M251final(fa09)

# M251final(fa09) - Name: MATH 251 Student Number: Final...

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MATH 251 Final Dec 16, 2009 Name: Student Number: Instructor: Section: There are 12 multiple choice questions and 5 partial credit questions. In order to obtain full credit for the partial credit problems, all work must be shown. Credit will not be given for an answer not supported by work on a partial credit prob- lem. The use of calculators is not permitted in this examination. For multiple choice problems, write the letter of your choice in the space pro- vided below. Your Answer : Points awarded 1. (5 pts) 7. (5 pts) Q. 13 (15 pts) 2. (5 pts) 8. (5 pts) Q. 14 (15 pts) 3. (5 pts) 9. (5 pts) Q. 15 (20 pts) 4. (5 pts) 10. (5 pts) Q. 16 (20 pts) 5. (5 pts) 11. (5 pts) Q. 17 (20 pts) 6. (5 pts) 12. (5 pts)

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MATH 251 -Final- 1. (5 points) Which of the following has a unique solution on the whole interval (0 )? (a) y 0 + y =0 ,y (0) = 0 ( π )=0. (b) y 0 +4 y 0 (0) = 0 0 ( π )=0 . (c) ( t +1) y 0 + ty (1) = 1 0 (1) = 0. (d) ( t 1) y 0 +2 y (0) = 0 0 (0) = 1. 2. (5 points) Let y 1 ( t )=1and y 2 ( t ) = 0. Which of the following three statements is true? (a) y 1 ( t )and y 2 ( t ) are linearly independent. (b) L [ y 1 ( t )] = 1 /s ,for s> 0. (c) y 2 ( t ) is the unique solution of y 0 = y 1 / 3 , y (0) = 0. (d) All three statements are false. 3. (5 points) For which of the following equations is it true that ALL solutions approach zero as t →∞ ? (a) y 0 y 0 + y . (b) y 0 2 y 0 + y =0. (c) y 0 + y (d) y 0 y Page 2 of 10
MATH 251 -Final- 4. (5 points) Consider the 2 π -periodic function f ( x )= | x | , when π<x<π , and f ( x +2 π f ( x ) . Find the fourth sine coeﬃcient b 4 of the Fourier series. (a) 1 2 . (b) 1 4 . (c) 0. (d) 1 2 . 5. (5 points) Suppose v ( x )=5 x, and v ( x ) is the steady-state solution of a heat conduction problem for a rod of length 10 cm. Which one of the following statements describes the boundary conditions?

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## This note was uploaded on 07/16/2011 for the course MATH 251 taught by Professor Chezhongyuan during the Spring '08 term at Penn State.

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M251final(fa09) - Name: MATH 251 Student Number: Final...

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