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Unformatted text preview: MATH 251 Examination II November 4, 2008 Name: Student Number: Section: This exam has 13 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 point value for each question is in parentheses to the right of the question number. You may not use a calculator on this exam. Please turn off and put away your cell phone. 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: Total: Do not write in this box. MATH 251 EXAMINATION II November 4, 2008 1. (5 points) Match the sketches of phase portraits for 2x2 homogeneous linear systems x ′ = A x with the names of their critical points at the origin. 1 2 3 4 5 6 (a) saddle (b) node (c) proper node (d) center (e) spiral Page 2 of 9 MATH 251 EXAMINATION II November 4, 2008 2. (5 points) Match the following formulas for general solutions of 2x2 homogeneous linear systems x ′ = A x with the sketches of the phase portraits given in Problem 1: (a) c 1 e 2 t parenleftbigg 1 1 parenrightbigg + c 2 e − t parenleftbigg 1 1 parenrightbigg (b) c 1 e t parenleftbigg cos t 2sin t parenrightbigg + c 2 e t parenleftbigg sin t 2cos t parenrightbigg (c) c 1 e − t parenleftbigg 1 parenrightbigg + c 2 e − t parenleftbigg 1 parenrightbigg (d) c 1 e t parenleftbigg 1 parenrightbigg + c 2 e − t parenleftbigg 1 parenrightbigg (e) c 1 parenleftbigg...
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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.
 Spring '08
 CHEZHONGYUAN
 Math, Differential Equations, Equations, Partial Differential Equations

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