Numerical Mathematics

Numerical mathematics 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.

This book provides the mathematical foundations of numerical methods and demonstrate their performance on examples, exercises and real-life applications. This is done using the MATLAB software environment, which allows an easy implementation and testing of the algorithms for any specific class of problems.

The book is addressed to students in Engineering, Mathematics, Physics and Computer Sciences. The attention to applications and software development makes it valuable also for users in a wide 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.

• Analysis
• MATLAB
• Numerical integration
• algorithm
• algorithms
• linear algebra
• numerical analysis
• numerical methods
• optimization
• scientific computing
• stability

“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…"

• Dipartimento di Matematica-MOX, Politecnico di Milano, 20133, Italy

  Alfio Quarteroni, Fausto Saleri

• Dipartimento di Matematica, Politecnico di Milano, 20133, Italy

  Riccardo Sacco

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.

Policies and ethics