Question

Find the Fourier serles of the function /() defined Dapatkan air Fourier untuk fungslf) yang didefinesikan oleh (1<t< (0<t<1) -en f(cosst) 1 Hence, find the value of the series when t Seterusnya, dapatkan nilai siri pada t 1. (12 marks/markah) eFind the solution to the following heat conduction problem: Dapatkan penyelesaian bagi masalah aliran haba berikut: 4u 0S$2,t>0 given the following boundary and initial conditions: diberi syarat awal dan sempadan u(0,t) = 0 u(2, t) = 0 sin() + 4sin(2nx) = f(x) ux,0)=2 sin( (12 marks/markah)

Answer 1

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u (0t)= Giutn Lio uL - (o,) put (1)e get Giucn 7L uetL{of put 2 25ch 7 t e hae ナe' he e 2Sn ul SinTT get Taking

ScTI. -at haue hie =7 uayt sonET>) e 25n( SanTn) Ypieltom