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    <Task-category name="&lt;default&gt;">
    </Task-category>
</Task-table>
<Task>
</Task>
<Group labelreference="L55" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Example 8.13 Heat Conduction in a Slab with Radiation Boundary Conditions</Text-field>
<Text-field style="Text" layout="Normal">Equation (8.1.29) is solved in Maple below:</Text-field>
</Input>
</Group>
<Group labelreference="L56" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart:with(inttrans):with(plots):</Text-field>
</Input>
</Group>
<Group labelreference="L4" 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>
</Output>
</Group>
<Group labelreference="L5" 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="L6" 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="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">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ1RzYiNiRJInhHRilJInRHRilGKyIiIQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L7" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc2:=diff(u(x,t),x)+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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">LywmLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInVHNiI2JEkieEdGKkkidEdGKkYsIiIiRihGLiIiIQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L8" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal256">eqs:=laplace(eq,t,s):</Text-field>
</Input>
</Group>
<Group labelreference="L9" 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="L10" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal256">bc1:=laplace(bc1,t,s):</Text-field>
</Input>
</Group>
<Group labelreference="L11" 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="L12" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal256">bc2:=laplace(bc2,t,s):</Text-field>
</Input>
</Group>
<Group labelreference="L13" 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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">LywmLUklZGlmZkclKnByb3RlY3RlZEc2JC1JIlVHNiI2I0kieEdGKkYsIiIiRihGLSIiIQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L14" 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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">Ly1JIlVHNiI2I0kieEdGJSwoKiYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2IyomKUkic0dGJSMiIiIiIiNGNEYnRjRGNEkkX0MyR0YlRjRGNComLUYrNiMsJEYwISIiRjRJJF9DMUdGJUY0RjQqJEYyRjtGNA==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L15" 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)+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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">LCgqJiZJImNHNiI2IyIiIkYoLUklY29zaEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJjYjKiYpSSJzR0YmI0YoIiIjRihJInhHRiZGKEYoRigqJiZGJTYjRjNGKC1JJXNpbmhHRitGLkYoRigqJEYxISIiRig=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L16" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq0:=eval(subs(x=0,bc1)):</Text-field>
</Input>
</Group>
<Group labelreference="L17" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq1:=eval(subs(x=1,bc2)):</Text-field>
</Input>
</Group>
<Group labelreference="L18" 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="L19" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U(x):=subs(con,U(x)):</Text-field>
</Input>
</Group>
<Group labelreference="L20" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U(x):=factor(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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">LCQqKCwoLUklY29zaEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjKiYpSSJzR0YqIyIiIiIiI0YwSSJ4R0YqRjBGMComLUklc2luaEdGJzYjKiRGLUYwRjBGLUYwISIiLUYmRjZGOEYwRi5GOCwmRjNGMEY5RjBGOEY4</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L21" 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="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">LCgtSSVjb3NoRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMqJilJInNHRigjIiIiIiIjRi5JInhHRihGLiEiIiomLUklc2luaEdGJTYjKiRGK0YuRi5GK0YuRi4tRiRGNUYu</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L22" 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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">KiZJInNHNiIiIiIsJiomLUklc2luaEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjKiQpRiMjRiUiIiNGJUYlRi9GJUYlLUklY29zaEdGKkYtRiVGJQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L58" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Maple cannot find the eigenvalues directly.</Text-field>
</Input>
</Group>
<Group labelreference="L23" 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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">NiQiIiEqJCktSSdSb290T2ZHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywqKiZJI19aR0YoIiIiKS1JJGV4cEdGKDYjRi8iIiNGMEYwRi8hIiIqJEYxRjBGMEYwRjBGNUYw</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eig:=sinh(s^(1/2))*s^(1/2)+cosh(s^(1/2));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCYqJi1JJXNpbmhHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IyokKUkic0dGKSMiIiIiIiNGL0YvRixGL0YvLUklY29zaEdGJkYqRi8=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L59" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">For convenience s=-\316\273</Font><Font subscript="true">2</Font> is substituted to find the eigenvalues.</Text-field>
</Input>
</Group>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eiglambda:=simplify(subs(s^(1/2)=I*lambda,s=-lambda^2,eig));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEqZWlnbGFtYmRhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEjOj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GIzYnLUY2Ni1RKiZ1bWludXMwO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZVLUYjNiYtRiM2Jy1GLDYlUSRzaW5GJy9GMEY9RjktRjY2LVEwJkFwcGx5RnVuY3Rpb247RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZORl1vLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2JVEnJiM5NTU7RidGaG5GOS8lK2ZvcmVncm91bmRHUShbMCwwLDBdRidGOUY5RmdvRjktRjY2LVExJkludmlzaWJsZVRpbWVzO0YnRjlGO0Y+RkBGQkZERkZGSEZcb0Zeb0Zkb0Y5LUY2Ni1RIitGJ0Y5RjtGPkZARkJGREZGRkhGVEZWLUYjNictRiw2JVEkY29zRidGaG5GOUZpbkZfb0Znb0Y5RjlGZ29GOQ==">LCYqJi1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdsYW1iZGFHRikiIiJGK0YsISIiLUkkY29zR0YmRipGLA==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot(eiglambda,lambda=0..20,thickness=3,title=&quot;Figure 8.23.&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">[encoded data, 6416 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L60" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The roots are:</Text-field>
</Input>
</Group>
<Group labelreference="L27" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">0,0,-lambda^2;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NiUiIiFGIywkKiQpSSdsYW1iZGFHNiIiIiMiIiIhIiI=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">fsolve(eiglambda,lambda=1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">JCIrISplTC4nKSEjNQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L61" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The first 20 eigenvalues are obtained numerically.</Text-field>
</Input>
</Group>
<Group labelreference="L29" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=20;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiTkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIzo9RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtSSNtbkdGJDYkUSMyMEYnRjkvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnRjk=">IiM/</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L30" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">l[1]:=fsolve(eiglambda,lambda=0..2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">JCIrISplTC4nKSEjNQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L31" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 2 to N do l[i]:=fsolve(eiglambda,lambda=l[i-1]..l[i-1]+4);od:</Text-field>
</Input>
</Group>
<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">seq(l[i],i=1..N);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NjYkIishKmVMLicpISM1JCIrZiU9Y1UkISIqJCIreiIpSFBrRigkIiswV0xIJipGKCQiK0EoR1hFIiEiKSQiKyhbR3JkIkYvJCIrJyo0QyEqPUYvJCIrdCdcTz8jRi8kIitMWUM8REYvJCIrJkdrNCRHRi8kIitrOXhXSkYvJCIrQUNrZU1GLyQiKyRHaER4JEYvJCIrTHFeJzMlRi8kIisjeiwwUyVGLyQiK3UoNFhyJUYvJCIrTW1gR11GLyQiK1shekRNJkYvJCIrR1dqY2NGLyQiK0oycXFmRi8=</Equation></Text-field>
</Output>
</Group>
<Text-field style="Normal" layout="Normal"></Text-field>
<Group labelreference="L33" 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="L34" 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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">KihJInNHNiIiIiIsKC1JJWNvc2hHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IyomKUYjI0YlIiIjRiVJInhHRiRGJSEiIiomLUklc2luaEdGKTYjKiRGLkYlRiVGLkYlRiUtRihGNkYlRiUsJkYzRiVGOEYlRjI=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L35" 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="L36" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">b[1]:=diff(b[2],s):</Text-field>
</Input>
</Group>
<Group labelreference="L37" 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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">IiIh</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L38" 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="L39" 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="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRIm5GJ0YyRjUvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnL0Y2USdub3JtYWxGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEjOj1GJ0ZALyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZLLyUpc3RyZXRjaHlHRksvJSpzeW1tZXRyaWNHRksvJShsYXJnZW9wR0ZLLyUubW92YWJsZWxpbWl0c0dGSy8lJ2FjY2VudEdGSy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlotRiM2Ji1GRjYtUSomdW1pbnVzMDtGJ0ZARklGTEZORlBGUkZURlYvRllRLDAuMjIyMjIyMmVtRicvRmZuRl1vLUkmbWZyYWNHRiQ2KC1GIzYpLUkjbW5HRiQ2JFEiMkYnRkAtRkY2LVExJkludmlzaWJsZVRpbWVzO0YnRkBGSUZMRk5GUEZSRlRGVi9GWVEmMC4wZW1GJy9GZm5GXHAtSShtZmVuY2VkR0YkNiQtRiM2KC1GIzYnLUYvNiVRJWNvc2hGJy9GM0ZLRkAtRkY2LVEwJkFwcGx5RnVuY3Rpb247RidGQEZJRkxGTkZQRlJGVEZWRltwRl1wLUZfcDYkLUYjNiUtRiM2Ji1JJm1zcXJ0R0YkNiMtRi82JVEnJiM5NTY7RidGaHBGQEZoby1GLzYlUSJ4RidGMkY1RkBGPUZARkBGPUZALUZGNi1RKCZtaW51cztGJ0ZARklGTEZORlBGUkZURlZGXG9GXm8tRiM2Ji1GIzYnLUYvNiVRJXNpbmhGJ0ZocEZARmlwLUZfcDYkLUYjNiUtRiM2JEZicUZARj1GQEZARj1GQEZob0ZicUZARltyLUYjNidGZXBGaXBGZXJGPUZARkBGQEZob0ZicUY9RkAtRiM2JS1GIzYoLUYjNigtRmVvNiRRIjRGJ0ZARmhvRmByRmhvRmVxRkAtRkY2LVEiK0YnRkBGSUZMRk5GUEZSRlRGVkZcb0Zeby1GIzYoRmRvRmhvRltzRmhvRmJxRkBGZnMtRiM2Ji1JJW1zdXBHRiQ2JUZlcS1GIzYnLUZlbzYkUSIzRidGQC1GRjYtUSIvRidGQEZJRkwvRk9GNEZQRlJGVEZWL0ZZUSwwLjE2NjY2NjdlbUYnL0ZmbkZqdEZkb0Y9RkAvJTFzdXBlcnNjcmlwdHNoaWZ0R0ZERmhvRltzRkBGQEY9RkAvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmN1LyUpYmV2ZWxsZWRHRktGPUZARj1GQA==">LCQqKiIiIyIiIiwoLUklY29zaEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjKiYpSSNtdUdGLCNGJUYkRiVJInhHRixGJUYlKiYtSSVzaW5oR0YpNiMqJEYvRiVGJUYvRiUhIiItRihGNkY4RiVGL0YlLCgqKCIiJUYlRjRGJUYwRiVGJSooRiRGJUY5RiVGL0YlRiUqJilGMCMiIiRGJEYlRjlGJUYlRjhGOA==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L40" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A[n]:=simplify(subs(mu^(1/2)=I*lambda,mu^(3/2)=-I*lambda^3,mu=-lambda^2,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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">LCQqKCIiIyIiIiwoLUkkY29zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMqJkknbGFtYmRhR0YsRiVJInhHRixGJUYlKiYtSSRzaW5HRik2I0YvRiVGL0YlRiUtRihGNCEiIkYlLCgqKCIiJUYlRjJGJUYvRiVGJSomRiRGJUY1RiVGNiomKUYvRiRGJUY1RiVGJUY2RiU=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L41" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">vars:={cos(lambda)=lambda*sin(lambda)};</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">PCMvLUkkY29zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJJ2xhbWJkYUc2IiomLUkkc2luRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJJ2xhbWJkYUc2IiIiIkknbGFtYmRhRzYiIiIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L42" 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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">LCQqLCIiIyIiIi1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjKiZJJ2xhbWJkYUdGK0YlSSJ4R0YrRiVGJS1JJHNpbkdGKDYjRi4hIiJGLkYzLCZGJEYlKiQpRi5GJEYlRiVGM0Yl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L43" 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="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEkYjFzRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEjOj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5LyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJ0Y5">IiIh</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L44" 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="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEkYjF0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEjOj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5LyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJ0Y5">IiIh</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L45" 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="L46" 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="L47" 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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">LCQqLiIiIyIiIi1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjKiZJJ2xhbWJkYUdGK0YlSSJ4R0YrRiVGJS1JJHNpbkdGKDYjRi4hIiJGLkYzLCZGJEYlKiQpRi5GJEYlRiVGMywmSSJzR0YrRiVJI211R0YrRjNGM0Yl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L48" 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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">LCQqLiIiIyIiIi1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjKiZJJ2xhbWJkYUdGK0YlSSJ4R0YrRiVGJS1JJHNpbkdGKDYjRi4hIiJGLkYzLCZGJEYlKiQpRi5GJEYlRiVGMy1JJGV4cEdGKDYjKiZJI211R0YrRiVJInRHRitGJUYlRiU=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L49" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">unt:=subs(mu=-l[n]^2,lambda=l[n],unt);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEkdW50RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEjOj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JJm1mcmFjR0YkNigtRiM2KS1JI21uR0YkNiRRIjJGJ0Y5LUY2Ni1RMSZJbnZpc2libGVUaW1lcztGJ0Y5RjtGPkZARkJGREZGRkgvRktRJjAuMGVtRicvRk5GZm4tRiM2Jy1GLDYlUSRjb3NGJy9GMEY9RjktRjY2LVEwJkFwcGx5RnVuY3Rpb247RidGOUY7Rj5GQEZCRkRGRkZIRmVuRmduLUkobWZlbmNlZEdGJDYkLUYjNiUtRiM2Ji1JJW1zdWJHRiQ2JS1GLDYlUSJsRidGL0YyLUYjNiUtRiw2JVEibkYnRi9GMi8lK2ZvcmVncm91bmRHUShbMCwwLDBdRidGOS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRlgtRiw2JVEieEYnRi9GMkY5RmNwRjlGOUZjcEY5RlgtSSVtc3VwR0YkNiUtRjY2LVEvJkV4cG9uZW50aWFsRTtGJ0Y5RjtGPkZARkJGREZGRkhGZW4vRk5RLDAuMTExMTExMWVtRictRiM2Ji1GNjYtUSomdW1pbnVzMDtGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GanEtRiM2Ji1JKG1zdWJzdXBHRiQ2J0ZbcEZecEZULyUxc3VwZXJzY3JpcHRzaGlmdEdGaHBGZnBGWC1GLDYlUSJ0RidGL0YyRjlGY3BGOUZhckZjcEY5LUYjNiktRiM2Jy1GLDYlUSRzaW5GJ0Zdb0Y5Rl5vLUZibzYkLUYjNiVGaG9GY3BGOUY5RmNwRjlGWEZob0ZYLUZibzYkLUYjNiZGVC1GNjYtUSIrRidGOUY7Rj5GQEZCRkRGRkZIRmlxRltyLUYjNiRGXnJGOUY5RjlGY3BGOS8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGX3QvJSliZXZlbGxlZEdGPUZjcEY5">LCQqLiIiIyIiIi1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjKiYmSSJsR0YrNiNJIm5HRitGJUkieEdGK0YlRiUtSSRzaW5HRig2I0YuISIiRi5GNiwmRiRGJSokKUYuRiRGJUYlRjYtSSRleHBHRig2IywkKiZGOUYlSSJ0R0YrRiVGNkYlRiU=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L62" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The solution obtained can then be plotted.</Text-field>
</Input>
</Group>
<Group labelreference="L50" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U:=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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">LUkkU3VtRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQsJCouIiIjIiIiLUkkY29zR0YkNiMqJiZJImxHRic2I0kibkdGJ0YsSSJ4R0YnRixGLC1JJHNpbkdGJDYjRjEhIiJGMUY5LCZGK0YsKiQpRjFGK0YsRixGOS1JJGV4cEdGJDYjLCQqJkY8RixJInRHRidGLEY5RixGLC9GNDtGLEkpaW5maW5pdHlHRiU=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L51" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u:=piecewise(t=0,1,t&gt;0,subs(infinity=20,U)):</Text-field>
</Input>
</Group>
<Group labelreference="L52" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u:=evalf(u):</Text-field>
</Input>
</Group>
<Group labelreference="L53" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot3d(u,x=0..1,t=0..0.5,axes=boxed,title=&quot;Figure 8.24.&quot;,labels=[x,t,&quot;u&quot;],orientation=[45,60]);</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="L54" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot([subs(t=0,u),subs(t=0.1,u),subs(t=0.2,u),subs(t=0.5,u)],x=0..1,title=&quot;Figure 8.25.&quot;,axes=boxed,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, 9068 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L57" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
</Worksheet>