transformaty1 (2)

328 Integra!. Equa tions and their Applications

Table B. 1: (Continued)

	F(s)	fU)
14.	s^2F(s) — .v/'(0) —/'(O)	f"i<)
15.	T'7(5)-.5"-'/(0) - j'^,-^2/'(0) »(0)	f^Mit)
16.	F'(s)	-tfi i)
17.	F"(s)	i-tffit)
18.	F<">(s)	i-tffit)
19.	m s	f mdz jo
20.	F(s) s^n	f ■- ffir)dr" Jo Jo f i‘ - r)’^,_I . "i,
21.	F(s)G(s)	fofi^T)Si' - ^T)^Jr =f*g
22.	fs^50 F(a)da	m i
23.	ir-irnw	m i"
24.	| rx+ioo z : / F\(<r)Fi(s - o)do 2.7H Jx—ioo	MO MO
25.	fo e~^srf(T)dT 1 — e~^h	f(t)=fil + k)
26.	F(a/5) s	751 ^A’»’
27.	ł'(i)	fo° Ą(^VrtY(x)dx
28.	MCi)	t"'^1 f™ T-^uUuyirydT
29.	F(s + l/s) s^2 + 1	fÓJoi2/x(l-T)YiT)dr
30.		fil^2)
31.	F(lns) slns	r '^7(r) dr Jo T(r+1)
32.	Pis) Q(s) *	ELi iPiak)/Q\ak))e^

* P(s) = polynomial of degrec less than n,

Q(s) = (s — a\)(s — ai)... (s — a_n),a\,a2,... ,a„ are all distinct.

33.

34.

35.

36.

37.

38.

39.

40.

41.

42.

43.

44.

45.

46.

47.

48.

Tablc B.2: Special Laplace transforms.

Fis)

fi')

1,«(0

,n-\

—, n= 1,2,3,...

s"

—,    n > 0

s"

s-a

1 + as

1

(s - a)ⁿ

1

01=1

r»

n— 1

, n= 1,2,3,..

e^al, 0!= 1

(s-a)"

s² I- a¹

s² + a²

(s - b)² + a²

s — b

(s - b)² + a²

s²—a²

s² — a²

— h\² — a²

i^s ~ ^b)

r(»)

-e^al

sin at

cos at

sinh at

cosh at

e^b> sinh at

49.

s — b

(s — b)² — a²

e^hl cosh at

50.

51.

52.

1

,ę(.v - a)

1

s(l + os)

1

(,v - a)(s - b)

V'-i)

a_

i -_e-^,/a

e°' - e^b‘

a —b

(Continued)