4 21 Oy Wie Sin Sin Ny 6 13 12 Derive The Following Representation Of Dirac Delta Function 610 07 Yoy 13 Con 1 (43.2 KiB) Viewed 23 times
4 21 Oy Wie Sin Sin Ny 6 13 12 Derive The Following Representation Of Dirac Delta Function 610 07 Yoy 13 Con 2 (43.2 KiB) Viewed 23 times
4 21 Oy WIE sin sin ny 6 (13) 12. Derive the following representation of Dirac delta function, 610-07-) - Yoy*/) 13. Consider the expansion δ(Ω - Y) ΣΑ (7) show that p(CON) Y..)Y?"") (10) 14. In a two-dimensional rectangular space the Green's function for Poisson's equation is defined by the differ- ential equation D'G{P.) G(xx'..) 83-)) Assuming Dirichlet boundary conditions such that G = 0 at r = 0, and G=0 at y = 0, show that the following expansions of the Green's function Gi(x,d"X)-(. in (12) Gald'..). lead to the following equivalent expressions for Gla...) G (X.) 2 xin e sin sinhas sinh (14) G...) 2_kin ಇ{ sin - inh Hinh Mಯದು! (15) Hinh | 15. In polar coordinates the Green's function for Poisson's equation is defined by the differential equation p*GC.7) = 1 (16) Using the following expansions GAAM) sulad, F-)(e-)) (17) For Dirichlet boundary condition at a such that 0 SPS (a) find the Green's function in the region S a Interior problem). (b) find the Green's function in the region 2 (Exterior Problem). (c) find the free space Green's function using (a) or (b). (d) find the Green's function in the region 5 (Interior problem) by using the following expansion G...) c. (0 - ) (-2) dp- // C.com - TITE Ninh اتر - )6 + 2.0.) ) P 21 P Note: Treat the cases and separately
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