Answers to Some of the Problems

Chapter 3

1.

g(t|τ)=ek(tτ)H(tτ)

2.

g(t|τ)=14[e3(tτ)e(tτ)]H(tτ)

3.

g(t|τ)=12[e(tτ)e3(tτ)]H(tτ)

4.

g(t|τ)=12sin[2(tτ)]etτH(tτ)

5.

g(t|τ)=[e2(tτ)etτ]H(tτ)

6.

g(t|τ)=(tτ)e2(tτ)H(tτ)

7.

g(t|τ)=16[e3(tτ)e3(tτ)]H(tτ)

8.

g(t|τ)=sin(tτ)H(tτ)

9.

g(t|τ)=[etτ1]H(tτ)

18.

g(x|ξ)=(Lx>)(α+x<)L+α

and

g(x|ξ)=2n=11+α2kn2sin[kn(Lξ)]sin[kn(Lx)][α+L(1+α2kn2)]kn2,

where kn is the nth root of tan(kL) = −αk.

19.

g(x|ξ)=(1+x<)(L1x>)/L

and

g(x|ξ)=2ex+ξe2L1+2L3π2n=1φn(ξ)φn(x)n2(n2π2+1),

where φn(x)=sin(nπx/L)+nπ cos(nπx/L)/L.

20.

g(x|ξ)=(1+x<)(L+1x>)2+L

and

g(x|ξ)=2n=1φn(ξ)φn(x)(2+L+kn2L)kn2,

where φn(x)=sin(knx)+kncos(knx) and kn is the nth root of tan(kL)=2k/(k21).

21.

g(x|ξ)=a3x>+x2+ξ

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