Solution 2.9.2.1
f(t)=e
;at
1(t);e
;a(t;T
1(t; T)
Then
F(s) = Lfe
;at
[1(t); 1(t;T)]g
= Lfe
;at
1(t)g;Lfe
;at
1(t; T)g
= Lfe
;at
1(t)g;Lfe
;aT
e
;a(t;T)
1(t; T)g
=
1
s + a
;
e
;aT
e
;Ts
s + a
=
1;e
;aT
e
;sT
s + a
Check:
F(s) =
Z
T
0
e
;at
e
;st
dt
=
;1
s + a
h
e
;(s+a)t
i
T
0
=
;1
s + a
h
e
;aT
e
;Ts
;1
i
=
1; e
;aT
e
;sT
s + a
1