Chemical Engineering Department
University of Florida
ECH 4323
Process Control Theory
HOMEWORK No. 3b — LAPLACE TRANSFORMS
1.0
Exercise 3.1.
Note
: You may use standard integration tables to solve the integrals that you pose. Do
not use Table 3.1 of the textbook.
2.0
Exercise 3.4.
Hint 1
: Split the interval of integration [0,
!
] used in the definition of the Laplace
transform into a series of connected subintervals. For example, in part 3.4(a) utilize the
integration subintervals [0, 2], [2, 6], and [6,
!
], and then express the integral from 0 to
!
as the sum of three integrals (each one corresponding to one integration subinterval). Use
integration tables
to solve the resulting integrals.
Hint 2
: The approach of Hint 1 is preferred for this exercise; however, there is an
alternative way to obtain a solution in a very effective
fashion using step functions and
delayed step functions. A step function S(t) is defined by the equation
S(t)
=
0 t
<
0
1 t
!
0
"
#
$
and a delayed step function (where the function is delayed by a timevalue
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 Spring '10
 Crissale
 Calculus, Derivative, Laplace

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