midterm sample 2

midterm sample 2 - HKUST MATH 152 Applied Linear Algebra...

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Unformatted text preview: HKUST MATH 152 Applied Linear Algebra and Differential Equations Mid-Term Examination Name: 19th March 2005 Student I.D.: 13:00–15:30 Tutorial Section: Directions: • Do NOT open the exam until instructed to do so. • All mobile phones and pagers should be switched off during the examination. • Please write your name, ID number, and Section in the space provided above. • Answer ALL questions. You are advised to try the problems you feel more comfortable with first. • This is a closed book examination. • No graphical calculators are allowed. • You may write on both sides of the examination papers. • Once you are allowed to open the exam, please check that you have 10 pages in addition to this cover page. • For answering Part II, you must show all your working steps in order to receive full marks. • Cheating is a serious offense. Students who commit this offense may receive zero mark in the examination. However, more serious penalty may be imposed. Question No. Marks Out of Q. 1-16 32 Q. 17 8 Q. 18 4 Q. 19 8 Q. 20 8 Q. 21 8 Q. 22 8 Q. 23 8 Q. 24 8 Q. 25 8 Total Marks 100 1 Part I: Answer each of the following 16 multiple choice questions. Each correct answer is worth 2 marks. Question 1 2 3 4 5 6 7 8 9 10 Answer Question 11 12 13 14 15 16 Total Answer 1. The function y = e- t is a solution of the differential equation (a) 2 y 000- 2 y 00- 9 y + 9 y = 0 (b) y 00 + y = 2 e- t (c) 4 t 2 y 00 + 8 ty + y = 0 (d) ty 00 + ( t + 1) y + y = 0 (e) y 00 + y = 0 2. Find a fundamental set of solutions for 2 y 00 + 5 y- 3 y = 0 . (a) e 1 2 t , e 3 t (b) e- 3 t , e 2 t (c) e- 3 t , e- 1 2 t (d) e 1 2 t , 1 (e) e 1 2 t- e- 3 t , e 1 2 t + e- 3 t 3. Find the integrating factor that can be used to solve the following first-order equation dr dθ + r tan θ = cos 2 θ, < θ < π 2 . (a) sin θ (b) cos θ (c) tan θ (d) sec θ (e) csc θ 4. The following equation is not exact but becomes exact when multiplied by the integrating factor. ( 3 xy + y 2 ) dx + ( x 2 + xy ) dy = 0 ....
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This note was uploaded on 09/30/2010 for the course MATH MATH152 taught by Professor Kcc during the Spring '10 term at HKUST.

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midterm sample 2 - HKUST MATH 152 Applied Linear Algebra...

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