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<Input>
<Text-field style="Text" layout="Normal">Example 8.12 Distribution of Overpotential in a Porous Electrode</Text-field>
<Text-field style="Text" layout="Normal">Equation (8.1.28) is solved in Maple and the results obtained are given below:</Text-field>
</Input>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYvLUkjbWlHRiQ2KVEocmVzdGFydEYnLyUnZmFtaWx5R1ErTW9ub3NwYWNlZEYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJTBmb250X3N0eWxlX25hbWVHUSxNYXBsZX5JbnB1dEYnLyUsbWF0aHZhcmlhbnRHUSVib2xkRicvJStmb250d2VpZ2h0R0Y9LUkjbW9HRiQ2MVEiOkYnRi9GMkY4RjtGPi8lJmZlbmNlR0Y3LyUqc2VwYXJhdG9yR0Y3LyUpc3RyZXRjaHlHRjcvJSpzeW1tZXRyaWNHRjcvJShsYXJnZW9wR0Y3LyUubW92YWJsZWxpbWl0c0dGNy8lJ2FjY2VudEdGNy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlQtRiw2KVEld2l0aEYnRi9GMkY1RjhGO0Y+LUkobWZlbmNlZEdGJDYoLUYjNigtRiw2KVEpaW50dHJhbnNGJ0YvRjJGNUY4RjtGPkYyLyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lK2V4ZWN1dGFibGVHRjdGO0Y+Ri9GMkY4RjtGPkZARlctRmVuNigtRiM2KC1GLDYpUSZwbG90c0YnRi9GMkY1RjhGO0Y+RjJGXG9GX29GO0Y+Ri9GMkY4RjtGPkZARjJGXG9GX29GO0Y+">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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)-nu^2*u(x,t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ1RzYiNiRJInhHRilJInRHRilGLCwmLUYkNiQtRiQ2JEYnRitGKyIiIiomKUkjbnVHRikiIiNGMkYnRjIhIiI=</Equation></Text-field>
</Output>
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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>
</Output>
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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)=-delta;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ1RzYiNiRJInhHRilJInRHRilGKywkSSZkZWx0YUdGKSEiIg==</Equation></Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc2:=diff(u(x,t),x)=delta*beta;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ1RzYiNiRJInhHRilJInRHRilGKyomSSZkZWx0YUdGKSIiIkklYmV0YUdGKUYv</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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">LyomSSJzRzYiIiIiLUkiVUdGJTYjSSJ4R0YlRiYsJi1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtRi02JEYnRipGKkYmKiYpSSNudUdGJSIiI0YmRidGJiEiIg==</Equation></Text-field>
</Output>
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<Group labelreference="L9" drawlabel="true">
<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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">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJVRzYiNiNJInhHRilGKywkKiZJJmRlbHRhR0YpIiIiSSJzR0YpISIiRjE=</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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">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJVRzYiNiNJInhHRilGKyooSSZkZWx0YUdGKSIiIkklYmV0YUdGKUYuSSJzR0YpISIi</Equation></Text-field>
</Output>
</Group>
<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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">Ly1JIlVHNiI2I0kieEdGJSwmKiZJJF9DMUdGJSIiIi1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjKiYpLCZJInNHRiUhIiIqJClJI251R0YlIiIjRitGNiNGK0Y6RitGJ0YrRitGKyomSSRfQzJHRiVGKy1JJGNvc0dGLkYxRitGKw==</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+nu^2)^(1/2)*x)+c[2]*sinh((s+nu^2)^(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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">LCYqJiZJImNHNiI2IyIiIkYoLUklY29zaEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJjYjKiYpLCZJInNHRiZGKCokKUkjbnVHRiYiIiNGKEYoI0YoRjZGKEkieEdGJkYoRihGKComJkYlNiNGNkYoLUklc2luaEdGK0YuRihGKA==</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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">LCYqLkkmZGVsdGFHNiIiIiIsJi1JJWNvc2hHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2IyokKSwmSSJzR0YlRiYqJClJI251R0YlIiIjRiZGJiNGJkY1RiZGJkklYmV0YUdGJUYmRiYtSSVzaW5oR0YqRi0hIiJGL0Y6RjFGOi1GKTYjKiZGL0YmSSJ4R0YlRiZGJkYmKipGJEYmRi9GOkYxRjotRjlGPEYmRjo=</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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">KixJJmRlbHRhRzYiIiIiLCYtSSVjb3NoRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMqJiksJkkic0dGJEYlKiQpSSNudUdGJCIiI0YlRiUjRiVGNEYlLCZJInhHRiRGJUYlISIiRiVGJSomLUYoNiMqJkYuRiVGN0YlRiVJJWJldGFHRiRGJUYlRiUtSSVzaW5oR0YpNiMqJEYuRiVGOEYuRjhGMEY4</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L20" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U1(x):=subs(s=s-nu^2,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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">KixJJmRlbHRhRzYiIiIiLCYtSSVjb3NoRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMqJilJInNHRiQjRiUiIiNGJSwmSSJ4R0YkRiVGJSEiIkYlRiUqJi1GKDYjKiZGLkYlRjNGJUYlSSViZXRhR0YkRiVGJUYlLUklc2luaEdGKTYjKiRGLkYlRjRGLkY0LCZGL0YlKiQpSSNudUdGJEYxRiVGNEY0</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L21" 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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">LCQqJkkmZGVsdGFHNiIiIiIsJi1JJWNvc2hHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2IyomKUkic0dGJSNGJiIiI0YmLCZJInhHRiVGJkYmISIiRiZGJiomLUYpNiMqJkYvRiZGNEYmRiZJJWJldGFHRiVGJkYmRiZGNQ==</Equation></Text-field>
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<Group labelreference="L22" 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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">KigtSSVzaW5oRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMqJClJInNHRigjIiIiIiIjRi5GLkYrRi4sJkYsISIiKiQpSSNudUdGKEYvRi5GLkYu</Equation></Text-field>
</Output>
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<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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">NiQiIiEqJClJI251RzYiIiIjIiIi</Equation></Text-field>
</Output>
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<Group labelreference="L24" 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>
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<Group labelreference="L25" 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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">NiUsJComKUkjUGlHJSpwcm90ZWN0ZWRHIiIjIiIiKUklX1oxfGlyRzYiRihGKSEiIiIiISokKUkjbnVHRixGKEYp</Equation></Text-field>
</Output>
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<Group labelreference="L57" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The roots are:</Text-field>
</Input>
</Group>
<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">0,0,nu^2,-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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">NiYiIiFGIyokKUkjbnVHNiIiIiMiIiIsJComKUkibkdGJ0YoRikpSSNQaUclKnByb3RlY3RlZEdGKEYpISIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L27" 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>
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<Group labelreference="L28" 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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">LCQqLClJInNHNiIjIiIkIiIjIiIiSSZkZWx0YUdGJkYqLCYtSSVjb3NoRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiMqJilGJSNGKkYpRiosJkkieEdGJkYqRiohIiJGKkYqKiYtRi42IyomRjRGKkY3RipGKkklYmV0YUdGJkYqRipGKi1JJXNpbmhHRi82IyokRjRGKkY4LCZGJUY4KiQpSSNudUdGJkYpRipGKkY4Rjg=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L29" 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="L30" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">b[1]:=diff(b[2],s):</Text-field>
</Input>
</Group>
<Group labelreference="L31" 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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">KiYsJiomSSZkZWx0YUc2IiIiIkklYmV0YUdGJkYnISIiRiVGKUYnKUkjbnVHRiYiIiNGKQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L32" 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="L33" 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="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRIm5GJ0YyRjUvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnL0Y2USdub3JtYWxGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEjOj1GJ0ZALyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZLLyUpc3RyZXRjaHlHRksvJSpzeW1tZXRyaWNHRksvJShsYXJnZW9wR0ZLLyUubW92YWJsZWxpbWl0c0dGSy8lJ2FjY2VudEdGSy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlotSSZtZnJhY0dGJDYoLUYjNistSSNtbkdGJDYkUSIyRidGQC1GRjYtUTEmSW52aXNpYmxlVGltZXM7RidGQEZJRkxGTkZQRlJGVEZWL0ZZUSYwLjBlbUYnL0ZmbkZkby1GLzYlUScmIzk0ODtGJy9GM0ZLRkBGYG8tSShtZmVuY2VkR0YkNiQtRiM2Ji1GIzYnLUYvNiVRJWNvc2hGJ0Zpb0ZALUZGNi1RMCZBcHBseUZ1bmN0aW9uO0YnRkBGSUZMRk5GUEZSRlRGVkZjb0Zlby1GW3A2JC1GIzYlLUYjNiYtSSZtc3FydEdGJDYjLUYvNiVRJyYjOTU2O0YnRmlvRkBGYG8tRltwNiQtRiM2Ji1GLzYlUSJ4RidGMkY1LUZGNi1RKCZtaW51cztGJ0ZARklGTEZORlBGUkZURlYvRllRLDAuMjIyMjIyMmVtRicvRmZuRl5yLUZdbzYkUSIxRidGQEZARkBGQEY9RkBGQEY9RkAtRkY2LVEiK0YnRkBGSUZMRk5GUEZSRlRGVkZdckZfci1GIzYmLUYjNidGYXBGZHAtRltwNiQtRiM2JS1GIzYmRl1xRmBvRmdxRkBGPUZARkBGPUZARmBvLUYvNiVRJyYjOTQ2O0YnRmlvRkBGQEZARkBGYG9GXXFGPUZALUYjNiUtRiM2Ki1GIzYmLUYjNidGYXBGZHAtRltwNiQtRiM2JS1GIzYkRl1xRkBGPUZARkBGPUZARmBvLUklbXN1cEdGJDYlRmBxLUYjNictRl1vNiRRIjNGJ0ZALUZGNi1RIi9GJ0ZARklGTC9GT0Y0RlBGUkZURlYvRllRLDAuMTY2NjY2N2VtRicvRmZuRl51RlxvRj1GQC8lMXN1cGVyc2NyaXB0c2hpZnRHRkRGQEZqcS1GIzYoRmlzRmBvRl1xRmBvLUZidDYlLUYvNiVRJyYjOTU3O0YnRmlvRkBGXG9GYHVGQEZjci1GIzYoRmZ0RmBvLUYjNictRi82JVElc2luaEYnRmlvRkBGZHBGW3RGPUZARmBvRmBxRkBGanEtRiM2JkZbdkZgb0ZkdUZARkBGPUZALyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Zndi8lKWJldmVsbGVkR0ZLRj1GQA==">LCQqLCIiIyIiIkkmZGVsdGFHNiJGJSwmLUklY29zaEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJzYjKiYpSSNtdUdGJyNGJUYkRiUsJkkieEdGJ0YlRiUhIiJGJUYlKiYtRio2IyomRjBGJUY0RiVGJUklYmV0YUdGJ0YlRiVGJUYwRiUsKiomLUYqNiMqJEYwRiVGJSlGMSMiIiRGJEYlRiUqKEY9RiVGMEYlKUkjbnVHRidGJEYlRjUqKEZCRiUtSSVzaW5oR0YrRj5GJUYxRiVGJSomRkdGJUZERiVGNUY1RiU=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L34" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A[0]:=subs(mu^(1/2)=nu,mu^(3/2)=nu^3,mu=nu^2,A[n]):</Text-field>
</Input>
</Group>
<Group labelreference="L35" 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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">KipJJmRlbHRhRzYiIiIiLCYtSSVjb3NoRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMqJkkjbnVHRiRGJSwmSSJ4R0YkRiVGJSEiIkYlRiUqJi1GKDYjKiZGLkYlRjBGJUYlSSViZXRhR0YkRiVGJUYlRi5GMS1JJXNpbmhHRik2I0YuRjE=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L36" 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="L37" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">vars:={cos(n*Pi)=(-1)^n,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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">PCQvLUkkY29zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMqJkkibkdGKSIiIkkjUGlHRidGLSkhIiJGLC8tSSRzaW5HRiZGKiIiIQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L38" 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="L39" 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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">LCQqLCIiIyIiIkkmZGVsdGFHNiJGJS1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJzYjKihJIm5HRidGJUkjUGlHRitGJUkieEdGJ0YlRiUsJiomKUYvRiRGJSlGMEYkRiVGJSokKUkjbnVHRidGJEYlRiUhIiIsJkYlRiUqJilGOSwkRi9GOUYlSSViZXRhR0YnRiVGJUYlRjk=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L40" 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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">KigsJiomSSZkZWx0YUc2IiIiIkklYmV0YUdGJkYnISIiRiVGKUYnKUkjbnVHRiYiIiNGKUkic0dGJkYp</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L41" 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="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">LCQqKCwmIiIiRiVJJWJldGFHNiJGJUYlKUkjbnVHRiciIiMhIiJJJmRlbHRhR0YnRiVGKw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L42" 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="L43" 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="L44" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u0s:=subs(mu=nu^2,A[0]/(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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">KixJJmRlbHRhRzYiIiIiLCYtSSVjb3NoRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMqJkkjbnVHRiRGJSwmSSJ4R0YkRiVGJSEiIkYlRiUqJi1GKDYjKiZGLkYlRjBGJUYlSSViZXRhR0YkRiVGJUYlRi5GMS1JJXNpbmhHRik2I0YuRjEsJkkic0dGJEYlKiQpRi4iIiNGJUYxRjE=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L45" 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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">KixJJmRlbHRhRzYiIiIiLCYtSSVjb3NoRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMqJkkjbnVHRiRGJSwmSSJ4R0YkRiVGJSEiIkYlRiUqJi1GKDYjKiZGLkYlRjBGJUYlSSViZXRhR0YkRiVGJUYlRi5GMS1JJXNpbmhHRik2I0YuRjEtSSRleHBHRik2IyomKUYuIiIjRiVJInRHRiRGJUYl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L46" 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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">LCQqLiIiIyIiIkkmZGVsdGFHNiJGJS1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJzYjKihJIm5HRidGJUkjUGlHRitGJUkieEdGJ0YlRiUsJiomKUYvRiRGJSlGMEYkRiVGJSokKUkjbnVHRidGJEYlRiUhIiIsJkYlRiUqJilGOSwkRi9GOUYlSSViZXRhR0YnRiVGJUYlLCZJInNHRidGJUkjbXVHRidGOUY5Rjk=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L47" 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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">LCQqLiIiIyIiIkkmZGVsdGFHNiJGJS1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJzYjKihJIm5HRidGJUkjUGlHRitGJUkieEdGJ0YlRiUsJiomKUYvRiRGJSlGMEYkRiVGJSokKUkjbnVHRidGJEYlRiUhIiIsJkYlRiUqJilGOSwkRi9GOUYlSSViZXRhR0YnRiVGJUYlLUkkZXhwR0YqNiMqJkkjbXVHRidGJUkidEdGJ0YlRiVGOQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L48" 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="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEkdW50RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEjOj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GIzYmLUY2Ni1RKiZ1bWludXMwO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZVLUkmbWZyYWNHRiQ2KC1GIzYtLUkjbW5HRiQ2JFEiMkYnRjktRjY2LVExJkludmlzaWJsZVRpbWVzO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTkZeby1GLDYlUScmIzk0ODtGJy9GMEY9RjlGam4tRiM2Jy1GLDYlUSRjb3NGJ0Zjb0Y5LUY2Ni1RMCZBcHBseUZ1bmN0aW9uO0YnRjlGO0Y+RkBGQkZERkZGSEZdb0Zfby1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYjNigtRiw2JVEibkYnRi9GMkZqbi1GLDYlUScmIzk2MDtGJ0Zjb0Y5RmpuLUYsNiVRInhGJ0YvRjJGOS8lK2ZvcmVncm91bmRHUShbMCwwLDBdRidGOUY5RlxxRjlGam4tRl1wNiQtRiM2Ji1GZ242JFEiMUYnRjktRjY2LVEiK0YnRjlGO0Y+RkBGQkZERkZGSEZURlYtRiM2Ji1JJW1zdXBHRiQ2JS1GXXA2JC1GIzYlRlFGY3FGOUY5LUYjNiZGUUZjcEZccUY5LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0Zqbi1GLDYlUScmIzk0NjtGJ0Zjb0Y5RjlGOUY5RmpuLUZccjYlLUY2Ni1RLyZFeHBvbmVudGlhbEU7RidGOUY7Rj5GQEZCRkRGRkZIRl1vL0ZOUSwwLjExMTExMTFlbUYnLUYjNiZGUS1GIzYoLUZccjYlRmNwRmZuRmRyRmpuLUZccjYlRmZwRmZuRmRyRmpuLUYsNiVRInRGJ0YvRjJGOUZccUY5RmRyRlxxRjktRiM2JS1GIzYmLUYjNiZGZXNGam5GZ3NGOUZmcS1GIzYkLUZccjYlLUYsNiVRJyYjOTU3O0YnRmNvRjlGZm5GZHJGOUY5RlxxRjkvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRl51LyUpYmV2ZWxsZWRHRj1GXHFGOUZccUY5">LCQqLiIiIyIiIkkmZGVsdGFHNiJGJS1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJzYjKihJIm5HRidGJUkjUGlHRitGJUkieEdGJ0YlRiUsJiomKUYvRiRGJSlGMEYkRiVGJSokKUkjbnVHRidGJEYlRiUhIiIsJkYlRiUqJilGOSwkRi9GOUYlSSViZXRhR0YnRiVGJUYlLUkkZXhwR0YqNiMsJCooRjRGJUY1RiVJInRHRidGJUY5RiVGOQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L49" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U:=b1t*exp(-nu^2*t)+b2t*exp(-nu^2*t)+simplify(u0t*exp(-nu^2*t))+exp(-nu^2*t)*Sum(unt,n=1..infinity);</Text-field>
</Input>
<Output>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u:=piecewise(t=0,0,t&gt;0,subs(infinity=20,U)):</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pars:={nu=1,delta=1,beta=0.1};</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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">PCUvSSNudUc2IiIiIi9JJWJldGFHRiUkRiYhIiIvSSZkZWx0YUdGJUYm</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot3d(subs(pars,u),x=0..1,t=0..0.5,axes=boxed,title=&quot;Figure Exp. 8.21.&quot;,labels=[x,t,&quot;u&quot;],orientation=[-60,60]);</Text-field>
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<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>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot([subs(t=0,pars,u),subs(t=0.05,pars,u),subs(t=0.1,pars,u),subs(t=0.2,pars,u)],x=0..1,axes=boxed,title=&quot;Figure Exp. 8.22.&quot;,thickness=5,labels=[x,&quot;u&quot;]);</Text-field>
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<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, 9084 characters]</Plot></Text-field>
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<Text-field style="Text" layout="Normal">In all the examples discussed in this chapter until now, the roots of q(s) were obtained analytically.  This is not always possible.  Often the roots should be obtained numerically as in section 7.1.4.  This is illustrated in the next example.</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRicvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
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