<電子ブック>
Partial Differential Equations / by Fritz John
(Applied Mathematical Sciences. ISSN:2196968X ; 1)
版 | 1st ed. 1971. |
---|---|
出版者 | (New York, NY : Springer New York : Imprint: Springer) |
出版年 | 1971 |
大きさ | 221 p : online resource |
著者標目 | *John, Fritz author SpringerLink (Online service) |
件 名 | LCSH:Mathematical analysis LCSH:Mathematics FREE:Analysis FREE:Applications of Mathematics |
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 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 HTTP:URL=https://doi.org/10.1007/978-1-4615-9966-1 |
目次/あらすじ
所蔵情報を非表示
電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
---|---|---|---|---|---|---|---|---|---|---|---|---|
電子ブック | オンライン | 電子ブック |
|
Springer eBooks | 9781461599661 |
|
電子リソース |
|
EB00205489 |
書誌詳細を非表示
データ種別 | 電子ブック |
---|---|
分 類 | LCC:QA299.6-433 DC23:515 |
書誌ID | 4000106460 |
ISBN | 9781461599661 |
類似資料
この資料の利用統計
このページへのアクセス回数:4回
※2017年9月4日以降