Methods Based on the Wiener-Hopf Technique for the Solution of Partial Differential Equations

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