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 time-value
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