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+//Caption:initial_values

+// example 1.6.7

+//page 13

+//F(s)=(4*s+1)/(s^3+2*s)

+s=%s;

+syms t;

+F=(4*s+1)/(s^3+2*s)

+f = ilaplace (F,s,t);

+y=limit(f,t,0);//initial value theorem

+y=dbl(y);

+disp(y,"f(0+)=")

+// since F'(s)=sF(s)-f(0+) where L(f'(t))=F'(s)=F1

+F1=(4*s+1)/(s^2+2)

+f1= ilaplace(F1,s,t);

+y1=limit(f1,t,0);//initial value theorem

+y1=dbl(y1);

+disp(y1,"f_prime(0+)=")

+// since F''(s)=(s^2)*F(s)-s*f(0+)-f'(0+) where L(f''(t))=F''(s)=F2

+F2=(s-8)/(s^2+2)

+f2= ilaplace(F2,s,t);

+y2=limit(f2,t,0);//initial value theorem

+y2=dbl(y2);

+disp(y2,"f_doubleprime(0+)=")
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