MATHS 2106 Lecture Notes - Lecture 10: Even And Odd Functions, Sine And Cosine Transforms, Fourier Transform
17 Jun 2021
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I 0 : tra n f s o r m m e. 1 a c e t r a n s h o d s f o r pdes o r m s f o r. P d e s t f we apply laplace transform int to feast ) , considering nasa parameter. Laplace transform of derivative with respect to timeto. Bcs : v10 : = f- (t) . line (verst)) = o. N co taking lt wrt t :l (ugt) ) = v6,s)=[ e-stvcqtldtdlvttcx. tl. Vasek,s) taking ltwrtt of the pde :l (vet) = edlund (cid:15482) 5 vk. si-ivantn. si (cid:15482) vase - ({ the ,s)=0 can be treated as an ode. = - gs = volos)=a(s)e% + bcs> e- % with bc : lying vcr,s)=l(lim(vk. tl)=l(01=0 1. (ogs) =l (210,1-1)=2 ( f- (t) ) = fcs) 2 v10 : = fcs) = bcs) = - vtr,s ) = ftse solution is s - space .
