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set_5_problem - Problem Set 5 MMAE 501 Engineering Analysis...

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Problem Set # 5 MMAE: 501 Engineering Analysis I Kevin W. Cassel Mechanical, Materials and Aerospace Engineering Department Illinois Institute of Technology 10 West 32nd Street Chicago, IL 60616 [email protected] Problem Reference Problem # 1: Jeffrey, Section 8.10, Problem 3 Problem # 2: Jeffrey, Section 8.10, Problem 7 Problem # 3: Jeffrey, Section 8.10, Problem 13 Problem # 4: Jeffrey, Section 8.10, Problem 15 Problem # 5: Jeffrey, Section 8.10, Problem 17 Problem # 6: Jeffrey, Section 8.10, Problem 23 Problem # 7: Jeffrey, Section 8.11, Problem 11 Problem # 8: Jeffrey, Section 18.10, Problem 12 c 2007 Kevin W. Cassel 1
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Problem # 1 Reduce the differential eigenproblem (1 - x 2 ) y 00 - xy 0 + λy = 0 to Sturm–Liouville form by the method described in note (1) at the end of sec- tion 3.4.2 in the lecture notes. Problem # 2 Find the eigenvalues and eigenfunctions of the differential eigenproblem y 00 + λy = 0 , y 0 (0) = 0 , y (1) = 0 . Problem # 3 Find the eigenvalues and eigenfunctions of the differential eigenproblem ( λ = k 2 ) x 2 y 00 + xy 0 + k 2 y = 0 , y (1) = 0 , y (4) = 0 .
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