Unformatted text preview: Applied Mathematics E2101y Introduction to Applied Mathematics Problem Set #9, due Tuesday, 5 May 2009 All references are to Zill & Cullen (3rd edition). Chapter 3, § 3.5: Variation of Parameters 3 21 (Note that both of these problems are perhaps more easily approached by the techniques of § 3.4, and the techniques of § 3.5 are more powerful and general than we need. However, to keep the analytical manipulation reasonable, we can illustrate Variation of Parameters on these constant- coefficient ODEs.) Chapter 3, § 3.6: 3 27 (It is not necessary to graph the solution for full credit.) Chapter 3, § 3.8: Harmonic Oscillators 39 40 Supplementary Problem: Sturm-Liouville standard form The concept of “exactness,” which was discussed for first-order differential equations in § 5.6, can be extended to second-order. The equation P ( x ) y 00 + Q ( x ) y + R ( x ) y = 0 ( * ) is said to be exact if it can be written in the form [ P ( x ) y ] + [ f ( x ) y ] = 0 , ( ** ) where f ( x ) is to be determined from...
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This note was uploaded on 11/02/2009 for the course APMA 2102 taught by Professor Keyes during the Spring '08 term at Columbia.
- Spring '08