527ass10 - it may be worth your time to look at both and...

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642:527 ASSIGNMENT 10 FALL 2009 No problems from this assignment will be collected. These exercises are just for you to look at simple Sturm-Liouville problems. Some solutions will be posted. Section 17.7: 1 (a), (b), (c), (d), (e), (f); 2 Comments, hints, instructions: Exercise 17.7.1: In (a,b,c) you should recognize by inspection that the problem will lead to one of the series studied in Section 17.4. There is no need to do any more. In (d) and (e) you will not be able to ±nd the eigenvalues explicitly; give a graphical interpretation as was done in class or in Figure 3. The two problems are similar but
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Unformatted text preview: it may be worth your time to look at both, and see why 0 is an eigenvalue in (e) but not in (d). • Part (f) is again like one of the series from 17.4, but here because the interval is [-1 , 1] the form of the solutions will look di²erent. I suggest that you work (f) out from the beginning, showing exactly what the eigenvalues and corresponding eigenfunctions are. Exercise 17.7.2 is just a quick review; in fact, it is already covered by 17.7.1(a,b,c)....
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