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MTHE 225 (6)
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quiz 5 (10).pdf

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School
Queen's University
Department
Mathematics & Engineering Courses
Course
MTHE 225
Professor
Gregory G Smith
Semester
Fall

Description
Quiz 5a Solutions 1 1. (5 marks) Find the inverse Laplace transform of F(s) = s + 2s + s We wish to ﬁnd A,B,C such that 1 A B C F(s) = 3 2 = + + 2 s + 2s + s s (s + 1) (s + 1) Multiplying both sides by s(s + 1) , this equation becomes 2 1 = A(s + 1) + Bs(s + 1) + Cs (1) Plugging in s = 0 gives A = 1. Plugging in s = −1 gives C = −1. To ﬁnd B, diﬀerentiate both sides of equation (1) and plug in s = −1 to ﬁnd B = −1. Thus 1 1 1 F(s) = s − s + 1− (s + 1) = L {1} − L {e } − L {te }−t so −t −t f(t) = 1 − e − te
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