Partial Differential Equations

  • Fritz John

Part of the Applied Mathematical Sciences book series (AMS, volume 1)

Table of contents

  1. Front Matter
    Pages N2-ix
  2. Fritz John
    Pages 1-5
  3. Fritz John
    Pages 6-47
  4. Back Matter
    Pages 215-221

About this book

Introduction

These Notes grew out of a course given by the author in 1952-53. Though the field of Partial Differential Equations has changed considerably since those days, particularly under the impact of methods taken from Functional Analysis, the author feels that the introductory material offered here still is basic for an understanding of the subject. It supplies the necessary intuitive foundation which motivates and anticipates abstract formulations of the questions and relates them to the description of natual phenomena. In the present edition, only minor corrections have been made in the text. An Index and up-to-date listing of books recommended for further study have been added. Fritz John New York November 19, 1970 v TABLE OF CONTENTS Introduetion 1 CHAPl'ER I - TEE SINGLE FIRST ORDER EQUATION 1. The linear and quasi-linear equations. 6 The general first order equation for a funetion 2. of two variables. • • • • • • • • • 15 The general first order equation for a funetion 3. of n independent variables. • • • • • 37 CHAPl'ER II - TEE CAUCIIT PROBLEM FOR HIGEER ORDER EQUATIONS 1. Analytie funetions of several real variables • Formulation of the Cauehy problem. The not ion 2. of eharaeteristies. • • • 54 3. The Cauehy problem for the general non-linear equation. 71 4. The Cauehy-Kowalewsky theorem. 76 CHAPl'ER 111 - SECOND ORDER EQUATIONS WITH CONSTANT COEFFICIENTS 1. Equations in two independent variables.

Keywords

analytic function Cauchy problem differential equation functional analysis hyperbolic equation integration partial differential equation Potential solution wave equation

Authors and affiliations

  • Fritz John
    • 1
  1. 1.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4615-9966-1
  • Copyright Information Springer-Verlag New York 1971
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-90021-6
  • Online ISBN 978-1-4615-9966-1
  • Series Print ISSN 0066-5452
  • About this book