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 i-xx
  2. Getting Started

    1. Alfio Quarteroni, Riccardo Sacco, Fausto Saleri
      Pages 1-32
    2. Alfio Quarteroni, Riccardo Sacco, Fausto Saleri
      Pages 33-56
  3. Numerical Linear Algebra

    1. Alfio Quarteroni, Riccardo Sacco, Fausto Saleri
      Pages 57-122
    2. Alfio Quarteroni, Riccardo Sacco, Fausto Saleri
      Pages 123-181
    3. Alfio Quarteroni, Riccardo Sacco, Fausto Saleri
      Pages 183-243
  4. Around Functions and Functionals

    1. Alfio Quarteroni, Riccardo Sacco, Fausto Saleri
      Pages 245-280
    2. Alfio Quarteroni, Riccardo Sacco, Fausto Saleri
      Pages 281-326
    3. Alfio Quarteroni, Riccardo Sacco, Fausto Saleri
      Pages 327-370
    4. Alfio Quarteroni, Riccardo Sacco, Fausto Saleri
      Pages 371-414
  5. Transforms, Differentiation and Problem Discretization

    1. Alfio Quarteroni, Riccardo Sacco, Fausto Saleri
      Pages 415-468
    2. Alfio Quarteroni, Riccardo Sacco, Fausto Saleri
      Pages 469-530
    3. Alfio Quarteroni, Riccardo Sacco, Fausto Saleri
      Pages 531-579
    4. Alfio Quarteroni, Riccardo Sacco, Fausto Saleri
      Pages 581-626
  6. Back Matter
    Pages 627-655

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 performances on examples and counterexamples which outline their pros and cons. This is done using the MATLAB 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 MATLAB 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.

Keywords

Algebra MATLAB algorithms calculus complexity equation function geometry linear algebra mathematics optimization

Authors and affiliations

  • Alfio Quarteroni
    • 1
  • Riccardo Sacco
    • 2
  • Fausto Saleri
    • 3
  1. 1.Department of MathematicsEcole Polytechnique, Fédérale de LausanneLausanneSwitzerland
  2. 2.Dipartimento di MatematicaPolitecnico di MilanoMilanItaly
  3. 3.Dipartimento di Matematica, “F. Enriques”Università degli Studi di MilanoMilanItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-22750-4
  • Copyright Information Springer Science+Business Media New York 2007
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4757-7394-1
  • Online ISBN 978-0-387-22750-4
  • Series Print ISSN 0939-2475
  • Series Online ISSN 2196-9949
  • About this book