A slightly different motivation for fourier integral operators and pseudo-differential operators is given in the first chapter of [book][1]. In first chapter of this book, V.Guillemin presents this subject from the conormal bundles point of view and then shows how pseudo-differential operators are a special case of operators coming out of the Fourier distributions. 

Section 3 of this chapter also provides a historic outline of this theory. 

Interesting, Guillemin also shows here that pseudo-differential operators can be used to fine tune the theory of conormal distributions themselves -- giving a natural but unexpected application of pseudo-differential operators. 




  [1]: http://books.google.co.in/books?id=Zi1UzHg64xsC&pg=PA1&lpg=PA1&dq=mathematics+past+and+present+fourier+integral+operators&source=bl&ots=uuKfr0Seuj&sig=Oz86sY8Ow8GdCQw7A5Dp_kslIII&hl=en&sa=X&ei=S4q6T6S7F4nMrQfQiNXYBw&ved=0CGMQ6AEwAg#v=onepage&q=mathematics%2520past%2520and%2520present%2520fourier%2520integral%2520operators&f=false