Bücher von Fritz John

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.

This book is a very well-accepted introduction to the subject. Now, in this fourth edition, the book has again been updated with an additional chapter on Lewy's example of a linear equation without solutions.

From the Preface: (...) The book is addressed to students on various levels, to mathematicians, scientists, engineers. Instead of obstructing the access to the wealth of facts by lengthy discussions of a fundamental nature we have sometimes postponed such discussions to appendices in the various chapters.

From the reviews: "...one of the best textbooks introducing several generations of mathematicians to higher mathematics. ... This excellent book is highly recommended both to instructors and students." --Acta Scientiarum Mathematicarum, 1991

From the reviews: "...one of the best textbooks introducing several generations of mathematicians to higher mathematics. ... This excellent book is highly recommended both to instructors and students." --Acta Scientiarum Mathematicarum, 1991