Partial Differential Equations

  • F. John

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

Table of contents

  1. Front Matter
    Pages i-ix
  2. F. John
    Pages 1-5
  3. F. John
    Pages 6-47
  4. Back Matter
    Pages 215-250

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. Added to this second corrected edition is a collection of problems and solutions, which illustrate and supplement the theories developed in the text. Fritz John New York September, 1974 vii TABLE OF CONTENTS Introd uction 1 CHAPrER I - THE SINGLE FIRST ORDER EQUATION 1. The linear and quasi-linear equations. 6 2. The general first order equation for a function of two variables. • • • • • • • • • 15 The general first order equation for a function 3. of n independent variables. • • • • • 37 CHAPrER II - THE CAUCHY PROBLEM FOR HIGHER ORDER EQUATIONS 1. Analytic functions of several real variables • 48 2. Formulation of the Cauchy problem. The notion of characteristics. • • • 54 3. The Cauchy problem for the general non-linear equation ••• 71 4. The Cauchy-Kowalewsky theorem. 76 CHAPTER III - SECOND ORDER EQUATIONS WITH CONSTANT COEFFICIENTS 1. Equations in two independent variables.

Keywords

Cauchy problem analytic function differential equation functional analysis partial differential equation

Authors and affiliations

  • F. John
    • 1
  1. 1.Courant InstituteNew York UniversityNew YorkUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4615-9979-1
  • Copyright Information Springer-Verlag New York 1975
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-90111-4
  • Online ISBN 978-1-4615-9979-1
  • Series Print ISSN 0066-5452
  • About this book
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