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<Highlighter-style name="Highlighter 2" pen-color="[255,204,0]" pen-height="14.0" pen-width="14.0" pen-opacity="0.8"/>
<Highlighter-style name="Highlighter 1" pen-color="[255,153,255]" pen-height="12.0" pen-width="8.0" pen-opacity="0.8"/>
<Highlighter-style name="Highlighter 4" pen-color="[0,255,255]" pen-height="32.0" pen-width="32.0" pen-opacity="0.8"/>
<Highlighter-style name="Highlighter 3" pen-color="[51,255,0]" pen-height="24.0" pen-width="24.0" pen-opacity="0.8"/>
<Highlighter-style name="Highlighter 5" pen-color="[255,255,0]" pen-height="48.0" pen-width="48.0" pen-opacity="0.8"/>
</Styles>
<Task-table>
    <Task-category name="&lt;default&gt;">
    </Task-category>
</Task-table>
<Task>
</Task>
<Group labelreference="L52" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Example 8.5 Heat Transfer in a Rectangle</Text-field>
<Text-field style="Text" layout="Normal">Equation (8.1.5) is solved in Maple below:<Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
</Input>
</Group>
<Group labelreference="L53" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart:with(inttrans):with(plots):</Text-field>
</Input>
</Group>
<Group labelreference="L54" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The governing equation and boundary conditions are entered and converted to the Laplace domain.</Text-field>
</Input>
</Group>
<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="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEjZXFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSM6PUYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUYjNictRiM2Jy1JJm1mcmFjR0YkNigtRiM2JS1GNjYtUSsmUGFydGlhbEQ7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZORmZuLyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJ0Y5LUYjNiUtRiM2JkZYLUYsNiVRInRGJ0YvRjJGaG5GOUZobkY5LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Znby8lKWJldmVsbGVkR0Y9LUY2Ni1RMSZJbnZpc2libGVUaW1lcztGJ0Y5RjtGPkZARkJGREZGRkhGZW5GZ24tRiM2Jy1GLDYlUSJ1RidGL0YyLUY2Ni1RMCZBcHBseUZ1bmN0aW9uO0YnRjlGO0Y+RkBGQkZERkZGSEZlbkZnbi1JKG1mZW5jZWRHRiQ2JC1GIzYnLUYsNiVRInhGJ0YvRjItRjY2LVEiLEYnRjlGOy9GP0YxRkBGQkZERkZGSEZlbi9GTlEsMC4zMzMzMzMzZW1GJ0Zfb0ZobkY5RjlGaG5GOUZobkY5LUY2Ni1RIj1GJ0Y5RjtGPkZARkJGREZGRkhGSkZNLUYjNictRlQ2KC1GIzYlLUklbXN1cEdGJDYlRlgtSSNtbkdGJDYkUSIyRidGOS8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGaG5GOS1GIzYlLUYjNiZGWC1GX3I2JUZccUZhckZlckZobkY5RmhuRjlGYm9GZW9GaG9Gam9GXHBGX3BGaG5GOUZobkY5RmhuRjk=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ1RzYiNiRJInhHRilJInRHRilGLC1GJDYkLUYkNiRGJ0YrRis=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L4" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal256">u(x,0):=1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">IiIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L5" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc1:=u(x,t)=0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JInVHNiI2JEkieEdGJUkidEdGJSIiIQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L6" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc2:=u(x,t)=0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEkYmMyRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEjOj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GIzYnLUYjNictRiw2JVEidUYnRi9GMi1GNjYtUTAmQXBwbHlGdW5jdGlvbjtGJ0Y5RjtGPkZARkJGREZGRkgvRktRJjAuMGVtRicvRk5GWi1JKG1mZW5jZWRHRiQ2JC1GIzYnLUYsNiVRInhGJ0YvRjItRjY2LVEiLEYnRjlGOy9GP0YxRkBGQkZERkZGSEZZL0ZOUSwwLjMzMzMzMzNlbUYnLUYsNiVRInRGJ0YvRjIvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnRjlGOUZnb0Y5LUY2Ni1RIj1GJ0Y5RjtGPkZARkJGREZGRkhGSkZNLUkjbW5HRiQ2JFEiMEYnRjlGZ29GOUZnb0Y5">Ly1JInVHNiI2JEkieEdGJUkidEdGJSIiIQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L7" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal256">eqs:=laplace(eq,t,s):</Text-field>
</Input>
</Group>
<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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">LywmKiZJInNHNiIiIiItSSJVR0YmNiNJInhHRiZGJ0YnRichIiItSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUYuNiRGKEYrRis=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L9" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal256">bc1:=laplace(bc1,t,s):</Text-field>
</Input>
</Group>
<Group labelreference="L10" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc1:=subs(diff(laplace(u(x,t),t,s),x)=D(U)(0),laplace(u(x,t),t,s)=U(0),bc1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JIlVHNiI2IyIiIUYn</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(diff(laplace(u(x,t),t,s),x)=D(U)(1),laplace(u(x,t),t,s)=U(1),bc2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JIlVHNiI2IyIiIiIiIQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L38" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The solution obtained in the Laplace domain is:</Text-field>
</Input>
</Group>
<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U(x):=rhs(dsolve({eqs,bc1,bc2},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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">LCgqKi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjKiYpSSJzR0YpIyIiIiIiI0YvSSJ4R0YpRi9GLywmRi8hIiItRiU2IywkKiRGLEYvRjNGL0YvRi1GMywmLUYlNiNGN0YzRjRGL0YzRjMqKi1GJTYjLCRGK0YzRi8sJkYvRjNGOUYvRi9GLUYzRjhGM0YvKiRGLUYzRi8=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L42" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Maple fails to invert the solution obtained:</Text-field>
</Input>
</Group>
<Group labelreference="L14" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">invlaplace(U(x),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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">LCwqJiMiIiIiIiNGJS1JK2ludmxhcGxhY2VHNiI2JSooLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YpNiMqJilJInNHRilGJEYlSSJ4R0YpRiVGJUY0ISIiLUklc2luaEdGLjYjKiRGM0YlRjZGNEkidEdGKUYlRjYtRig2JSooRjRGNiwmLUYtRjlGNi1GLTYjLCRGOkY2RiVGNi1GLTYjLCZGMkYlRjpGNkYlRjRGO0Y2KiZGJEYlLUYoNiUqKC1GLTYjLCRGMkY2RiVGNEY2RjdGNkY0RjtGJUYlLUYoNiUqKEY0RjZGP0Y2LUYtNiMsJkYyRjZGOkYlRiVGNEY7RiVGJUYl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L39" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The first two terms of U(x) are expressed as an infinite series below:</Text-field>
</Input>
</Group>
<Group labelreference="L15" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U1s:=-exp(s^(1/2)*x)/s/(exp(s^(1/2))+1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqKC1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjKiYpSSJzR0YpIyIiIiIiI0YvSSJ4R0YpRi9GL0YtISIiLCYtRiU2IyokRixGL0YvRi9GL0YyRjI=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L16" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U2s:=-exp(-s^(1/2)*x)*exp(s^(1/2))/s/(exp(s^(1/2))+1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqKi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCQqJilJInNHRikjIiIiIiIjRjBJInhHRilGMCEiIkYwLUYlNiMqJEYtRjBGMEYuRjMsJkY0RjBGMEYwRjNGMw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L40" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">We want to write a series in terms of S=exp(-s^(1/2)) so that the series will converge:</Text-field>
</Input>
</Group>
<Group labelreference="L17" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U1S:=series(subs(exp(s^(1/2))=1/S,U1s),S);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ky9JIlNHNiIsJComLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMqJilJInNHRiQjIiIiIiIjRjFJInhHRiRGMUYxRi8hIiJGNEYxRiZGMkYlIiIkRiYiIiVGJSIiJi1JIk9HRio2I0YxIiIn</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L18" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U1S:=subs(S=exp(-s^(1/2)),U1S);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LC4qKC1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjKiYpSSJzR0YpIyIiIiIiI0YvSSJ4R0YpRi9GL0YtISIiLUYlNiMsJCokRixGL0YyRi9GMiooRiRGL0YtRjIpRjNGMEYvRi8qKEYkRi9GLUYyKUYzIiIkRi9GMiooRiRGL0YtRjIpRjMiIiVGL0YvKihGJEYvRi1GMilGMyIiJkYvRjItSSJPR0YnNiMqJClGMyIiJ0YvRi8=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L19" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">simplify(U1S);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KiYsLi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjKiYpSSJzR0YpIyIiIiIiI0YvLCZJInhHRilGL0YvISIiRi9GMy1GJTYjKiZGLEYvLCZGMkYvRjBGM0YvRi8tRiU2IyomRixGLywmRjJGLyIiJEYzRi9GMy1GJTYjKiZGLEYvLCZGMkYvIiIlRjNGL0YvLUYlNiMqJkYsRi8sJkYyRi8iIiZGM0YvRjMqJi1JIk9HRic2Iy1GJTYjLCQqJiIiJ0YvRixGL0YzRi9GLUYvRi9GL0YtRjM=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L43" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Hence, U1S can be written as the infinite series:</Text-field>
</Input>
</Group>
<Group labelreference="L20" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U1S:=Sum((-1)^n*exp(s^(1/2)*(x-n))/s,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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">LUkkU3VtRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQqKCkhIiJJIm5HRiciIiItSSRleHBHRiQ2IyomKUkic0dGJyNGLSIiI0YtLCZJInhHRidGLUYsRitGLUYtRjNGKy9GLDtGLUkpaW5maW5pdHlHRiU=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L44" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The general term in the above series is:</Text-field>
</Input>
</Group>
<Group labelreference="L21" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u1s:=(-1)^n*exp(s^(1/2)*(x-n))/s;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KigpISIiSSJuRzYiIiIiLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiMqJilJInNHRiYjRiciIiNGJywmSSJ4R0YmRidGJUYkRidGJ0YwRiQ=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L45" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The time domain solution for this expression is:</Text-field>
</Input>
</Group>
<Group labelreference="L22" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u1t:=invlaplace(u1s,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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">KiYpISIiSSJuRzYiIiIiLUkraW52bGFwbGFjZUdGJjYlKiYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiY2IyomKUkic0dGJiNGJyIiI0YnLCZJInhHRiZGJ0YlRiRGJ0YnRjRGJEY0SSJ0R0YmRic=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L46" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Hence, the inverse of U1S is the infinite series given by:</Text-field>
</Input>
</Group>
<Group labelreference="L23" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U1t:=Sum(u1t,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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">LUkkU3VtRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQqJikhIiJJIm5HRiciIiItSStpbnZsYXBsYWNlR0YnNiUqJi1JJGV4cEdGJDYjKiYpSSJzR0YnI0YtIiIjRi0sJkkieEdGJ0YtRixGK0YtRi1GN0YrRjdJInRHRidGLS9GLDtGLUkpaW5maW5pdHlHRiU=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L47" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Similarly, U2S is inverted below:</Text-field>
</Input>
</Group>
<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U2S:=series(subs(exp(s^(1/2))=1/S,U2s),S);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KzFJIlNHNiIsJComLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJComKUkic0dGJCMiIiIiIiNGMkkieEdGJEYyISIiRjJGMEY1RjUiIiFGJkYyRiVGM0YmIiIkRiUiIiVGJiIiJi1JIk9HRio2I0YyIiIn</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U2S:=subs(S=exp(-s^(1/2)),U2S);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LDAqJi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCQqJilJInNHRikjIiIiIiIjRjBJInhHRilGMCEiIkYwRi5GM0YzKihGJEYwRi5GMy1GJTYjLCQqJEYtRjBGM0YwRjAqKEYkRjBGLkYzKUY1RjFGMEYzKihGJEYwRi5GMylGNSIiJEYwRjAqKEYkRjBGLkYzKUY1IiIlRjBGMyooRiRGMEYuRjMpRjUiIiZGMEYwLUkiT0dGJzYjKiQpRjUiIidGMEYw</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">simplify(U2S);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KiYsMC1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCQqJilJInNHRikjIiIiIiIjRjBJInhHRilGMCEiIkYzLUYlNiMsJComRi1GMCwmRjJGMEYwRjBGMEYzRjAtRiU2IywkKiZGLUYwLCZGMkYwRjFGMEYwRjNGMy1GJTYjLCQqJkYtRjAsJkYyRjAiIiRGMEYwRjNGMC1GJTYjLCQqJkYtRjAsJkYyRjAiIiVGMEYwRjNGMy1GJTYjLCQqJkYtRjAsJkYyRjAiIiZGMEYwRjNGMComLUkiT0dGJzYjLUYlNiMsJComIiInRjBGLUYwRjNGMEYuRjBGMEYwRi5GMw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L27" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U2S:=Sum((-1)^n*exp(-s^(1/2)*(x+n-1))/s,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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">LUkkU3VtRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQqKCkhIiJJIm5HRiciIiItSSRleHBHRiQ2IywkKiYpSSJzR0YnI0YtIiIjRi0sKEkieEdGJ0YtRixGLUYtRitGLUYrRi1GNEYrL0YsO0YtSSlpbmZpbml0eUdGJQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u2s:=(-1)^n*exp(-s^(1/2)*(x+n-1))/s;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KigpISIiSSJuRzYiIiIiLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiMsJComKUkic0dGJiNGJyIiI0YnLChJInhHRiZGJ0YlRidGJ0YkRidGJEYnRjFGJA==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L29" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u2t:=invlaplace(u2s,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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">KiYpISIiSSJuRzYiIiIiLUkraW52bGFwbGFjZUdGJjYlKiYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiY2IyomLChJInhHRiZGJEYlRiRGJ0YnRicpSSJzR0YmI0YnIiIjRidGJ0Y2RiRGNkkidEdGJkYn</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L30" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U2t:=Sum(u2t,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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">LUkkU3VtRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQqJikhIiJJIm5HRiciIiItSStpbnZsYXBsYWNlR0YnNiUqJi1JJGV4cEdGJDYjKiYsKEkieEdGJ0YrRixGK0YtRi1GLSlJInNHRicjRi0iIiNGLUYtRjlGK0Y5SSJ0R0YnRi0vRiw7Ri1JKWluZmluaXR5R0Yl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L48" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The final solution for u in the time domain is:</Text-field>
</Input>
</Group>
<Group labelreference="L31" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Ut:=U1t+U2t+1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCgtSSRTdW1HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JComKSEiIkkibkdGKCIiIi1JK2ludmxhcGxhY2VHRig2JSomLUkkZXhwR0YlNiMqJilJInNHRigjRi4iIiNGLiwmSSJ4R0YoRi5GLUYsRi5GLkY4RixGOEkidEdGKEYuL0YtO0YuSSlpbmZpbml0eUdGJkYuLUYkNiQqJkYrRi4tRjA2JSomLUY0NiMqJiwoRjxGLEYtRixGLkYuRi5GN0YuRi5GOEYsRjhGPUYuRj5GLkYuRi4=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L49" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">For plotting purposes, infinity is replaced by N = 20:</Text-field>
</Input>
</Group>
<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u:=subs(infinity=N,Ut);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCgtSSRTdW1HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JComKSEiIkkibkdGKCIiIi1JK2ludmxhcGxhY2VHRig2JSomLUkkZXhwR0YlNiMqJilJInNHRigjRi4iIiNGLiwmSSJ4R0YoRi5GLUYsRi5GLkY4RixGOEkidEdGKEYuL0YtO0YuSSJOR0YoRi4tRiQ2JComRitGLi1GMDYlKiYtRjQ2IyomLChGPEYsRi1GLEYuRi5GLkY3Ri5GLkY4RixGOEY9Ri5GPkYuRi5GLg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L33" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u:=subs(N=20,u);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCgtSSRTdW1HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JComKSEiIkkibkdGKCIiIi1JK2ludmxhcGxhY2VHRig2JSomLUkkZXhwR0YlNiMqJilJInNHRigjRi4iIiNGLiwmSSJ4R0YoRi5GLUYsRi5GLkY4RixGOEkidEdGKEYuL0YtO0YuIiM/Ri4tRiQ2JComRitGLi1GMDYlKiYtRjQ2IyomLChGPEYsRi1GLEYuRi5GLkY3Ri5GLkY4RixGOEY9Ri5GPkYuRi5GLg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L50" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The following plots can be obtained:</Text-field>
</Input>
</Group>
<Group labelreference="L34" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot3d(u,x=0..1,t=1e-6..0.1,axes=boxed,title=&quot;Figure 8.9.&quot;,labels=[x,t,&quot;u&quot;],orientation=[60,60]);</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="L35" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot([subs(t=1e-6,u),subs(t=1e-3,u),subs(t=0.01,u),subs(t=0.05,u)],x=0..1,axes=boxed,title=&quot;Figure 8.10.&quot;,thickness=5,labels=[x,&quot;u&quot;]);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="300" type="two-dimensional" width="400" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="false">[encoded data, 9596 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L51" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Note that for plotting purposes t = 0 is replaced by t = <Equation executable="false" style="Text" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYlLUkjbW5HRiQ2JFEjMTBGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2KC1JI21vR0YkNi1RKiZ1bWludXMwO0YnRjIvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGTC1GLzYkUSI2RidGMi8lJ2l0YWxpY0dRJXRydWVGJy8lK2ZvcmVncm91bmRHUSxbMjAwLDAsMjAwXUYnLyUscGxhY2Vob2xkZXJHRlQvRjNRJ2l0YWxpY0YnLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy1GODYtUSJ+RidGMkY7Rj5GQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZORl1vRjI=</Equation>to avoid singularity at t = 0.</Text-field>
</Input>
</Group>
<Group labelreference="L36" 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>