_ TIME SERIES = »» r T o_ _ + r 



Use T (L,o,t) = of temperatures = T + 2 a n cos K m L+b n sin K m L cos g7 L + a n sin K, n L- b n 

 AT POINT (L,0) n =i L J T L n ln n 



cosKmLJsin-^^- 



Solving for Fourier coefficients for a specific value J? of n in a similiar manner to preceding: 

 ajcosKuL+bj{SinK, A L=-Y-/ T(L,o,t)cos-^y^- dt 

 ay sin K,j| L-bjj cos K| j L= y J* T T(L,o,t)sin ^JL dt 



Knowing ae and bj| solve these simultaneous equations for sin K|£and cos Kjj^ and thereby 



evaluate K\% 



_ v TIME SERIES m ^ T 1 2-jrnt T 



Use T(o,L,t) = of temperatures=T+2 a n cos K_ n L + b n sin K Pn L cos-M*^- + a n sinK ?n L- 

 AT POINT (o,U n=|L n zn n dn J T L n dn 



b n cosK 2n L]sin-^Y^ 



Again solving for Fourier coefficients for a specific value 9. of n: 



ajjCOsK 2J jL + bpinK 2 JiL= y /* T(o,L,t) cos -^^dt 

 ajsinK 2 j(-bj(COsK 2 jjL= yj T(o,L,t) sin^y^- dt 



Solve for sin K 2 nand cos K 2 « and thereby evaluate K.. 



Using K,^ + K^ = «f solve for Kjj 



Solve for 0$ = cos H ^$L 

 ■ -i K 2 * 



35 



