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Unformatted text preview: MATH 251 Midterm Exam II March 29, 2007 Name: Student Number: Instructor: Section: This exam has 9 questions for a total of 100 points. In order to obtain full credit for partial credit problems, all work must be shown. Credit will not be given for an answer not supported by work. THE USE OF CALCULATORS IS NOT PERMITTED IN THIS EXAMINATION. At the end of the examination, the booklet will be collected. 1: 2: 3: 4: 5: 6: 7: 8: 9: Total: Do not write in this box. MATH 251 Spring 2007 Exam II 1. (10 points) Use the Laplace transform to solve the equation y ′ +2 y = 2 e 4 t , with initial condition y (0) = 1. You must use the Laplace transform to receive any credit. Page 2 of 10 MATH 251 Spring 2007 Exam II 2. (10 points) Solve the initial value problem y ′′ + 4 y = δ ( t 1) , y (0) = 1 , y ′ (0) = 0 . Page 3 of 10 MATH 251 Spring 2007 Exam II 3. (12 points) Express the following piecewise continuous function in terms of step functions and then find its Laplace transform: f ( t ) = 2 t ≤ t < 2 t 2 t 2 ≤ t < 2 t ≥ 3 ....
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 Spring '08
 CHEZHONGYUAN
 Math, Differential Equations, Equations, Partial Differential Equations, Laplace, Continuous function, Boundary value problem, Lipschitz continuity

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