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<Text-field style="Text" layout="Normal">Example 8.15 Heat Conduction in a Rectangle with a Time Dependent Boundary Condition</Text-field>
<Text-field style="Text" layout="Normal">Equation (8.1.35) is solved in Maple below for a general time dependent function, w(t), and plots are obtained for a particular step function.</Text-field>
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<Group labelreference="L58" drawlabel="true">
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="restart:" display="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">QyhJKHJlc3RhcnRHJSpwcm90ZWN0ZWRHISIiLUkld2l0aEc2IjYjSSlpbnR0cmFuc0c2JEYkSShfc3lzbGliR0YoRiUtRic2I0kmcGxvdHNHRitGJQ==</Equation></Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal256">eq:=diff(u(x,t),t)=diff(u(x,t),x$2);</Text-field>
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<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="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUYjNictSSNtaUdGJDYlUSJ1RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjVRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y/LyUpc3RyZXRjaHlHRj8vJSpzeW1tZXRyaWNHRj8vJShsYXJnZW9wR0Y/LyUubW92YWJsZWxpbWl0c0dGPy8lJ2FjY2VudEdGPy8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRk4tSShtZmVuY2VkR0YkNiQtRiM2Jy1GLjYlUSJ4RidGMUY0LUY4Ni1RIixGJ0Y7Rj0vRkFGM0ZCRkRGRkZIRkpGTC9GUFEsMC4zMzMzMzMzZW1GJy1JI21uR0YkNiRRIjBGJ0Y7LyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJ0Y7RjtGXW9GOy1GODYtUSM6PUYnRjtGPUZARkJGREZGRkhGSi9GTVEsMC4yNzc3Nzc4ZW1GJy9GUEZkb0ZpbkZdb0Y7">IiIh</Equation></Text-field>
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<Group labelreference="L5" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc1:=u(x,t)=0;</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JInVHNiI2JEkieEdGJUkidEdGJSIiIQ==</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)=w(t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEkYmMyRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEjOj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GIzYnLUYjNictRiw2JVEidUYnRi9GMi1GNjYtUTAmQXBwbHlGdW5jdGlvbjtGJ0Y5RjtGPkZARkJGREZGRkgvRktRJjAuMGVtRicvRk5GWi1JKG1mZW5jZWRHRiQ2JC1GIzYnLUYsNiVRInhGJ0YvRjItRjY2LVEiLEYnRjlGOy9GP0YxRkBGQkZERkZGSEZZL0ZOUSwwLjMzMzMzMzNlbUYnLUYsNiVRInRGJ0YvRjIvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnRjlGOUZnb0Y5LUY2Ni1RIj1GJ0Y5RjtGPkZARkJGREZGRkhGSkZNLUYjNictRiw2JVEid0YnRi9GMkZWLUZnbjYkLUYjNiVGZG9GZ29GOUY5RmdvRjlGZ29GOUZnb0Y5">Ly1JInVHNiI2JEkieEdGJUkidEdGJS1JIndHRiU2I0Yo</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal256">eqs:=laplace(eq,t,s):</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal256">eqs:=subs(laplace(u(x,t),t,s)=U(x),eqs);</Text-field>
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<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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<Text-field prompt="&gt; " style="Maple Input" layout="Normal256">bc1:=laplace(bc1,t,s):</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc1:=subs(laplace(u(x,t),t,s)=U(x),laplace(w(t),t,s)=W(s),bc1);</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JIlVHNiI2I0kieEdGJSIiIQ==</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal256">bc2:=laplace(bc2,t,s):</Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc2:=subs(laplace(u(x,t),t,s)=U(x),laplace(w(t),t,s)=W(s),bc2);</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JIlVHNiI2I0kieEdGJS1JIldHRiU2I0kic0dGJQ==</Equation></Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dsolve(eqs,U(x));</Text-field>
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<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>
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<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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">KigtSSJXRzYiNiNJInNHRiUiIiItSSVzaW5oRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiMqJClGJyNGKCIiI0YoISIiLUYqNiMqJkYwRihJInhHRiVGKEYo</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L19" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U(x):=factor(combine(simplify(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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">KigtSSJXRzYiNiNJInNHRiUiIiItSSVzaW5oRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiMqJClGJyNGKCIiI0YoISIiLUYqNiMqJkYwRihJInhHRiVGKEYo</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L61" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Next U1(x) is written as a product of two functions (see equations (8.1.31) and (8.1.33)):</Text-field>
</Input>
</Group>
<Group labelreference="L20" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U1(x):=simplify(U(x)/W(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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">KigtSSVzaW5oRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMqJClJInNHRigjIiIiIiIjRi4hIiItRiQ2IyomRitGLkkieEdGKEYuRi5GLEYw</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L62" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">U1(x) is chosen so that q(s) is a higher order than p(s) (see equation (8.1.32)):</Text-field>
</Input>
</Group>
<Group labelreference="L21" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">G(s):=W(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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">KiYtSSJXRzYiNiNJInNHRiUiIiJGJ0Yo</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L63" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">where W(s) is the Laplace transform of the time dependent boundary condition w(t) in equation (8.11.35.).  Next, U1(X) is inverted to the time domain as illustrated in section 8.1.7 to obtain f(t) as:</Text-field>
</Input>
</Group>
<Group labelreference="L22" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">P(s):=numer(U1(x));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LUklc2luaEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjKiYpSSJzR0YnIyIiIiIiI0YtSSJ4R0YnRi0=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L23" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Q(s):=denom(U1(x));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KiYtSSVzaW5oRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMqJClJInNHRigjIiIiIiIjRi5GLkYsRi4=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L24" 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">IiIh</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">_EnvAllSolutions := true;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVExX0VudkFsbFNvbHV0aW9uc0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIzo9RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtRiw2JUYxRi9GMi8lK2ZvcmVncm91bmRHUShbMCwwLDBdRidGOQ==">SSV0cnVlRyUqcHJvdGVjdGVkRw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L26" 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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">NiQsJComKUkjUGlHJSpwcm90ZWN0ZWRHIiIjIiIiKUklX1oxfGlyRzYiRihGKSEiIiIiIQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L27" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">0,0,-n^2*Pi^2;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NiUiIiFGIywkKiYpSSJuRzYiIiIjIiIiKUkjUGlHJSpwcm90ZWN0ZWRHRilGKiEiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">mu0:=0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEoJiM5NTY7MEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIzo9RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtSSNtbkdGJDYkUSIwRidGOS8lK2ZvcmVncm91bmRHUShbMCwwLDBdRidGOQ==">IiIh</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L29" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">b[2]:=(s-mu0)^2*P(s)/Q(s);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KihJInNHNiIiIiItSSVzaW5oRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMqJilGIyNGJSIiI0YlSSJ4R0YkRiVGJS1GJzYjKiRGLUYlISIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L30" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">B[2]:=limit(b[2],s=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>
</Output>
</Group>
<Group labelreference="L31" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">b[1]:=diff(b[2],s):</Text-field>
</Input>
</Group>
<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">B[1]:=limit(b[1],s=0);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">SSJ4RzYi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L33" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A(s):=P(s)/diff(Q(s),s):</Text-field>
</Input>
</Group>
<Group labelreference="L34" 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="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRIm5GJ0YyRjUvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnL0Y2USdub3JtYWxGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEjOj1GJ0ZALyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZLLyUpc3RyZXRjaHlHRksvJSpzeW1tZXRyaWNHRksvJShsYXJnZW9wR0ZLLyUubW92YWJsZWxpbWl0c0dGSy8lJ2FjY2VudEdGSy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlotSSZtZnJhY0dGJDYoLUYjNictSSNtbkdGJDYkUSIyRidGQC1GRjYtUTEmSW52aXNpYmxlVGltZXM7RidGQEZJRkxGTkZQRlJGVEZWL0ZZUSYwLjBlbUYnL0ZmbkZkby1GIzYnLUYvNiVRJXNpbmhGJy9GM0ZLRkAtRkY2LVEwJkFwcGx5RnVuY3Rpb247RidGQEZJRkxGTkZQRlJGVEZWRmNvRmVvLUkobWZlbmNlZEdGJDYkLUYjNiUtRiM2Ji1JJm1zcXJ0R0YkNiMtRi82JVEnJiM5NTY7RidGW3BGQEZgby1GLzYlUSJ4RidGMkY1RkBGPUZARkBGPUZARj1GQC1GIzYlLUYjNiYtRiM2Ji1GIzYnLUYvNiVRJWNvc2hGJ0ZbcEZARlxwLUZgcDYkLUYjNiUtRiM2JEZmcEZARj1GQEZARj1GQEZgb0ZmcEZALUZGNi1RIitGJ0ZARklGTEZORlBGUkZURlYvRllRLDAuMjIyMjIyMmVtRicvRmZuRmRyLUYjNiZGXG9GYG8tRiM2J0Zob0ZccEZqcUY9RkBGQEZARj1GQC8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGX3MvJSliZXZlbGxlZEdGS0Y9RkA=">LCQqKCIiIyIiIi1JJXNpbmhHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IyomKUkjbXVHRisjRiVGJEYlSSJ4R0YrRiVGJSwmKiYtSSVjb3NoR0YoNiMqJEYuRiVGJUYuRiVGJSomRiRGJS1GJ0Y2RiVGJSEiIkYl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L35" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A[n]:=simplify(subs(mu^(1/2)=I*n*Pi,mu^(3/2)=-I*n^3*Pi^3,mu=-n^2*Pi^2,A[n])):</Text-field>
</Input>
</Group>
<Group labelreference="L36" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">vars:={sin(n*Pi)=0};</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">PCMvLUkkc2luRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMqJkkibkc2IiIiIkkjUGlHJSpwcm90ZWN0ZWRHIiIiIiIh</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L37" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A[n]:=simplify(subs(vars,A[n])):</Text-field>
</Input>
</Group>
<Group labelreference="L38" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A[n]:=simplify(subs(vars,expand(A[n])));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqLCIiIyIiIi1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjKihJIm5HRitGJUkjUGlHRilGJUkieEdGK0YlRiUtSSRjb3NHRig2IyomRi5GJUYvRiUhIiJGLkY1Ri9GNUYl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L39" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">b1s:=B[1]*subs(mu0=0,1/(s-mu0));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KiZJInhHNiIiIiJJInNHRiQhIiI=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L40" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">b1t:=invlaplace(b1s,s,t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEkYjF0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEjOj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSJ4RidGL0YyLyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJ0Y5">SSJ4RzYi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L41" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">b2s:=B[2]*subs(mu0=0,1/(s-mu0)^2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEkYjJzRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEjOj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5LyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJ0Y5">IiIh</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L42" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">b2t:=invlaplace(b2s,s,t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEkYjJ0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEjOj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5LyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJ0Y5">IiIh</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L43" 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="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">LCQqLiIiIyIiIi1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjKihJIm5HRitGJUkjUGlHRilGJUkieEdGK0YlRiUtSSRjb3NHRig2IyomRi5GJUYvRiUhIiJGLkY1Ri9GNSwmSSJzR0YrRiVJI211R0YrRjVGNUYl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L44" 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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">LCQqLiIiIyIiIi1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjKihJIm5HRitGJUkjUGlHRilGJUkieEdGK0YlRiUtSSRjb3NHRig2IyomRi5GJUYvRiUhIiJGLkY1Ri9GNS1JJGV4cEdGKDYjKiZJI211R0YrRiVJInRHRitGJUYlRiU=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L45" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">unt:=subs(mu=-n^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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">LCQqLiIiIyIiIi1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjKihJIm5HRitGJUkjUGlHRilGJUkieEdGK0YlRiUtSSRjb3NHRig2IyomRi5GJUYvRiUhIiJGLkY1Ri9GNS1JJGV4cEdGKDYjLCQqKClGLkYkRiUpRi9GJEYlSSJ0R0YrRiVGNUYlRiU=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L46" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">f(t):=b1t+b2t+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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">LCZJInhHNiIiIiItSSRTdW1HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2JCwkKi4iIiNGJS1JJHNpbkdGKDYjKihJIm5HRiRGJUkjUGlHRilGJUYjRiVGJS1JJGNvc0dGKDYjKiZGM0YlRjRGJSEiIkYzRjlGNEY5LUkkZXhwR0YoNiMsJCooKUYzRi5GJSlGNEYuRiVJInRHRiRGJUY5RiVGJS9GMztGJUkpaW5maW5pdHlHRilGJQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L64" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Next, a step function is chosen for w(t) and plotted:</Text-field>
</Input>
</Group>
<Group labelreference="L47" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">w(t):=Heaviside(t-1)-1/2*Heaviside(t-2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCYtSSpIZWF2aXNpZGVHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywmSSJ0R0YoIiIiRiwhIiJGLComI0YsIiIjRiwtRiQ2IywmRitGLEYwRi1GLEYt</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L48" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot(w(t),t=0..5,thickness=3,title=&quot;Figure Exp. 8.28.&quot;,axes=boxed);</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="L66" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The Laplace transform of w(t) is:</Text-field>
</Input>
</Group>
<Group labelreference="L49" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">W(s):=laplace(w(t),t,s);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqKCMiIiIiIiNGJSwmKiZGJkYlLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJEkic0dGLiEiIkYlRiUtRio2IywkKiZGJkYlRjFGJUYyRjJGJUYxRjJGJQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L67" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The function g(t) is obtained by inverting G(s):</Text-field>
</Input>
</Group>
<Group labelreference="L50" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">G(s):=s*W(s);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkSSJzR0YoISIiIiIiKiYjRi0iIiNGLS1GJDYjLCQqJkYwRi1GK0YtRixGLUYs</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L51" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">g(t):=invlaplace(G(s),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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">LCYtSSZEaXJhY0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCZJInRHRigiIiJGLCEiIkYsKiYjRiwiIiNGLC1GJDYjLCZGK0YsRjBGLUYsRi0=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L68" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Next, the convolution integral is carried out to obtain the final time domain solution as:</Text-field>
</Input>
</Group>
<Group labelreference="L52" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">gtau:=subs(t=tau,g(t));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCYtSSZEaXJhY0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCZJJHRhdUdGKCIiIkYsISIiRiwqJiNGLCIiI0YsLUYkNiMsJkYrRixGMEYtRixGLQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L53" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ftau:=subs(t=t-tau,f(t));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCZJInhHNiIiIiItSSRTdW1HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2JCwkKi4iIiNGJS1JJHNpbkdGKDYjKihJIm5HRiRGJUkjUGlHRilGJUYjRiVGJS1JJGNvc0dGKDYjKiZGM0YlRjRGJSEiIkYzRjlGNEY5LUkkZXhwR0YoNiMsJCooKUYzRi5GJSlGNEYuRiUsJkkidEdGJEYlSSR0YXVHRiRGOUYlRjlGJUYlL0YzO0YlSSlpbmZpbml0eUdGKUYl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L54" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U:=int(ftau*gtau,tau=0..t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCYqKCMiIiIiIiNGJS1JKkhlYXZpc2lkZUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCZJInRHRixGJUYmISIiRiUsJkkieEdGLEYlLUkkU3VtR0YpNiQsJCouRiZGJS1JJHNpbkdGKTYjKihJIm5HRixGJUkjUGlHRipGJUYyRiVGJS1JJGNvc0dGKTYjKiZGPEYlRj1GJUYwRjxGMEY9RjAtSSRleHBHRik2IywkKigpRjxGJkYlKUY9RiZGJUYuRiVGMEYlRiUvRjw7RiVJKWluZmluaXR5R0YqRiVGJUYwKiYtRig2IywmRi9GJUYlRjBGJSwmRjJGJS1GNDYkLCQqLkYmRiVGOEYlRj5GMEY8RjBGPUYwLUZDNiMsJCooRkdGJUZIRiVGT0YlRjBGJUYlRklGJUYlRiU=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L55" 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="L56" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot3d(simplify(u),x=0..1,t=0..5,axes=boxed,title=&quot;Figure Exp. 8.29.&quot;,labels=[x,t,&quot;u&quot;],orientation=[135,45]);</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, 13692 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L69" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The dimensionless temperature at different points inside the rectangle are plotted as:</Text-field>
</Input>
</Group>
<Group labelreference="L57" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot([simplify(subs(x=1,u)),simplify(subs(x=0.75,u)),simplify(subs(x=0.5,u)),simplify(subs(x=0.25,u)),simplify(subs(x=0.0,u))],t=0..5.,thickness=3,axes=boxed,title=&quot;Figure Exp. 8.30.&quot;,labels=[t,&quot;u&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">[encoded data, 15484 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L60" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRicvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group>
</Worksheet>