University of Florida/Egm6321/F10.TEAM1.WILKS/Mtg23

Mtg 23: Thurs, 15Octt09

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HW: Non-homogeneous L2_ODE_VC [[media: http://books.google.com/books?id=9Cg3HWCnCjAC&printsec=frontcover&dq=differential+equations+billingham&ei=pGR4SpPVLojSMpb07Qw#v=onepage&q=&f=false | (cf. K. p28, problem 1.1.ab) ]] a) $$ (x-1)y-xy'+y=x \ $$ b) $$ xy+2y'+xy=x \ $$ using: 1) Variation of parameters (after knowing $$ u_1(x), u_2(x)) \ $$ 2) Alternative method: [[media: Egm6321.f09.mtg21.djvu |  P.21-2 ]] and [[media: Egm6321.f09.mtg21.djvu  |  P.21-3 ]] Engineering application: Motivate L2_ODE_VC Ware equation: Drums=vibrating membrane Rectangular membrane Circular membrane (Bessel functions) Bessel differential equation Chladni: Experimental method for vibrating modes of plates

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Wave eq: (PDE) solution by separation of variables