Applied Mathematical Sciences

Partial Differential Equations

Authors: John, F.

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About this Textbook

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.

Table of contents (5 chapters)

Table of contents (5 chapters)

Buy this book

eBook $74.99
price for USA in USD (gross)
  • ISBN 978-1-4615-9979-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Partial Differential Equations
Authors
Series Title
Applied Mathematical Sciences
Series Volume
1
Copyright
1975
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York Inc.
eBook ISBN
978-1-4615-9979-1
DOI
10.1007/978-1-4615-9979-1
Series ISSN
0066-5452
Edition Number
2
Topics