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# ps8 - 18.03 Problem Set 8 This is the complete version of...

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18.03 Problem Set 8 This is the complete version of PS8. Part II 29 (b) (iv) has been slightly changed (correcting a mistake) and renumbered 29 (c) . Due by 12:45 P.M., Friday, May 2, 2008, in the boxes at 2-106, next to the Undergraduate 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 . III. Fourier series, Dirac delta function, and Laplace transform L29 F 18 Apr Pole diagram; Weight and transfer function: SN 22, 23, EP 4.4. L30 W 23 Apr Review. R19 Th 24 Apr Exam preparation. L31 F 25 Apr Hour Exam III IV. First order systems L32 M 28 Apr Linear systems and matrices: EP 5.1–5.3, SN 25, Notes LS.1. R20 T 29 Apr Linear systems and matrices; Trajectories vs solutions. L33 W 30 Apr Eigenvalues, eigenvectors: EP 5.4, Notes LS.2. R21 Th 1 May Normal modes. L34 F 2 May Complex or repeated eigenvalues: EP 5.4, Notes LS.3. Part I. 29. (F 18 Apr) Nothing. 30. (W 23 Apr) Nothing. 31. (F 25 Apr) Nothing: Hour Exam. 32. (M 28 Apr) (a) Compute the matrix products ± 1 2 ² ³ x y ´ , ³ 1 2 ´ ± x y ² , ³ a b c d ´ ³ x y ´ , ± 1 2 ² ³ a b c d ´ , ³ a b c d ´ ³ x u y v ´ . (b) Notes 4A-2, 4B-1, 4B-6. 33. (W 28 Apr) Notes 4C-1. (See EP p. 344 for a description of how to ﬁnd the determinant of a 3 × 3 matrix.)

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Part II. 29. (F 18 Apr)
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ps8 - 18.03 Problem Set 8 This is the complete version of...

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