Wave Propagation in Linear Media | re-examined

Exact solution
7 Mathematica implementation of a quadrature function
For the exact solution of (7.6) we must distinguish several cases: when f(x) is monotonically
decreasing (a + b0) or below (b<
>:
a((k+o) ,d), p b2 ((a2 ,b2 )c+((k+o) ,d) 2 )
a2 ,b2 p
a((k+o) ,d)+ b2 ((a2 ,b2 )c+((k+o) ,d) 2 )
a2 ,b2 p
a((,k+o) ,d)+ b2 ((a2 ,b2 )c+((,k+o) ,d) 2 )
a2 ,b2 a((,k+o) ,d), p b 2 ((a 2 ,b 2 )c+((,k+o) ,d) 2 )
a 2 ,b 2
((k+o) ,d) 2 ,a 2 c
2a((k+o) ,d)
if a + b>0; b>0
if a + b>0; b<
>:
b d,p (b 2 ,a 2 )c c if jbj > jaj; b0
b d+bp c c if jbj jaj; a+b