2302-practice-mid3

2302-practice-mid3 - MAP 2302 Fall 2010 — Midterm 3...

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Unformatted text preview: MAP 2302, Fall 2010 — Midterm 3 Review Problems 1 The exam will cover sections 7.2, 7.3, 7.4, 7.5, 7.6, and 7.8. All topics from this review sheet or from the suggested exercises are fair game. 1 Solve for L {y } given the following initial value problems. a. y − 4y + 8y = e2t cos 3t; y (0) = 1; y (0) = 3. b. y + 2y − 3y = et + t + 1; y (0) = 9; y (0) = −3. c. y − 4y = sin t 0 < t < π, ; y (0) = y (0) = 0. − sin t t > π. d. y + y − 2y = f (t), where f (t) is the half-rectified sine wave below; y (0) = y (0) = 1. 1 π 2π 3π 4π 5π 6π −1 e. y + y − 2y = f (t), where f (t) is the sawtooth function below; y (0) = y (0) = 0. 1 1 2 3 4 5 6 −1 f. y − 4y + ty = 0; y (0) = 1; y (0) = 0. (Find a differential equation satisfied by L {y }.) g. y + 4y = δ(t − 2), where δ is the Dirac delta function; y (0) = y (0) = 0. 2 Compute the following inverse Laplace transforms. a. L −1 b. L −1 c. L −1 d. L −1 2s2 − 1 . s3 + s2 − 6s 1 . 2 − 8s + 17 s 9 − s2 . (s2 + 9)2 3s . 2 + 4s + 6 s e. L −1 f. L −1 (1 − e−s )2 . s3 e−πs . s2 + 2s + 5 g. L −1 {7}. h. L −1 s2 + 2s . s2 + 4 ...
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This note was uploaded on 12/10/2011 for the course MAP 2302 taught by Professor Tuncer during the Fall '08 term at University of Florida.

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