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

Mtg 23: Thurs, 15Octt09

Page 23-1

HW: Non-homogeneous L2_ODE_VC (cf. K. p28, problem 1.1.ab)

a) $(x-1)y^{″}-x{y}^{\prime }+y=x$

b) $x{y}^{″}+2y^{\prime }+xy=x$

using:
1) Variation of parameters (after knowing $u_1(x),u_2(x))$
2) Alternative method: P.21-2 and 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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File:EGM6321 F10 TEAM1 WILKS xc mtg23 1.svg
Wave eq: (PDE) solution by separation of variables
File:EGM6321 F10 TEAM1 WILKS xc mtg23 2.svg

References

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