ps2 - 18.03 Problem Set 2 Due by 12:45 P.M., Friday,...

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18.03 Problem Set 2 Due by 12:45 P.M., Friday, February 22, 2008, in the boxes at 2-106, next to the Under- graduate Mathematics Office. I encourage collaboration on homework in this course. However, if you do your homework in a group, be sure it works to your advantage rather than against you. Good grades for homework you have not thought through will translate to poor grades on exams. You must turn in your own writeups of all problems, and, if you do collaborate, you must write on the front of your solution sheet the names of the students you worked with. Because the solutions will be available immediately after the problem sets are due, no extensions will be possible . I. First-order differential equations L4 W 13 Feb Solution of linear equations; integrating factors: EP 1.5, SN § 3. R4 Th 14 Feb Ditto L5 F 15 Feb Complex numbers, roots of unity: SN 5–6; Notes C.1–3. L6 T 19 Feb Complex exponentials; sinusoidal functions: Notes C.4; SN 4; Notes IR.6. L7 W 20 Feb Linear system response to exponential and sinusoidal input; gain, phase lag: SN 4, Notes IR.6. R5 Th 21 Feb Complex numbers and exponentials. L8 F 22 Feb Autonomous equations; the phase line, stability: EP 1.7, 7.1. Part I. 4. (W 15 Feb) EP 1.5: 1, 2, 5. [Remember to check to see if the equation is separable first.] 5. (F 17 Feb) Notes 2E-1, 2, 7. 6. (T 21 Feb) Notes 2E-9, 10. Write each of the following functions f ( t ) in the form A cos( ωt - φ ). In each case, begin by drawing a right triangle with sides a and b . (a) cos(2 t ) + sin(2 t ). (b) cos( πt ) - 3 sin( πt ). (c) cos( t - π/ 8) + sin( t - π/ 8). 7. (W 22 Feb)
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ps2 - 18.03 Problem Set 2 Due by 12:45 P.M., Friday,...

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