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<Text-field style="Text" layout="Normal">Example 8.9 Heat Conduction with the Time Dependent Boundary Conditions</Text-field>
<Text-field style="Text" layout="Normal">Equation (8.1.19) is solved by slightly modifying the Maple program used for example 8.7 as:</Text-field>
</Input>
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<Group labelreference="L43" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
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<Group labelreference="L3" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal256">eq:=diff(u(x,t),t)=diff(u(x,t),x$2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ1RzYiNiRJInhHRilJInRHRilGLC1GJDYkLUYkNiRGJ0YrRis=</Equation></Text-field>
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<Group labelreference="L4" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal256">u(x,0):=0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">IiIh</Equation></Text-field>
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<Group labelreference="L5" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc1:=diff(u(x,t),x)=0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEkYmMxRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEjOj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GIzYnLUYjNictSSZtZnJhY0dGJDYoLUYjNiUtRjY2LVErJlBhcnRpYWxEO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTkZmbi8lK2ZvcmVncm91bmRHUShbMCwwLDBdRidGOS1GIzYlLUYjNiZGWC1GLDYlUSJ4RidGL0YyRmhuRjlGaG5GOS8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGZ28vJSliZXZlbGxlZEdGPS1GNjYtUTEmSW52aXNpYmxlVGltZXM7RidGOUY7Rj5GQEZCRkRGRkZIRmVuRmduLUYjNictRiw2JVEidUYnRi9GMi1GNjYtUTAmQXBwbHlGdW5jdGlvbjtGJ0Y5RjtGPkZARkJGREZGRkhGZW5GZ24tSShtZmVuY2VkR0YkNiQtRiM2J0Zfby1GNjYtUSIsRidGOUY7L0Y/RjFGQEZCRkRGRkZIRmVuL0ZOUSwwLjMzMzMzMzNlbUYnLUYsNiVRInRGJ0YvRjJGaG5GOUY5RmhuRjlGaG5GOS1GNjYtUSI9RidGOUY7Rj5GQEZCRkRGRkZIRkpGTS1JI21uR0YkNiRRIjBGJ0Y5RmhuRjlGaG5GOQ==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ1RzYiNiRJInhHRilJInRHRilGKyIiIQ==</Equation></Text-field>
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<Group labelreference="L6" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc2:=u(x,t)=exp(-t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JInVHNiI2JEkieEdGJUkidEdGJS1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjLCRGKCEiIg==</Equation></Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal256">eqs:=laplace(eq,t,s):</Text-field>
</Input>
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<Group labelreference="L8" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal256">eqs:=subs(laplace(u(x,t),t,s)=U(x),eqs);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LyomSSJzRzYiIiIiLUkiVUdGJTYjSSJ4R0YlRiYtSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUYsNiRGJ0YqRio=</Equation></Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal256">bc1:=laplace(bc1,t,s):</Text-field>
</Input>
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<Group labelreference="L10" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc1:=subs(laplace(u(x,t),t,s)=U(x),bc1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJVRzYiNiNJInhHRilGKyIiIQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L11" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal256">bc2:=laplace(bc2,t,s):</Text-field>
</Input>
</Group>
<Group labelreference="L12" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc2:=subs(laplace(u(x,t),t,s)=U(x),bc2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JIlVHNiI2I0kieEdGJSokLCYiIiJGKkkic0dGJUYqISIi</Equation></Text-field>
</Output>
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<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dsolve(eqs,U(x));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JIlVHNiI2I0kieEdGJSwmKiZJJF9DMUdGJSIiIi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjKiYpSSJzR0YlI0YrIiIjRitGJ0YrRitGKyomSSRfQzJHRiVGKy1GLTYjLCRGMiEiIkYrRis=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L14" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U(x):=c[1]*cosh(s^(1/2)*x)+c[2]*sinh(s^(1/2)*x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCYqJiZJImNHNiI2IyIiIkYoLUklY29zaEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJjYjKiYpSSJzR0YmI0YoIiIjRihJInhHRiZGKEYoRigqJiZGJTYjRjNGKC1JJXNpbmhHRitGLkYoRig=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L15" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq0:=eval(subs(x=0,bc1)):</Text-field>
</Input>
</Group>
<Group labelreference="L16" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq1:=eval(subs(x=1,bc2)):</Text-field>
</Input>
</Group>
<Group labelreference="L17" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">con:=solve({eq0,eq1},{c[1],c[2]}):</Text-field>
</Input>
</Group>
<Group labelreference="L18" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U(x):=subs(con,U(x));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KigtSSVjb3NoRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMqJClJInNHRigjIiIiIiIjRi4hIiIsJkYuRi5GLEYuRjAtRiQ2IyomRitGLkkieEdGKEYuRi4=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L19" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">P(s):=numer(U(x));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUYjNictSSNtaUdGJDYlUSJQRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjVRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y/LyUpc3RyZXRjaHlHRj8vJSpzeW1tZXRyaWNHRj8vJShsYXJnZW9wR0Y/LyUubW92YWJsZWxpbWl0c0dGPy8lJ2FjY2VudEdGPy8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRk4tSShtZmVuY2VkR0YkNiQtRiM2JS1GLjYlUSJzRidGMUY0LyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJ0Y7RjtGWUY7LUY4Ni1RIzo9RidGO0Y9RkBGQkZERkZGSEZKL0ZNUSwwLjI3Nzc3NzhlbUYnL0ZQRmpuLUYjNictRi42JVElY29zaEYnL0YyRj9GO0Y3LUZSNiQtRiM2JS1GIzYmLUkmbXNxcnRHRiQ2I0ZWLUY4Ni1RMSZJbnZpc2libGVUaW1lcztGJ0Y7Rj1GQEZCRkRGRkZIRkpGTEZPLUYuNiVRInhGJ0YxRjRGO0ZZRjtGO0ZZRjtGWUY7">LUklY29zaEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjKiYpSSJzR0YnIyIiIiIiI0YtSSJ4R0YnRi0=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L20" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Q(s):=denom(U(x));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KiYtSSVjb3NoRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMqJClJInNHRigjIiIiIiIjRi5GLiwmRi5GLkYsRi5GLg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L21" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A(s):=P(s)/diff(Q(s),s);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KiYtSSVjb3NoRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMqJilJInNHRigjIiIiIiIjRi5JInhHRihGLkYuLCYqKkYtRi4tSSVzaW5oR0YlNiMqJEYrRi5GLkYrISIiLCZGLkYuRixGLkYuRi4tRiRGNUYuRjc=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L22" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">solve(Q(s),s);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NiQsJComIyIiIiIiJUYmKUkjUGlHJSpwcm90ZWN0ZWRHIiIjRiYhIiJGLA==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L23" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">_EnvAllSolutions := true:</Text-field>
</Input>
</Group>
<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">solve(Q(s),s):</Text-field>
</Input>
</Group>
<Group labelreference="L45" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The roots are:</Text-field>
</Input>
</Group>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">-1,-((2*n-1)*Pi/2)^2;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NiQhIiIsJCooIyIiIiIiJUYnKSwmKiYiIiNGJ0kibkc2IkYnRidGJ0YjRixGJylJI1BpRyUqcHJvdGVjdGVkR0YsRidGIw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A[n]:=simplify(subs(s=mu,A(s)));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqKiIiIyIiIi1JJWNvc2hHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IyomKUkjbXVHRisjRiVGJEYlSSJ4R0YrRiVGJUYuRiUsKC1JJXNpbmhHRig2IyokRi5GJUYlKiZGM0YlRi9GJUYlKihGJEYlLUYnRjVGJUYuRiVGJSEiIkYl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L27" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A[0]:=subs(mu^(1/2)=I,mu=-1,A[n]):</Text-field>
</Input>
</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A[0]:=simplify(A[0]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KiYtSSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kieEdGKCIiIi1GJDYjRishIiI=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L29" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A[n]:=simplify(subs(mu^(1/2)=I*(2*n-1)/2*Pi,mu=-((2*n-1)*Pi/2)^2,A[n])):</Text-field>
</Input>
</Group>
<Group labelreference="L30" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">vars:={cos(1/2*(2*n-1)*Pi)=0,sin(1/2*(2*n-1)*Pi)=(-1)^(n-1)}:</Text-field>
</Input>
</Group>
<Group labelreference="L31" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A[n]:=simplify(subs(vars,A[n]));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRIm5GJ0YyRjUvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnL0Y2USdub3JtYWxGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEjOj1GJ0ZALyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZLLyUpc3RyZXRjaHlHRksvJSpzeW1tZXRyaWNHRksvJShsYXJnZW9wR0ZLLyUubW92YWJsZWxpbWl0c0dGSy8lJ2FjY2VudEdGSy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlotSSZtZnJhY0dGJDYoLUYjNi0tSSNtbkdGJDYkUSI0RidGQC1GRjYtUTEmSW52aXNpYmxlVGltZXM7RidGQEZJRkxGTkZQRlJGVEZWL0ZZUSYwLjBlbUYnL0ZmbkZkby1JJW1zdXBHRiQ2JS1JKG1mZW5jZWRHRiQ2JC1GIzYlLUZGNi1RKiZ1bWludXMwO0YnRkBGSUZMRk5GUEZSRlRGVi9GWVEsMC4yMjIyMjIyZW1GJy9GZm5GYnAtRl1vNiRRIjFGJ0ZARkBGQC1GIzYmRl5wRjpGPUZALyUxc3VwZXJzY3JpcHRzaGlmdEdGREZgby1Gam82JC1GIzYmLUYjNiYtRl1vNiRRIjJGJ0ZARmBvRjpGQC1GRjYtUSgmbWludXM7RidGQEZJRkxGTkZQRlJGVEZWRmFwRmNwRmRwRkBGQEZgby1GLzYlUScmIzk2MDtGJy9GM0ZLRkBGYG8tRiM2Jy1GLzYlUSRjb3NGJ0ZqcUZALUZGNi1RMCZBcHBseUZ1bmN0aW9uO0YnRkBGSUZMRk5GUEZSRlRGVkZjb0Zlby1Gam82JC1GIzYlLUYjNictRmhuNihGZHBGYXEvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmBzLyUpYmV2ZWxsZWRHRktGYG8tRiM2KEZbcUZgb0ZncUZgby1GLzYlUSJ4RidGMkY1RkBGPUZARj1GQEZARj1GQEY9RkAtRiM2JS1GIzYrRl5wRlxvLUZGNi1RIitGJ0ZARklGTEZORlBGUkZURlZGYXBGY3AtRiM2KEZcb0Zgby1GZ282JUZncUZhcUZpcEZgby1GZ282JUY6RmFxRmlwRkBGZHEtRiM2KEZcb0Zgb0ZjdEZgb0Y6RkBGXnQtRiM2JEZjdEZARkBGPUZARltzRl5zRmFzRmNzRj1GQA==">LCQqLiIiJSIiIikhIiIsJEkibkc2IkYnRiUsJiomIiIjRiVGKUYlRiVGJUYnRiVJI1BpRyUqcHJvdGVjdGVkR0YlLUkkY29zRzYkRi9JKF9zeXNsaWJHRio2IywkKiojRiVGLUYlRitGJUYuRiVJInhHRipGJUYlRiUsKkYkRicqKEYkRiUpRi5GLUYlKUYpRi1GJUYlKihGJEYlRjtGJUYpRiVGJyokRjtGJUYlRidGJQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u0s:=A[0]*subs(mu=-1,1/(s-mu));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KigtSSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kieEdGKCIiIi1GJDYjRishIiIsJkYrRitJInNHRihGK0Yu</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L33" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u0t:=invlaplace(u0s,s,t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KigtSSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kieEdGKCIiIi1GJDYjRishIiItSSRleHBHRiU2IywkSSJ0R0YoRi5GKw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L34" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">uns:=A[n]/(s-mu);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEkdW5zRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEjOj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JJm1mcmFjR0YkNigtRiM2LS1JI21uR0YkNiRRIjRGJ0Y5LUY2Ni1RMSZJbnZpc2libGVUaW1lcztGJ0Y5RjtGPkZARkJGREZGRkgvRktRJjAuMGVtRicvRk5GZm4tSSVtc3VwR0YkNiUtSShtZmVuY2VkR0YkNiQtRiM2JS1GNjYtUSomdW1pbnVzMDtGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GZG8tRlU2JFEiMUYnRjlGOUY5LUYjNiZGYG8tRiw2JVEibkYnRi9GMi8lK2ZvcmVncm91bmRHUShbMCwwLDBdRidGOS8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGWC1GXG82JC1GIzYmLUYjNiYtRlU2JFEiMkYnRjlGWEZbcEY5LUY2Ni1RKCZtaW51cztGJ0Y5RjtGPkZARkJGREZGRkhGY29GZW9GZm9GOUY5RlgtRiw2JVEnJiM5NjA7RicvRjBGPUY5RlgtRiM2Jy1GLDYlUSRjb3NGJ0ZjcUY5LUY2Ni1RMCZBcHBseUZ1bmN0aW9uO0YnRjlGO0Y+RkBGQkZERkZGSEZlbkZnbi1GXG82JC1GIzYlLUYjNictRlA2KEZmb0ZqcC8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGaXIvJSliZXZlbGxlZEdGPUZYLUYjNihGZHBGWEZgcUZYLUYsNiVRInhGJ0YvRjJGOUZecEY5Rl5wRjlGOUZecEY5Rl5wRjktRiM2Jy1GXG82JC1GIzYrRmBvRlQtRjY2LVEiK0YnRjlGO0Y+RkBGQkZERkZGSEZjb0Zlby1GIzYoRlRGWC1GaW42JUZgcUZqcEZhcEZYLUZpbjYlRltwRmpwRmFwRjlGXXEtRiM2KEZURlhGXnRGWEZbcEY5RmlzLUYjNiRGXnRGOUY5RjlGWC1GXG82JC1GIzYmLUYsNiVRInNGJ0YvRjJGXXEtRiw2JVEnJiM5NTY7RidGY3FGOUY5RjlGXnBGOUZkckZnckZqckZcc0ZecEY5">LCQqMCIiJSIiIikhIiIsJEkibkc2IkYnRiUsJiomIiIjRiVGKUYlRiVGJUYnRiVJI1BpRyUqcHJvdGVjdGVkR0YlLUkkY29zRzYkRi9JKF9zeXNsaWJHRio2IywkKiojRiVGLUYlRitGJUYuRiVJInhHRipGJUYlRiUsKkYkRicqKEYkRiUpRi5GLUYlKUYpRi1GJUYlKihGJEYlRjtGJUYpRiVGJyokRjtGJUYlRicsJkkic0dGKkYlSSNtdUdGKkYnRidGJQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L35" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">unt:=invlaplace(uns,s,t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqMCIiJSIiIi1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCQqKiNGJSIiI0YlLCYqJkYwRiVJIm5HRitGJUYlRiUhIiJGJUkjUGlHRilGJUkieEdGK0YlRiVGJS1JJGV4cEdGKDYjKiZJI211R0YrRiVJInRHRitGJUYlRjVGJSlGNCwkRjNGNEYlLCYqJCksJiooRjBGJUY1RiVGM0YlRiVGNUY0RjBGJUYlRiRGNEY0RjFGJUYl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L36" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">unt:=subs(mu=-((2*n-1)/2*Pi)^2,unt);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqMCIiJSIiIi1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCQqKiNGJSIiI0YlLCYqJkYwRiVJIm5HRitGJUYlRiUhIiJGJUkjUGlHRilGJUkieEdGK0YlRiVGJS1JJGV4cEdGKDYjLCQqKiNGJUYkRiUpRjFGMEYlKUY1RjBGJUkidEdGK0YlRjRGJUY1RiUpRjQsJEYzRjRGJSwmKiQpLCYqKEYwRiVGNUYlRjNGJUYlRjVGNEYwRiVGJUYkRjRGNEYxRiVGJQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L37" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U:=u0t+Sum(unt,n=1..infinity);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCYqKC1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSJ4R0YpIiIiLUYlNiNGLCEiIi1JJGV4cEdGJjYjLCRJInRHRilGL0YsRiwtSSRTdW1HRiY2JCwkKjAiIiVGLC1GJTYjLCQqKiNGLCIiI0YsLCYqJkZARixJIm5HRilGLEYsRixGL0YsSSNQaUdGJ0YsRitGLEYsRiwtRjE2IywkKiojRixGOkYsKUZBRkBGLClGREZARixGNEYsRi9GLEZERiwpRi8sJEZDRi9GLCwmKiQpLCYqKEZARixGREYsRkNGLEYsRkRGL0ZARixGLEY6Ri9GL0ZBRixGLC9GQztGLEkpaW5maW5pdHlHRidGLA==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L38" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u:=piecewise(t=0,0,t&gt;0,subs(infinity=20,U)):</Text-field>
</Input>
</Group>
<Group labelreference="L46" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The following plots are obtained:</Text-field>
</Input>
</Group>
<Group labelreference="L39" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot3d(u,x=0..1,t=0..1,axes=boxed,title=&quot;Figure 8.16.&quot;,labels=[x,t,&quot;u&quot;],orientation=[-150,50]);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="300" type="three-dimensional" width="400" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0">[encoded data, 13684 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L47" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The dimensionless temperature at the surface x =0 reaches a maximum and then decreases as a function of time:</Text-field>
</Input>
</Group>
<Group labelreference="L40" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot(subs(x=0,u),t=0..2,thickness=3,axes=boxed,title=&quot;Figure Exp. 8.17.&quot;,labels=[t,&quot;u(0,t)&quot;]);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="496" type="two-dimensional" width="496" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="false">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</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L41" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L42" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
</Worksheet>