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Partial Differential Equations

  • Textbook
  • © 1971

Overview

Authors:
  1. Fritz John

    1. Courant Institute of Mathematical Sciences, New York University, New York, USA

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

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Table of contents (5 chapters)

  1. Front Matter

    Pages N2-ix
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  2. Introduction

    • Fritz John
    Pages 1-5

  3. The Single First Order Equation

    • Fritz John
    Pages 6-47

  4. The Cauchy Problem for Higher Order Equations

    • Fritz John
    Pages 48-86

  5. Second Order Linear Equations with Constant Coefficients

    • Fritz John
    Pages 87-185

  6. The Cauchy Problem for Linear Hyperbolic Equations in General

    • Fritz John
    Pages 186-214

  7. Back Matter

    Pages 215-221
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Keywords

About this book

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.

Authors and Affiliations

  • Courant Institute of Mathematical Sciences, New York University, New York, USA

    Fritz John

Bibliographic Information

  • Book Title: Partial Differential Equations

  • Authors: Fritz John

  • Series Title: Applied Mathematical Sciences

  • DOI: https://doi.org/10.1007/978-1-4615-9966-1

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York Inc. 1971

  • eBook ISBN: 978-1-4615-9966-1Published: 11 November 2013

  • Series ISSN: 0066-5452

  • Series E-ISSN: 2196-968X

  • Edition Number: 1

  • Number of Pages: 221

  • Topics: Analysis, Applications of Mathematics

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