Methods Based On The Wiener-hopf Technique For The Solution Of Partial Differential Equations (ams/chelsea Publication)

CONTENTS PREFACE SOME BASIC NOTATION AND RESULTSFROM CHAPTER 1 I. COMPLEX VARIABLE AND FOURIERTRANSFORMS 1.1 Introduction 1.2 Complex variable theory 1.3 Analytic functions defined by integrals 1.4 The Fourier integral 1.5 The wave equation 1.6 Contour integrals of a certain type 1.7 The Wiener-Hopf procedure Miscellaneous Examples and Results I II. BASIC PROCEDURES : HALF-PLANE PROBLEMS 2.1 Introduction 2.2 Jones's method 2.3 A dual integral equation method 2.4 Integral equation formulations 2.5 Solution of the integral equations 2.6 Discussion of the solution 2.7 Comparison of methods 2.8 Boundary conditions specified by general functions 2.9 Radiation-type boundary conditions Miscellaneous Examples and Results II III. FURTHER WAVE PROBLEMS 3.1 Introduction 3.2 A plane wave incident on two semi-infinite parallel planes 3.3 Radiation from two parallel semi-infinite plates 3.4 Radiation from a cylindrical pipe 3.5 Semi-infinite strips parallel to the walls of a duct 3.6 A strip across a duct Miscellaneous Examples and Results III lV. EXTENSIONS AND LIMITATIONS OF THE METHOD 4.1 Introduction 4.2 The Hilbert problem 4.3 General considerations 4.4 Simultaneous Wiener-Hopf equations 4.5 Approximate factorization 4.6 Laplace's equation in polar co-ordinates Miscellaneous Examples and Results IV V. SOME APPHOXIMATE METHODS 5.1 Introduction 5.2 Some problems which cannot be solved exactly 5.3 General theory of a special equation 5.4 Diffraction by a thick semi-infinite strip 5.5 General theory of another special equation 5.6 Diffraction by strips and slits of finite width Miscellaneous Examples and Results V VI. THE GENERAL SOLUTION OF THE BASIC WIENER-HOPF PROBLEM 6.1 Introduction 6.2 The exact solution of certain dual integral equations Miscellaneous Examples and Results VI Bibliography Index Presents a comprehensive summary of Wiener-Hopf technique. This book is suitable for those who is familiar with the Laplace transform, its complex inversion formula, and integration in the complex plane.