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Unformatted text preview: Mathematics 265 Section: 103 Version B Full Name: Midterm Test Nov 10, 2010 Student Number: Instructions: There are 6 pages in this test (including this cover page). 1. Caution: There may (or may not) be more than one version of this test paper. 2. Ensure that your full name and student number appears on this page. Circle your section number. 3. No calculators, books, notes, or electronic devices of any kind are permitted. 4. Show all your work. Answers not supported by calculations or reasoning will not receive credit. Messy work will not be graded. 5. Five minutes before the end of the test period you will be given a verbal notice. After that time, you must remain seated until all test papers have been collected. 6. When the test period is over, you will be instructed to put away writing implements. Put away all pens and pencils at this point. Continuing to write past this instruction will be considered dishonest behaviour. 7. Please remain seated and pass your test paper down the row to the nearest indicated aisle. Once all the test papers have been collected, you are free to leave. 8. Exposing your test paper, copying from another students paper, or sharing information about this test constitutes academic dishonesty. Such behaviour may jeopardize your grade on this test, in this course, and your standing at this university. 9. There is a table of Laplace Transforms on p 6 of this test paper. Question number Grade Value 1 18 2 10 3 16 4 16 Total 60 I have read and understood the instructions and agree to abide by them. Signed: 1 Problem 1: Multiple Choice Questions: Circle ONE correct answer (a, b, c, d, or e). There is no partial credit in this question. Illegible or multiple answers will get no credit. NOTE: In these questions, the notation for step functions includes u c ( t ) = H ( t- c ). 1 : The Laplace transform of the function f ( t ) = 1 t- 2 is (a) 1, (b) e 2 s , (c) u 2 ( s ) e 2 s , (d) e 2 s , (e) None of these. Solution: The function f ( t ) is not of exponential order, since it has a singularity at t = 2. Therefore the answer is None of these. 2 Which of the below corresponds to the inverse Laplace transform of F ( s ) = 1 s 3 e s (a) H ( t- 1) e t 1 , (b) H ( t- 1) e 3( t 1) , (c) H ( t- 3) e t 3 , (d) H ( t- 3) e t , (e) H ( t- 3) e t Solution: H ( t- 1) e 3( t 1) 3 For the differential equation y + 2 y + y = ( t ) with initial conditions y (0) = 0 ,y (0) = 0, we find that F ( s ) =...
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