Partial Differential Equations

1. Front Matter

   Pages N2-ix

   PDF

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

   PDF

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.

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

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

  Fritz John

Policies and ethics