Sample.TermTest2S08

Sample.TermTest2S08 - UNIVERSITY OF WATERLOO TERM TEST #2...

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Unformatted text preview: UNIVERSITY OF WATERLOO TERM TEST #2 SPRING TERM 2008 COURSE COURSE TITLE SECTION(S) HELD WITH COURSE(S) SECTION(S) OF HELD WITH COURSE(S) DATE OF EXAM TIME PERIOD DURATION OF EXAM NUMBER OF EXAM PAGES (including this cover sheet) INSTRUCTOR EXAM TYPE ADDITIONAL MATERIALS ALLOWED AM 250 INTRODUCTION TO DIF F EREN- TIAL EQUATIONS 001 N/A N/A July 14th, 2008 4:30 » 5:30 pm. 60 minutes 5 pages D. Harmsworth Closed book Scientific Calculator Name (print) ID Number Signature Instructions: 1. Print your name and ID Number on this page and sign it. 2. Answer the questions in the space pro— vided. Continue on the back of the page if necessary, Show all your work. 3. The last page may be removed and used for rough work. 4. Your grade will be influenced by how clearly you express your ideas and by how well you organize your solutions. MARKING SCHEME Question Value Mark I I5 2 19 3 11 Total 45 AM 250 — Term Test #2 Page 2 of 5 Spring Term 2008 1. Use the Characteristic equations and the method of undetermined coefficients to solve the following: [4] a) y” + 23/ + 10 = O [11] b) y” + 63/ + 93/ 2 2t; y(0) = O, y’(0) = 0. AM 250 - Term Test #2 Page 3 of 5 Spring Term 2008 [5] 2. a) Evaluate [5—1 6 b E 1 t 5-1 ~——5 H ) mu“ {32+65+13} [8] 0) Write the following function in terms of Heaviside functions and find its Laplace trans- form: t, for 0<t<1 f(t)= 1, for 1St<2 5—152, for 2:22 AM 250 - Term Test #2 Page 4 of 5 Spring Term 2008 '————————————————————————_———.——_——_—.____—____— [6] 3. (a) Use Laplace transforms to solve the IVP IE” + 436’ + 4x = 26‘”, 17(0) 2 0, :E’(0) : 2. [5] (b) Evaluate / te‘gt sin 3tdt. HINT: Compare this expression to the definition of the 0 Laplace transform. AM 250 — Term Test #2 Page 5 of 5 Spring Term 2008 (This page is for rough work) ...
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This note was uploaded on 03/20/2011 for the course AMATH 250 taught by Professor Ducharme during the Summer '09 term at Waterloo.

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Sample.TermTest2S08 - UNIVERSITY OF WATERLOO TERM TEST #2...

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