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＜電子ブック＞
Partial Differential Equations / by F. John
(Applied Mathematical Sciences. ISSN:2196968X ; 1)

版	2nd ed. 1975.
出版者	New York, NY : Springer New York : Imprint: Springer
出版年	1975
本文言語	英語
大きさ	online resource
冊子体	Partial differential equations / F. John ; : ger,: us
著者標目	*John, F author SpringerLink (Online service)
件　名	LCSH:Mathematical analysis FREE:Analysis
一般注記	I — The Single First Order Equation -- 1. The linear and quasi-linear equations -- 2. The general first order equation for a function of two variables -- 3. The general first order equation for a function of n independent variables -- II — The Cauchy Problem for Higher Order Equations -- 1. Analytic functions of several real variables -- 2. Formulation of the Cauchy problem. The notion of characteristics -- 3. The Cauchy problem for the general non-linear equation -- 4. The Cauchy-Kowalewsky theorem -- III — Second Order Equations with Constant Coefficients -- 1. Equations in two independent variables. Canonical forms -- 2. The one-dimensional wave equation -- 3. The wave equation in higher dimensions. Method of spherical means. Method of descent -- 4. The inhomogeneous wave equation by Duhamel’s principle -- 5. The potential equation in two dimensions -- 6. The Dirichlet problem -- 7. The Green’s function and the fundamental solution -- 8. Equations related to the potential equation -- 9. Continuation of harmonic functions -- 10. The heat equation -- IV — The Cauchy Problem for Linear Hyperbolic Equations in General -- 1. Riemann’s method of integration -- 2. Higher order equations in two independent variables -- 3. The method of plane waves -- List of Books Recommended for Further Study -- Problems 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 Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/978-1-4615-9979-1

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