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Analytic Methods for Partial Differential Equations

  • Gwynne A. Evans
  • Jonathan M. Blackledge
  • Peter D. Yardley

Part of the Springer Undergraduate Mathematics Series book series (SUMS)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Gwynne A. Evans, Jonathan M. Blackledge, Peter D. Yardley
    Pages 1-48
  3. Gwynne A. Evans, Jonathan M. Blackledge, Peter D. Yardley
    Pages 49-94
  4. Gwynne A. Evans, Jonathan M. Blackledge, Peter D. Yardley
    Pages 95-122
  5. Gwynne A. Evans, Jonathan M. Blackledge, Peter D. Yardley
    Pages 123-162
  6. Gwynne A. Evans, Jonathan M. Blackledge, Peter D. Yardley
    Pages 163-224
  7. Back Matter
    Pages 225-299

About this book

Introduction

The subject of partial differential equations holds an exciting and special position in mathematics. Partial differential equations were not consciously created as a subject but emerged in the 18th century as ordinary differential equations failed to describe the physical principles being studied. The subject was originally developed by the major names of mathematics, in particular, Leonard Euler and Joseph-Louis Lagrange who studied waves on strings; Daniel Bernoulli and Euler who considered potential theory, with later developments by Adrien-Marie Legendre and Pierre-Simon Laplace; and Joseph Fourier's famous work on series expansions for the heat equation. Many of the greatest advances in modern science have been based on discovering the underlying partial differential equation for the process in question. J ames Clerk Maxwell, for example, put electricity and magnetism into a unified theory by estab­ lishing Maxwell's equations for electromagnetic theory, which gave solutions for problems in radio wave propagation, the diffraction of light and X-ray developments. Schrodinger's equation for quantum mechankal processes at the atomic level leads to experimentally verifiable results which have changed the face of atomic physics and chemistry in the 20th century. In fluid mechanics, the Navier-Stokes' equations form a basis for huge number-crunching activities associated with such widely disparate topics as weather forcasting and the design of supersonic aircraft. Inevitably the study of partial differential equations is a large undertaking, and falls into several areas of mathematics.

Keywords

Boundary value problem Fourier series calculus differential equation functional analysis partial differential equation scattering theory wave equation

Authors and affiliations

  • Gwynne A. Evans
    • 1
  • Jonathan M. Blackledge
    • 1
  • Peter D. Yardley
    • 1
  1. 1.Faculty of Computing Sciences & EngineeringDe Montfort UniversityLeicesterUK

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4471-0379-0
  • Copyright Information Springer-Verlag London Limited 1999
  • Publisher Name Springer, London
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-76124-2
  • Online ISBN 978-1-4471-0379-0
  • Series Print ISSN 1615-2085
  • Buy this book on publisher's site