Math 322 Spring 2003 Exam I: Laplace Transforms and Circuit Analysis, Exams of Mathematics

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Math 322 – Spring 2003 – Exam I

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Partial Credit is possible, but you must show all work.

1. Find the Laplace transform for:

(a) t et

(b) t ∗ et

(c) t^2 u(t − 2)

1

2. Find the inverse Laplace transforms for:

(a)

s (s + 1) (s + 3)

(b)

s^2 (s + 5)

(c)

s e−^2 s

s + 2

4. Solve the integral equation y(t) = sin 2t − 2

∫ (^) t 0 y(t^ −^ τ^ ) cos(2τ^ )dτ^.

5. Show that L−^1 (arctan(as )) = sint^ at. Hint: (arctan u)′^ = u

′ 1+u^2.