Read more
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.
List 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.
About the author
Andrea Manzoni, PhD, is an Associate Professor of Numerical Analysis at Politecnico of Milan. He is the author of 2 books and of approximately 50 papers. In 2012 he won the ECCOMAS Award for the best PhD thesis in Europe about Computational Methods in Applied Sciences and Engineering and the Biannual SIMAI prize (Italian Society of Applied and Industrial Mathematics) in 2017. His research interests include the development of reduced-order modelling techniques for PDEs, PDE-constrained optimization, uncertainty quantification, computational statistics, and machine/deep learning.
Alfio Quarteroni is a Professor of Numerical Analysis at Politecnico of Milan and Professor Emeritus at EPFL, Lausanne. He is the author of 25 books, editor of 12 books, author of about 400 papers. He is the recipient of two ERC Advanced Grants. He is a member of the Italian Academy of Science, the European Academy of Science, Academia Europaea, and the Lisbon Academy of Science. His research Group at EPFL has carried out the mathematical simulation for the Alinghi sailing boat, the winner of two editions (2003 and 2007) of America's Cup. His research interests include mathematical modeling and its applications at large.
Sandro Salsa is a Professor of Mathematical Analysis at the Department of Mathematics of the Politecnico of Milan, where he has been one of the main founders of the educational program in Mathematical Engineering. His research interest ranges over diverse aspects of nonlinear, nonlocal, singular or degenerate elliptic and parabolic equations, with particular emphasis on free boundary problems. He is an author of 13 books and several papers in the most prestigious scientific mathematical journals.
Summary
This extremely popular textbook on numerical analysis provides the mathematical foundations of numerical methods. It demonstrates 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. 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. 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.
Additional text
“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…"
Report
"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..."
