Mathematical Analysis and Numerical Methods for Science and Technology

Volume 2 Functional and Variational Methods

  • Robert Dautray
  • Jacques-Louis Lions

Table of contents

  1. Front Matter
    Pages I-XV
  2. Robert Dautray, Jacques-Louis Lions
    Pages 1-91
  3. Robert Dautray, Jacques-Louis Lions
    Pages 92-147
  4. Robert Dautray, Jacques-Louis Lions
    Pages 148-268
  5. Robert Dautray, Jacques-Louis Lions
    Pages 269-374
  6. Robert Dautray, Jacques-Louis Lions
    Pages 375-456
  7. Back Matter
    Pages 457-589

About this book

Introduction

These 6 volumes - the result of a 10 year collaboration between the authors, two of France's leading scientists and both distinguished international figures - compile the mathematical knowledge required by researchers in mechanics, physics, engineering, chemistry and other branches of application of mathematics for the theoretical and numerical resolution of physical models on computers. Since the publication in 1924 of the "Methoden der mathematischen Physik" by Courant and Hilbert, there has been no other comprehensive and up-to-date publication presenting the mathematical tools needed in applications of mathematics in directly implementable form. The advent of large computers has in the meantime revolutionised methods of computation and made this gap in the literature intolerable: the objective of the present work is to fill just this gap. Many phenomena in physical mathematics may be modeled by a system of partial differential equations in distributed systems: a model here means a set of equations, which together with given boundary data and, if the phenomenon is evolving in time, initial data, defines the system. The advent of high-speed computers has made it possible for the first time to calculate values from models accurately and rapidly. Researchers and engineers thus have a crucial means of using numerical results to modify and adapt arguments and experiments along the way. Every facet of technical and industrial activity has been affected by these developments. Modeling by distributed systems now also supports work in many areas of physics (plasmas, new materials, astrophysics, geophysics), chemistry and mechanics and is finding increasing use in the life sciences.

Keywords

CON_D038 Boundary value problem differential equation differential operator distribution Fourier series inequality manifold Mathematica mathematical analysis modeling numerical method operator partial differential equation Sobolev space solution

Authors and affiliations

  • Robert Dautray
    • 1
  • Jacques-Louis Lions
    • 2
  1. 1.ParisFrance
  2. 2.Collège de FranceParis Cedex 5France

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-61566-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 2000
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-66098-9
  • Online ISBN 978-3-642-61566-5
  • Buy this book on publisher's site