Unformatted text preview: , etc. Then T (9) = 0 , (2.12) and the continuity of the temperature implies that lim t → 10+ j = T j +1 (10 + j ) , j = 0 , 1 , 2 , . . . . (2.13) According to the work of the heating unit, the temperature satisFes the equation dT j dt = · 1 − T j , if j = 2 k − T j , if j = 2 k + 1 , 9 + j < t < 10 + j k = 0 , 1 , . . . . The general solutions of these equations are: for j even dT j dt = 1 − T j ⇒ dT j 1 − T j = dt ⇒ ln  1 − T j  = − t + c j ⇒ T j ( t ) = 1 − C j e − t ; 57...
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 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations, Integrals, Cos

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