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A final exam for a Differential Equations course at Carnegie Mellon University. The exam consists of 10 questions, each with a varying number of points. The exam covers topics such as solving initial value problems, finding general solutions to differential equations, Fourier series representation, and heat conduction problems. No calculators are allowed and students are required to show all work and provide clear explanations.
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Mathematical Sciences Department Carnegie Mellon University Differential Equations21-
Fall 2007 Final Exam
No calculator of any kind is permitted. Show all work and give clear explanations. NAME: Question Points Score Pres Pt 1 18+ 2 18+ 3 19+ 4 21+ 5 17+ 6 22+ 7 18+ 8 19+ 9 19+ 10 19+ Total 200
{ (^0) for 0 ≤ t < π/ 2 − cos t for t ≥ π/ 2
f (t) =
{ (^1) for − 2 ≤ t < 1 0 for 1 ≤ t ≤ 2 Find a Fourier series representation for f.
u^ u(0xx, t^ ) ==^ u 1 t for 0for all^ < x < t > 0 3 , t >^0 u^ u((3x,, t 0))^ ==^4 x^ for all^ t >^0
