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{SECT 0 {EXCHG {PARA 257 "" 0 "" {TEXT -1 26 "Heat Flow and Diffusion,
 I" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 216 "Th
e cell below works with a model that is similar to the models we used \+
in the previous module.  We include it here to facilitate comparisons \+
between the models in this module and the models in the previous modul
e.  " }{TEXT 256 16 "Evaluate it now." }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 365 "with(plottools):\nwith
(plots):\n\nAmbient := t -> sin(3.1416 * t / 12):\n\nEndTime := 72:\n
\nk := 0.50:\n\nIVP := \{diff(T(t), t) = k * (Ambient(t) - T(t)),\n   \+
     T(0) = 3\}:\n\nsolution := dsolve(IVP, \{T(t)\}, numeric):\n\nplt
 := display(\{odeplot(solution, [t, T(t)], 0..EndTime, color=red)\}):
\n\ngraf := plot(Ambient(t), t = 0..EndTime, -3..3, color=blue):\n\ndi
splay([plt, graf]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 80 "The next cell works with a model like the first
 model discussed in this module. " }{TEXT 257 115 " Evaluate it now an
d then compare it to the model above.  Then use this cell as a basis f
or further experimentation" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 642 "k := 0.50:\nc :=
 0.50:\n\nExterior := t -> sin(3.1416 * t / 12):\n\nIVP := \{diff(Inte
rior(t), t) = c * (Brick(t) - Interior(t)),\n        diff(Brick(t), t)
 = k * (Exterior(t) - Brick(t)) +\n                            k * (In
terior(t) - Brick(t)),\n        Interior(0) = 3,\n        Brick(0) = 2
\}:\n\nsolution := dsolve(IVP, \{Interior(t), Brick(t)\}, numeric):\n
\nplot1 := display(\{odeplot(solution, [t, Brick(t)], \n              \+
    0..EndTime, color=red)\}):\n\nplot2 := display(\{odeplot(solution,
 [t, Interior(t)], \n                  0..EndTime, color=blue)\}):\n\n
graf := plot(Exterior(t), t = 0..EndTime, -3..3, color=black):\n\ndisp
lay([plot1, plot2, graf]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
0 "" }}}}{MARK "0 2 1" 16 }{VIEWOPTS 1 1 0 1 1 1803 }