0. PROJECT. Comments on Sec. 6.2. (a) Give reasonswhy Theorems 1 and 2 are more important thanTheorem 3. (b) Extend Theorem 1 by showing that if f(o is continuous, except for an ordinary discontinuity (finite jump) at some t = a(>0), the other conditions remaining gas in Theorem 1. then (see Fig i17) \left(1^{*}\right) \mathscr{L}\left(f^{\prime}\right)=s \mathscr{S}(f)-f(0)-[f(a+0)-f(a-0)] e^{-a s} \text { (c) Verify }\left(1^{*}\right) \text { for } f(t)=e^{-t} \text { if } 0<t<1 \text { and } 0 \text { if } (d) Compare the Laplace transform of solving ODES with the method in Chap. 2. Give examples of your own to illustrate the advantages of the present method(to the extent we have seen them so far).

Fig: 1

Fig: 2

Fig: 3

Fig: 4

Fig: 5

Fig: 6