
en Limba Engleză Hardback – 19 oct 2006

Evoluția matematicii numerice în ultimele decenii reflectă o tranziție fundamentală de la analize pur teoretice către o disciplină ancorată în calculul științific, unde eficiența algoritmilor este validată prin simulări computerizate complexe. Observăm în Numerical Mathematics o sinteză riguroasă a fundamentelor matematice necesare pentru a aborda probleme din inginerie, fizică și informatică. Lucrarea, publicată sub egida Springer, nu se limitează la expunerea teoremelor, ci pune un accent deosebit pe performanța metodelor în aplicații reale.

Subliniem structura logică a volumului, care ghidează cititorul de la principiile de bază ale analizei matriciale către subiecte avansate precum aproximarea valorilor proprii și soluționarea numerică a ecuațiilor diferențiale cu derivate parțiale (parabolice și hiperbolice). Această progresie este susținută constant de utilizarea mediului MATLAB, facilitând o tranziție rapidă de la concept la execuție. Remarcăm că această a doua ediție a fost optimizată pentru o mai bună lizibilitate a tabelelor și programelor, reflectând feedback-ul comunității academice.

În contextul operei autorului Alfio Quarteroni, acest titlu reprezintă pilonul teoretic central, completând abordările practice din Modeling Reality with Mathematics sau A Primer on Mathematical Modelling. Dacă lucrările anterioare se concentrau pe formularea modelelor, Numerical Mathematics oferă instrumentarul necesar pentru rezolvarea lor efectivă. Ca alternativă la An Introduction to Numerical Methods pentru cursurile de analiză numerică, această lucrare se distinge prin rigoarea demonstrațiilor matematice și prin acoperirea extinsă a problemelor la limită, fiind mai potrivită pentru un nivel de cercetare. De asemenea, față de Scientific Computing with MATLAB and Octave, volumul de față oferă un fundament teoretic mult mai dens, fiind o resursă de referință pentru studiul aprofundat.

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Specificații

ISBN-13: 9783540346586
ISBN-10: 3540346589
Pagini: 676
Ilustrații: XVIII, 657 p. 135 illus.
Dimensiuni: 155 x 235 x 32 mm
Greutate: 1.09 kg
Ediția:2nd ed. 2007
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Texts in Applied Mathematics

Locul publicării:Berlin, Heidelberg, Germany

Public țintă

Research

De ce să citești această carte

Recomandăm această lucrare studenților și cercetătorilor care au nevoie de o bază matematică solidă pentru calculul științific. Cititorul câștigă nu doar o înțelegere teoretică a metodelor numerice, ci și competențe practice de implementare în MATLAB. Este o resursă esențială pentru cei care doresc să treacă dincolo de simpla utilizare a unor pachete software, înțelegând stabilitatea și convergența algoritmilor utilizați în modelarea fenomenelor fizice.

Despre autor

Autorii sunt personalități marcante ale matematicii aplicate contemporane. Alfio Quarteroni, Riccardo Sacco și Fausto Saleri sunt profesori la EPFL (École Polytechnique Fédérale de Lausanne), o instituție de elită în cercetarea tehnologică. Quarteroni este recunoscut la nivel mondial pentru contribuțiile sale în modelarea matematică, de la sistemul cardiovascular uman până la optimizarea aerodinamicii ambarcațiunilor de competiție. Expertiza lor combinată transformă acest manual dintr-un simplu curs universitar într-o lucrare de referință care face legătura între rigoarea teoretică italiană și pragmatismul computațional elvețian.

Cuprins

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.

Recenzii

“It is a joy to read the book, it is carefully written and well printed.” (Werner H.Schmidt, zbMATH 0957.65001, 2021)
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…"

Notă biografică

Alfio Quarteroni (see http://www.cirs-tm.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 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.

Textul de pe ultima copertă

 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

Caracteristici

Extremely popular textbook on numerical analysis Includes supplementary material: sn.pub/extras