Page 60 - Standard Handbook Of Petroleum & Natural Gas Engineering

Differential and Integral Calculus 49

Table 1-8
Laplace Transforms

Ae"'

sin Pt

S
cos pt s2 + p'
1
- sin pt
P

Ae-" - Be-w
C
A=a-a
where B = a - p
C=P-a
e-&
- - -
e-a
+
+
A B C
A = (p - a)(6 - a)
where B = (a - p)(6 - P)
c = (a - S)(P - 6)
n!
-
tn gt'
d/dt[f(t)] sF(s) - f(0')
df
d2/dt2[f(t)] s2F(s)-sf(0+)--(0+)
dt
df d2f
d3/dt3[f(t)] s3F(s) - s2f(0') - s-(O+) - -(O+)
dt dt2
+
~[F(s) jf(t)dt I of]
hdt S
1 1
-sinh at
a s2 - a2
S
cosh at
s2 - a2