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<Text-field style="Heading 3" layout="Heading 3"><Font italic="false">Example 4.7  Unsteady State Diffusion with a First-Order Reacton</Font></Text-field>
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<Text-field style="Text" layout="Normal">Consider the transient diffusion problem.[6]  The governing equation is</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
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<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">                                                                             u(x,0) = 0                                                    (4.1.7)</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">                                                                                                                                 </Text-field>
<Text-field style="Text" layout="Normal">                                                                           <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEidUYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMg==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEidUYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMg==</Equation> (0,t) = 1<Font encoding="UTF-8"> and u(\342\210\236,t) is defined    </Font></Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">where D is the diffusivity (m<Font superscript="true" size="10">2</Font>/s)  and k is the rate constant (s<Font superscript="true" size="10">-1</Font>) .  Equation (4.1.7) is solved in Maple below using the Laplace transform technique:</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal256">restart:with(linalg):with(inttrans):with(plots):</Text-field>
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<Group labelreference="L4" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal256">eq:=diff(u(x,t),t)=D*diff(u(x,t),x$2)-k*u(x,t);</Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjZXFHNiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInVHRiQ2JEkieEdGJEkidEdGJEYuLCYqJkkiREc2JEYoSShfc3lzbGliR0YkIiIiLUYnNiRGKi1JIiRHRig2JEYtIiIjRjRGNComSSJrR0YkRjRGKkY0ISIi">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ1RzYiNiRJInhHRilJInRHRilGLCwmKiZJIkRHNiRGJUkoX3N5c2xpYkdGKSIiIi1GJDYkLUYkNiRGJ0YrRitGMkYyKiZJImtHRilGMkYnRjIhIiI=</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal256">u(x,0):=0;</Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi1JInVHNiI2JEkieEdGJSIiIUYo">IiIh</Equation></Text-field>
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<Group labelreference="L6" drawlabel="true">
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc1:=u(0,t)=1;</Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMxRzYiLy1JInVHRiQ2JCIiIUkidEdGJCIiIg==">Ly1JInVHNiI2JCIiIUkidEdGJSIiIg==</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc2:=u(infinity,t)=defined;</Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMyRzYiLy1JInVHRiQ2JEkpaW5maW5pdHlHJSpwcm90ZWN0ZWRHSSJ0R0YkSShkZWZpbmVkR0Yk">Ly1JInVHNiI2JEkpaW5maW5pdHlHJSpwcm90ZWN0ZWRHSSJ0R0YlSShkZWZpbmVkR0Yl</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 style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkZXFzRzYiLyomSSJzR0YkIiIiLUkobGFwbGFjZUdGJDYlLUkidUdGJDYkSSJ4R0YkSSJ0R0YkRjBGJ0YoLCYqJkkiREc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJEYoLUklZGlmZkdGNTYkRiktSSIkR0Y1NiRGLyIiI0YoRigqJkkia0dGJEYoRilGKCEiIg==">LyomSSJzRzYiIiIiLUkobGFwbGFjZUdGJTYlLUkidUdGJTYkSSJ4R0YlSSJ0R0YlRi5GJEYmLCYqJkkiREc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJUYmLUklZGlmZkdGMzYkLUY2NiRGJ0YtRi1GJkYmKiZJImtHRiVGJkYnRiYhIiI=</Equation></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="PkkkZXFzRzYiLyomSSJzR0YkIiIiLUkiVUdGJDYjSSJ4R0YkRigsJiomSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkRigtSSVkaWZmR0YxNiRGKS1JIiRHRjE2JEYsIiIjRihGKComSSJrR0YkRihGKUYoISIi">LyomSSJzRzYiIiIiLUkiVUdGJTYjSSJ4R0YlRiYsJiomSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlRiYtSSVkaWZmR0YvNiQtRjI2JEYnRipGKkYmRiYqJkkia0dGJUYmRidGJiEiIg==</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 style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMxRzYiLy1JKGxhcGxhY2VHRiQ2JS1JInVHRiQ2JCIiIUkidEdGJEYtSSJzR0YkKiRGLiEiIg==">Ly1JKGxhcGxhY2VHNiI2JS1JInVHRiU2JCIiIUkidEdGJUYrSSJzR0YlKiRGLCEiIg==</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc1:=subs(laplace(u(0,t),t,s)=U(0),bc1);</Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMxRzYiLy1JIlVHRiQ2IyIiISokSSJzR0YkISIi">Ly1JIlVHNiI2IyIiISokSSJzR0YlISIi</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U(x):=rhs(dsolve({eqs,bc1}));</Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi1JIlVHNiI2I0kieEdGJSwmKigsJiIiIiEiIiomSSRfQzJHRiVGK0kic0dGJUYrRitGK0YvRiwtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2IyooKUkiREdGMiNGKyIiI0YsKSwmRi9GK0kia0dGJUYrRjlGK0YnRitGK0YsKiZGLkYrLUYxNiMsJEY2RixGK0Yr">LCYqKCwmISIiIiIiKiZJJF9DMkc2IkYmSSJzR0YpRiZGJkYmRipGJS1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGKTYjKihJIkRHRi0jRiUiIiMsJkYqRiZJImtHRilGJiNGJkY0SSJ4R0YpRiZGJkYlKiZGKEYmLUYsNiMsJEYxRiVGJkYm</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal256">eqc:=coeff(U(x),exp(1/D^(1/2)*(s+k)^(1/2)*x));</Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkZXFjRzYiLCQqJiwmIiIiISIiKiZJJF9DMkdGJEYoSSJzR0YkRihGKEYoRixGKUYp">LCQqJiwmISIiIiIiKiZJJF9DMkc2IkYmSSJzR0YpRiZGJkYmRipGJUYl</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">_C2:=solve(eqc,_C2);</Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkX0MyRzYiKiRJInNHRiQhIiI=">KiRJInNHNiIhIiI=</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal256">U(x):=eval(U(x));</Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi1JIlVHNiI2I0kieEdGJSomSSJzR0YlISIiLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiMsJCooKUkiREdGLSMiIiIiIiNGKiksJkYpRjZJImtHRiVGNkY1RjZGJ0Y2RipGNg==">KiZJInNHNiIhIiItSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IywkKihJIkRHRigjRiUiIiMsJkYjIiIiSSJrR0YkRjIjRjJGMEkieEdGJEYyRiVGMg==</Equation></Text-field>
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<Text-field style="Text" layout="Normal">Here again Maple cannot find the inverse Laplace transform:</Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">invlaplace(U(x),s,t);</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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">LUkraW52bGFwbGFjZUc2IjYlKiZJInNHRiQhIiItSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IywkKihJIkRHRisjRigiIiMsJkYnIiIiSSJrR0YkRjUjRjVGM0kieEdGJEY1RihGNUYnSSJ0R0Yk</Equation></Text-field>
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<Text-field style="Text" layout="Normal">From the poperty of the laplace transform,[7] we n=know that</Text-field>
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<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L17" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U1:=U(x)*s;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjVTFHNiItSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IywkKigpSSJER0YnIyIiIiIiIyEiIiksJkkic0dGJEYwSSJrR0YkRjBGL0YwSSJ4R0YkRjBGMg==">LUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJCooSSJER0YkIyEiIiIiIywmSSJzR0YnIiIiSSJrR0YnRjEjRjFGLkkieEdGJ0YxRi0=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L44" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Again, Maple cannot invert U1 directly:</Text-field>
</Input>
</Group>
<Group labelreference="L18" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">invlaplace(U1,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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">LUkraW52bGFwbGFjZUc2IjYlLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJCooSSJER0YoIyEiIiIiIywmSSJzR0YkIiIiSSJrR0YkRjQjRjRGMUkieEdGJEY0RjBGM0kidEdGJA==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L45" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Another formula[7] is used:</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L19" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U2:=subs(s=s-k,U1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjVTJHNiItSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IywkKigpSSJER0YnIyIiIiIiIyEiIilJInNHRiRGL0YwSSJ4R0YkRjBGMg==">LUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJCooSSJER0YkIyEiIiIiI0kic0dGJyMiIiJGLkkieEdGJ0YxRi0=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L46" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The inverse transform for U2 is:</Text-field>
</Input>
</Group>
<Group labelreference="L51" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U2:=subs({D=D1,x=x1},U2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjVTJHNiItSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IywkKigpSSNEMUdGJCMiIiIiIiMhIiIpSSJzR0YkRi9GMEkjeDFHRiRGMEYy">LUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJCooSSNEMUdGJyMhIiIiIiNJInNHRicjIiIiRi5JI3gxR0YnRjFGLQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L49" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">assume(D1&gt;0,x1&gt;0);</Text-field>
</Input>
</Group>
<Group labelreference="L20" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u2:=invlaplace(U2,s,t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjdTJHNiIsJCosIyIiIiIiI0YoKSomSSREMXxpckdGJEYoSSNQaUclKnByb3RlY3RlZEdGKEYnISIiKUkidEdGJCMiIiRGKUYvSSR4MXxpckdGJEYoLUkkZXhwRzYkRi5JKF9zeXNsaWJHRiQ2IywkKiojRigiIiVGKClGNEYpRihGLEYvRjFGL0YvRihGKA==">LCQqKiomSSREMXxpckc2IiIiIkkjUGlHJSpwcm90ZWN0ZWRHRicjISIiIiIjSSJ0R0YmIyEiJEYsSSR4MXxpckdGJkYnLUkkZXhwRzYkRilJKF9zeXNsaWJHRiY2IywkKihGMEYsRiVGK0YtRisjRisiIiVGJyNGJ0Ys</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L52" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u2:=subs({D1=D,x1=x},u2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjdTJHNiIsJCosIyIiIiIiI0YoKSomSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkRihJI1BpR0YuRihGJyEiIilJInRHRiQjIiIkRilGMUkieEdGJEYoLUkkZXhwR0YtNiMsJCoqI0YoIiIlRigpRjZGKUYoRixGMUYzRjFGMUYoRig=">LCQqKiomSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiIiIiSSNQaUdGJ0YqIyEiIiIiI0kidEdGKSMhIiRGLkkieEdGKUYqLUkkZXhwR0YmNiMsJCooRjJGLkYlRi1GL0YtI0YtIiIlRiojRipGLg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L47" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The inverse transform for U1 iS:</Text-field>
</Input>
</Group>
<Group labelreference="L21" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u1:=exp(-k*t)*u2;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjdTFHNiIsJCouIyIiIiIiI0YoLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJComSSJrR0YkRihJInRHRiRGKCEiIkYoKSomSSJER0YsRihJI1BpR0YtRihGJ0Y0KUYzIyIiJEYpRjRJInhHRiRGKC1GKzYjLCQqKiNGKCIiJUYoKUY8RilGKEY3RjRGM0Y0RjRGKEYo">LCQqLC1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCQqJkkia0dGKSIiIkkidEdGKUYuISIiRi4qJkkiREdGJkYuSSNQaUdGJ0YuI0YwIiIjRi8jISIkRjVJInhHRilGLi1GJTYjLCQqKEY4RjVGMkYwRi9GMCNGMCIiJUYuI0YuRjU=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L22" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">I1:=int(u1,t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjSTFHNiItSSRpbnRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2JCwkKi4jIiIiIiIjRi4tSSRleHBHRic2IywkKiZJImtHRiRGLkkidEdGJEYuISIiRi4pKiZJIkRHRidGLkkjUGlHRihGLkYtRjcpRjYjIiIkRi9GN0kieEdGJEYuLUYxNiMsJCoqI0YuIiIlRi4pRj9GL0YuRjpGN0Y2RjdGN0YuRi5GNg==">LUkkaW50RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQsJCosLUkkZXhwR0YkNiMsJComSSJrR0YnIiIiSSJ0R0YnRjEhIiJGMSomSSJER0YkRjFJI1BpR0YlRjEjRjMiIiNGMiMhIiRGOEkieEdGJ0YxLUYsNiMsJCooRjtGOEY1RjNGMkYzI0YzIiIlRjEjRjFGOEYy</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L23" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">with(student):</Text-field>
</Input>
</Group>
<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">I1:=simplify(changevar(t=x^2/4/D/T^2,I1,T));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjSTFHNiIsJCosIiIjIiIiKUkjUGlHJSpwcm90ZWN0ZWRHI0YoRichIiIpSSJER0koX3N5c2xpYkdGJEYsRi1JInhHRiRGKC1JJGludEc2JEYrRjA2JCooLUkkZXhwR0Y0NiMsJCoqI0YoIiIlRigsJiomSSJrR0YkRigpRjFGJ0YoRigqKEY9RigpSSJUR0YkRj1GKEYvRihGKEYoRi9GLSlGREYnRi1GLUYoRkRGLSkqKEZBRihGL0YtRkVGLUYsRi1GREYoRi0=">LCQqKkkjUGlHJSpwcm90ZWN0ZWRHIyEiIiIiI0kiREdJKF9zeXNsaWJHNiJGJkkieEdGKyIiIi1JJGludEc2JEYlRio2JCooLUkkZXhwR0YwNiMsJCooLCYqJkkia0dGK0YtRixGKEYtKiZJIlRHRisiIiVGKUYtRj1GLUYpRidGPCEiIyNGJ0Y9Ri1GPEYnKihGLEYoRilGJ0Y8Rj5GJkY8Ri1GPg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">I1:=subs(T=T1,x=x1,D=D1,I1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjSTFHNiIsJCosIiIjIiIiKUkjUGlHJSpwcm90ZWN0ZWRHI0YoRichIiIpSSREMXxpckdGJEYsRi1JJHgxfGlyR0YkRigtSSRpbnRHNiRGK0koX3N5c2xpYkdGJDYkKigtSSRleHBHRjM2IywkKiojRigiIiVGKCwmKiZJImtHRiRGKClGMEYnRihGKCooRj1GKClJI1QxR0YkRj1GKEYvRihGKEYoRi9GLSlGREYnRi1GLUYoRkRGLSkqKEZBRihGL0YtRkVGLUYsRi1GREYoRi0=">LCQqKkkjUGlHJSpwcm90ZWN0ZWRHIyEiIiIiI0kkRDF8aXJHNiJGJkkkeDF8aXJHRioiIiItSSRpbnRHNiRGJUkoX3N5c2xpYkdGKjYkKigtSSRleHBHRi82IywkKigsJiomSSJrR0YqRixGK0YoRiwqJkkjVDFHRioiIiVGKUYsRj1GLEYpRidGPCEiIyNGJ0Y9RixGPEYnKihGK0YoRilGJ0Y8Rj5GJkY8RixGPg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">assume(T1&gt;0);</Text-field>
</Input>
</Group>
<Group labelreference="L27" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">I1:=simplify(I1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjSTFHNiIsJiooIyIiIiIiI0YoLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMqKEkkeDF8aXJHRiRGKClJJEQxfGlyR0YkRichIiIpSSJrR0YkRidGKEYoLUkkZXJmR0YsNiMsJCoqRidGKCwmKihGKUYoRjNGKClJJFQxfGlyR0YkRilGKEYoKihGMUYoRjJGKEY1RihGKEYoRj9GNEYzRjRGKEYoRjQqKEYnRigtRis2IywkRjBGNEYoLUY4NiMsJCoqRidGKCwmRj1GNEZARihGKEY/RjRGM0Y0RihGKEYo">LCYqJi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjKihJJHgxfGlyR0YpIiIiSSREMXxpckdGKSMhIiIiIiNJImtHRikjRi1GMUYtLUkkZXJmR0YmNiMsJCooLCYqJkYuRi1JJFQxfGlyR0YpRjFGMSooRixGLUYuRjNGMkYzRi1GLUY7RjBGLkYwRjNGLUYvKiYtRiU2IywkRitGMEYtLUY1NiMsJCooLCZGOiEiI0Y8Ri1GLUY7RjBGLkYwRjNGLUYz</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">I1:=subs({x1=x,T1=T,D1=D},I1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjSTFHNiIsJiooIyIiIiIiI0YoLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMqKEkieEdGJEYoKUkiREdGLkYnISIiKUkia0dGJEYnRihGKC1JJGVyZkdGLDYjLCQqKkYnRigsJiooRilGKEYzRigpSSJUR0YkRilGKEYoKihGMUYoRjJGKEY1RihGKEYoRj9GNEYzRjRGKEYoRjQqKEYnRigtRis2IywkRjBGNEYoLUY4NiMsJCoqRidGKCwmRj1GNEZARihGKEY/RjRGM0Y0RihGKEYo">LCYqJi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjKihJInhHRikiIiJJIkRHRigjISIiIiIjSSJrR0YpI0YtRjFGLS1JJGVyZkdGJjYjLCQqKCwmKiZGLkYtSSJUR0YpRjFGMSooRixGLUYuRjNGMkYzRi1GLUY7RjBGLkYwRjNGLUYvKiYtRiU2IywkRitGMEYtLUY1NiMsJCooLCZGOiEiI0Y8Ri1GLUY7RjBGLkYwRjNGLUYz</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L29" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">I1:=expand(I1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjSTFHNiIsJiooIyIiIiIiI0YoLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMqKEkieEdGJEYoKUkiREdGLkYnISIiKUkia0dGJEYnRihGKC1JJGVyZkdGLDYjLCZJIlRHRiRGKCosRidGKEY7RjRGMkY0RjFGKEY1RihGKEYoRjQqKEYnRihGKkY0LUY4NiMsJkY7RihGPEY0RihGNA==">LCYqJi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjKihJInhHRikiIiJJIkRHRigjISIiIiIjSSJrR0YpI0YtRjFGLS1JJGVyZkdGJjYjLCZJIlRHRilGLSoqRjhGMEYuRi9GLEYtRjJGM0YzRi1GLyomRiRGMC1GNTYjLCZGOEYtRjlGL0YtRi8=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L30" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">I2:=eval(subs(T=infinity,I1));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjSTJHNiIsJiomIyIiIiIiI0YoLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMqKEkieEdGJEYoKUkiREdGLkYnISIiKUkia0dGJEYnRihGKEY0KiZGJ0YoRipGNEY0">LCYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IyooSSJ4R0YoIiIiSSJER0YnIyEiIiIiI0kia0dGKCNGLEYwRi4qJEYjRi9GLg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L31" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u:=I1-I2;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkidUc2IiwqKigjIiIiIiIjRigtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IyooSSJ4R0YkRigpSSJER0YuRichIiIpSSJrR0YkRidGKEYoLUkkZXJmR0YsNiMsJkkiVEdGJEYoKixGJ0YoRjtGNEYyRjRGMUYoRjVGKEYoRihGNCooRidGKEYqRjQtRjg2IywmRjtGKEY8RjRGKEY0KiZGJ0YoRipGKEYoKiZGJ0YoRipGNEYo">LCoqJi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjKihJInhHRikiIiJJIkRHRigjISIiIiIjSSJrR0YpI0YtRjFGLS1JJGVyZkdGJjYjLCZJIlRHRilGLSoqRjhGMEYuRi9GLEYtRjJGM0YzRi1GLyomRiRGMC1GNTYjLCZGOEYtRjlGL0YtRi9GJEYzKiRGJEYwRjM=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u:=collect(u,exp(x/D^(1/2)*k^(1/2)));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkidUc2IiwmKiYsJiomIyIiIiIiI0YqLUkkZXJmRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJkkiVEdGJEYqKixGKUYqRjMhIiIpSSJER0YwRilGNUkieEdGJEYqKUkia0dGJEYpRipGKkYqRjVGKUYqRiotSSRleHBHRi42IyooRjhGKkY2RjVGOUYqRipGKiomLCYqJkYpRiotRi02IywmRjNGKkY0RjVGKkY1RilGKkYqRjtGNUYq">LCYqJiwmLUkkZXJmRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJkkiVEdGKiIiIioqRi0hIiJJIkRHRikjRjAiIiNJInhHRipGLkkia0dGKiNGLkYzRjZGMkY2Ri5GLi1JJGV4cEdGJzYjKihGNEYuRjFGMkY1RjZGLkYuKiYsJi1GJjYjLCZGLUYuRi9GMkYyRjZGLkYuRjdGMEYu</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L33" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u:=convert(u,erfc);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkidUc2IiwmKigjIiIiIiIjRigtSSVlcmZjRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJkkiVEdGJEYoKixGJ0YoRjEhIiIpSSJER0YuRidGM0kieEdGJEYoKUkia0dGJEYnRihGKEYoLUkkZXhwR0YsNiMqKEY2RihGNEYzRjdGKEYoRigqKEYnRigtRis2IywmRjFGKEYyRjNGKEY5RjNGKA==">LCYqJi1JJWVyZmNHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywmSSJUR0YpIiIiKipGLCEiIkkiREdGKCNGLyIiI0kieEdGKUYtSSJrR0YpI0YtRjJGNUYtLUkkZXhwR0YmNiMqKEYzRi1GMEYxRjRGNUYtRjUqJi1GJTYjLCZGLEYtRi5GMUYtRjZGL0Y1</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L34" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u:=subs(T=x/2/(D*t)^(1/2),u);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkidUc2IiwmKigjIiIiIiIjRigtSSVlcmZjRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJiooRidGKEkieEdGJEYoKSomSSJER0YuRihJInRHRiRGKEYnISIiRigqKEYzRigpRjVGJ0Y3KUkia0dGJEYnRihGKEYoLUkkZXhwR0YsNiMqKEYyRihGOUY3RjpGKEYoRigqKEYnRigtRis2IywmRjFGKEY4RjdGKEY8RjdGKA==">LCYqJi1JJWVyZmNHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywmKiZJInhHRikiIiIqJkkiREdGKEYuSSJ0R0YpRi4jISIiIiIjI0YuRjQqKEYvRjVGMEYySSJrR0YpRjVGLkYuLUkkZXhwR0YmNiMqKEYtRi5GMEYyRjdGNUYuRjUqJi1GJTYjLCZGLEY1RjZGM0YuRjhGM0Y1</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L35" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">convert(expand(simplify(eval(subs(k=0,u)))),erfc);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LUklZXJmY0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCQqJkkieEdGJyIiIiomSSJER0YmRixJInRHRidGLCMhIiIiIiMjRixGMg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L36" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">expand(D*(expand(-eval(subs(x=0,diff(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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">LCYqKkkiREdJKF9zeXNsaWJHNiIiIiJJI1BpRyUqcHJvdGVjdGVkRyMhIiIiIiMtSSRleHBHNiRGKUYlNiMqJkkia0dGJkYnSSJ0R0YmRidGKyomRiRGJ0YzRidGKkYnKihGJCNGJ0YsRjJGNi1JJGVyZkdGLzYjKihGNEY2RiRGKkYyRjZGJ0Yn</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L37" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pars:={D=1e-6,k=0.1};</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklcGFyc0c2IjwkL0kiREdJKF9zeXNsaWJHRiQkIiIiISInL0kia0dGJCRGKiEiIg==">PCQvSSJER0koX3N5c2xpYkc2IiQiIiIhIicvSSJrR0YmJEYoISIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L38" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot3d(subs(pars,u),x=1e-3..0,t=10..0,axes=boxed,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, 13644 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L39" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pfs:=plot([subs(pars,t=0.01,u),subs(pars,t=0.1,u),subs(pars,t=1,u),subs(pars,t=2,u)],x=0..1e-3,axes=boxed,thickness=5,labels=[x,&quot;u&quot;]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="[encoded data, 6832 characters]">[encoded data, 6800 characters]</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L41" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pts:=textplot([[0.00016,evalf(subs(pars,t=0.01,x=0.0001,u)),&quot;t=0.01&quot;],[0.00036,evalf(subs(pars,t=0.1,x=0.0003,u)),&quot;t=0.1&quot;],[0.00053,evalf(subs(pars,t=1,x=0.0006,u)),&quot;t=1&quot;],[0.00069,evalf(subs(pars,t=2,x=0.0006,u)),&quot;t=2&quot;]]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkcHRzRzYiLUkvSU5URVJGQUNFX1BMT1RHRiQ2Ji1JJVRFWFRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2JDckJCIjOyEiJiQiK3dgKyR6JSEjNVEndD0wLjAxRiQtRik2JDckJCIjT0YxJCIraTVGLl1GNFEmdD0wLjFGJC1GKTYkNyQkIiNgRjEkIitpaHBIbEY0USR0PTFGJC1GKTYkNyQkIiNwRjEkIitONFFOdEY0USR0PTJGJA==">LSUlUExPVEc2Ji1JJVRFWFRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JDckJCIjOyEiJiQiK3dgKyR6JSEjNVEndD0wLjAxRiotRiY2JDckJCIjT0YvJCIraTVGLl1GMlEmdD0wLjFGKi1GJjYkNyQkIiNgRi8kIitpaHBIbEYyUSR0PTFGKi1GJjYkNyQkIiNwRi8kIitONFFOdEYyUSR0PTJGKg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L53" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display({pfs,pts});</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="400" type="two-dimensional" width="400" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="false">[encoded data, 9568 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L54" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
</Worksheet>