Numerical Mathematics

  • Alfio Quarteroni
  • Riccardo Sacco
  • Fausto Saleri
Part of the Texts in Applied Mathematics book series (TAM, volume 37)

Table of contents

  1. Front Matter
    Pages 424-424
  2. Getting Started

    1. Front Matter
      Pages 1-1
    2. Alfio Quarteroni, Riccardo Sacco, Fausto Saleri
      Pages 3-31
    3. Alfio Quarteroni, Riccardo Sacco, Fausto Saleri
      Pages 33-56
  3. Numerical Linear Algebra

    1. Front Matter
      Pages 58-58
    2. Alfio Quarteroni, Riccardo Sacco, Fausto Saleri
      Pages 59-124
    3. Alfio Quarteroni, Riccardo Sacco, Fausto Saleri
      Pages 125-182
    4. Alfio Quarteroni, Riccardo Sacco, Fausto Saleri
      Pages 183-244
  4. Around Functions and Functionals

    1. Front Matter
      Pages 246-246
    2. Alfio Quarteroni, Riccardo Sacco, Fausto Saleri
      Pages 247-284
    3. Alfio Quarteroni, Riccardo Sacco, Fausto Saleri
      Pages 285-331
    4. Alfio Quarteroni, Riccardo Sacco, Fausto Saleri
      Pages 333-377
    5. Alfio Quarteroni, Riccardo Sacco, Fausto Saleri
      Pages 379-422
  5. Transforms, Differentiation and Problem Discretization

    1. Front Matter
      Pages 424-424
    2. Alfio Quarteroni, Riccardo Sacco, Fausto Saleri
      Pages 425-478
    3. Alfio Quarteroni, Riccardo Sacco, Fausto Saleri
      Pages 479-538
    4. Alfio Quarteroni, Riccardo Sacco, Fausto Saleri
      Pages 539-587
    5. Alfio Quarteroni, Riccardo Sacco, Fausto Saleri
      Pages 589-633
  6. Back Matter
    Pages 635-656

About this book

Introduction

 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

Keywords

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

Authors and affiliations

  • Alfio Quarteroni
    • 1
  • Riccardo Sacco
    • 2
  • Fausto Saleri
    • 3
  1. 1.Dipartimento di Matematica-MOXPolitecnico di Milano20133Italy
  2. 2.Dipartimento di MatematicaPolitecnico di Milano20133Italy
  3. 3.Dipartimento di Matematica-MOXPolitecnico di Milano20133Italy

Bibliographic information

  • DOI https://doi.org/10.1007/b98885
  • Copyright Information Springer-Verlag Berlin Heidelberg 2007
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-34658-6
  • Online ISBN 978-3-540-49809-4
  • Series Print ISSN 0939-2475
  • Series Online ISSN 2196-9949
  • About this book