1. INTRODUCTION 



Tha Wiener-Eopf technique was devised in 1931 [1] to deal with 

 an integral equation arisfjig in neutron transport theory, though its 

 origins— and indued its ees-sntiaio— coae from Russian work in the 

 1870's on singular integral equations [2,3]. During the var the tech- 

 nique was extensively applied by Schwinger aud his colleagues [4] to 

 problems in electromagnetic wave propagation, and much of the sub- 

 sequent development of the method has taken place in application* to 

 wave diffraction processes. Standard books on the method are those 

 by Noble [51, Ueinstein [6], while several books (e.g., Carrier, Krook 

 and Pearson [7], Horse and Feshbach [8]) have chapters which attempt to 

 introduce tha method. In such introductions, two-dimensional boundary 

 value problems involving a partial differential equation for some 

 field variable are invariably used as the simplest demonstration prob- 

 lems (the Sofflaerfeld problem of plane wave diffraction by a eemi- 

 infinite rigid screen being the best kr.wn). Such problems, however, 

 brlag in at once a number of issues which /ire irrelevant to the exposi- 

 tion of the tt-U method; the introduction of branch cuts in the complex 

 wavenuaber plane is one cuch issue which — while it is an important 

 one, and one which must be understood by anyone wishing to deal, with 

 wave diffraction problems— causes great difficulties for most students. 



Accordingly, an attempt will be made in these course notes to 

 illustrate the W-H method in a Much simpler context than usual. We 

 shall study one-di.jensional time-harmonic waves on strings and bare, and 

 in particular we will study the reflection and transmission properties 

 of changes in properties of the medium, abrupt changes of density giving 



