Partial differential equations. 3rd ed
type: Item
instance of: scholarly article
title: Partial differential equations. 3rd ed
zbMATH Open document ID: 0426.35002
author: Fritz John
published in: Applied Mathematical Sciences
publication date: 1978-01-01T00:00:00Z
review text: This new edition is.completely rewritten. Now, the book is divided into 7 chapters entitled as follows: 1. The single first-order equation. 2. Second-order equations: hyperbolic equations for functions of two independent variables. 3. Characteristic manifolds and the Cauchy problem. 4. The Laplace equation. 5. Hyperbolic equations in higher dimensions. 6. Higher-order elliptic equations with constant coefficients. 7. Parabolic equations. As compared with the former edition, an extensive use is made of Fourier transform techniques, Hilbert space, and finite difference methods. Almost all sections contain a subsection with problems. Naturally, the characterization that ``this book still serves as an excellent introduction to partial differential equations'' [see the first edition (1971; Zbl 0209.40001)] is now even more justified. As concerns the spirit of the book, let us quote from the author's Preface to this edition: ``In this book emphasis is put on discovering significant features of a differential equation, and on exploring them as far as possible with a limited amount of machinery from mathematical analysis. Entanglement in a mass of technical details has been avoided, even when this resulted in less general or less complete results''.
reviewed by: Alois Kufner
Mathematics Subject Classification ID: 35-01
zbMATH DE Number: 3663608
zbMATH Keywords: first-order equation
zbMATH Keywords: second-order equations
zbMATH Keywords: characteristic manifolds
zbMATH Keywords: Cauchy problem
zbMATH Keywords: Laplace equation
zbMATH Keywords: hyperbolic equations
zbMATH Keywords: higher-order elliptic equations with constant coefficients
zbMATH Keywords: parabolic equations
zbMATH Keywords: Fourier transform techniques
zbMATH Keywords: Hilbert space
zbMATH Keywords: finite difference methods
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3663608