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<Input>
<Text-field style="Heading 3" layout="Heading 3"><Font italic="false">Example 2.4 Time Varying Input to a CSTR with a Series Reaction</Font></Text-field>
</Input>
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<Input>
<Text-field style="Text" layout="Normal">The concentration as a function of time in this CSTR reactor can be obtained by following the procedure described earlier for nonhomogeneous linear ordinary differential equations.</Text-field>
</Input>
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<Group labelreference="L34" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart:</Text-field>
</Input>
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<Group labelreference="L4" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">with(linalg):with(plots):with(Units):</Text-field>
</Input>
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<Group labelreference="L35" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Specify the number of ordinary differential equations (ODEs).</Text-field>
</Input>
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<Group labelreference="L5" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=3;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiTkc2IiIiJA==">IiIk</Equation></Text-field>
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<Group labelreference="L36" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Use Maple commands to generate the three governing equations.</Text-field>
</Input>
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<Group labelreference="L6" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq[1]:=diff(C[A](t),t)=1/tau*(C[Ain]-C[A](t))-k[1]*C[A](t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJDR0YlNiNJIkFHRiU2I0kidEdGJUYzLCYqJkkkdGF1R0YlISIiLCYmRi82I0kkQWluR0YlRidGLUY3RidGJyomJkkia0dGJUYmRidGLUYnRjc=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkiQ0c2IjYjSSJBR0YqNiNJInRHRipGLiwmKiZJJHRhdUdGKiEiIiwmJkYpNiNJJEFpbkdGKiIiIkYnRjJGN0Y3KiYmSSJrR0YqNiNGN0Y3RidGN0Yy</Equation></Text-field>
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<Group labelreference="L7" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq[2]:=diff(C[B](t),t)=-1/tau*(C[B](t))+k[1]*C[A](t)-k[2]*C[B](t);</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiMvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJDR0YlNiNJIkJHRiU2I0kidEdGJUYzLCgqJkkkdGF1R0YlISIiRi0iIiJGNyomJkkia0dGJTYjRjhGOC0mRi82I0kiQUdGJUYyRjhGOComJkY7RiZGOEYtRjhGNw==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkiQ0c2IjYjSSJCR0YqNiNJInRHRipGLiwoKiZJJHRhdUdGKiEiIkYnIiIiRjIqJiZJImtHRio2I0YzRjMtJkYpNiNJIkFHRipGLUYzRjMqJiZGNjYjIiIjRjNGJ0YzRjI=</Equation></Text-field>
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<Group labelreference="L8" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq[3]:=diff(C[C](t),t)=-1/tau*(C[C](t))+k[2]*C[B](t);</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiQvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJDR0YlNiNGLzYjSSJ0R0YlRjIsJiomSSR0YXVHRiUhIiJGLSIiIkY2KiYmSSJrR0YlNiMiIiNGNy0mRi82I0kiQkdGJUYxRjdGNw==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkiQ0c2IjYjRik2I0kidEdGKkYtLCYqJkkkdGF1R0YqISIiRiciIiJGMSomJkkia0dGKjYjIiIjRjItJkYpNiNJIkJHRipGLEYyRjI=</Equation></Text-field>
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<Group labelreference="L37" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Specify the input to the reactor as pars here.</Text-field>
</Input>
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<Group labelreference="L9" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pars:={C[Ain]=1+sin(2*t)};</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklcGFyc0c2IjwjLyZJIkNHRiQ2I0kkQWluR0YkLCYiIiJGLC1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjLCQqJiIiI0YsSSJ0R0YkRixGLEYs">PCMvJkkiQ0c2IjYjSSRBaW5HNiIsJiIiIiIiIi1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCQqJiIiIyIiIkkidEc2IiIiIiIiIiIiIg==</Equation></Text-field>
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<Group labelreference="L38" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Name the dependent variables.</Text-field>
</Input>
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<Group labelreference="L10" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal262">vars:=[C[A](t),C[B](t),C[C](t)];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkldmFyc0c2IjclLSZJIkNHRiQ2I0kiQUdGJDYjSSJ0R0YkLSZGKDYjSSJCR0YkRistJkYoNiNGKEYr">NyUtJkkiQ0c2IjYjSSJBR0YmNiNJInRHRiYtJkYlNiNJIkJHRiZGKS0mRiU2I0YlRik=</Equation></Text-field>
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<Group labelreference="L39" drawlabel="true">
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<Text-field style="Text" layout="Normal">Specify the right hand sides of the governing equations.</Text-field>
</Input>
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<Group labelreference="L11" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal262">eqs:=[seq(rhs(eq[i]),i=1..3)];</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkZXFzRzYiNyUsJiomSSR0YXVHRiQhIiIsJiZJIkNHRiQ2I0kkQWluR0YkIiIiLSZGLDYjSSJBR0YkNiNJInRHRiRGKUYvRi8qJiZJImtHRiQ2I0YvRi9GMEYvRiksKComRihGKS0mRiw2I0kiQkdGJEY0Ri9GKUY2Ri8qJiZGODYjIiIjRi9GPEYvRiksJiomRihGKS0mRiw2I0YsRjRGL0YpRkBGLw==">NyUsJiomSSR0YXVHNiIhIiIsJiZJIkNHRiY2I0kkQWluR0YmIiIiLSZGKjYjSSJBR0YmNiNJInRHRiZGJ0YtRi0qJiZJImtHRiY2I0YtRi1GLkYtRicsKComRiVGJy0mRio2I0kiQkdGJkYyRi1GJ0Y0Ri0qJiZGNjYjIiIjRi1GOkYtRicsJiomRiVGJy0mRio2I0YqRjJGLUYnRj5GLQ==</Equation></Text-field>
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<Group labelreference="L40" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Form the set of right hand sides of the equations with the time dependent input to the tank.</Text-field>
</Input>
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<Group labelreference="L12" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqs:=subs(pars,eqs);</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkZXFzRzYiNyUsJiomSSR0YXVHRiQhIiIsKCIiIkYrLUkkc2luRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJComIiIjRitJInRHRiRGK0YrRistJkkiQ0dGJDYjSSJBR0YkNiNGNUYpRitGKyomJkkia0dGJDYjRitGK0Y2RitGKSwoKiZGKEYpLSZGODYjSSJCR0YkRjtGK0YpRjxGKyomJkY+NiNGNEYrRkJGK0YpLCYqJkYoRiktJkY4NiNGOEY7RitGKUZGRis=">NyUsJiomSSR0YXVHNiIhIiIsKCIiIkYpLUkkc2luRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiMsJComIiIjRilJInRHRiZGKUYpRiktJkkiQ0dGJjYjSSJBR0YmNiNGM0YnRilGKSomJkkia0dGJjYjRilGKUY0RilGJywoKiZGJUYnLSZGNjYjSSJCR0YmRjlGKUYnRjpGKSomJkY8NiNGMkYpRkBGKUYnLCYqJkYlRictJkY2NiNGNkY5RilGJ0ZERik=</Equation></Text-field>
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<Group labelreference="L41" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Use 'eqs' and 'vars' to find the coefficient matrix A and the forcing function vector b.  In this case, we find b1 and then b since b = - b.  The A matrix and b1 vector are generated as described in the procedure for nonlinear homogeneous ODEs:</Text-field>
</Input>
</Group>
<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal262">A:=genmatrix(eqs,vars,'b1');</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiQUc2Ii1JJ21hdHJpeEdGJDYjNyU3JSwmKiRJJHRhdUdGJCEiIkYtJkkia0dGJDYjIiIiRi0iIiFGMjclRi4sJkYrRi0mRi82IyIiI0YtRjI3JUYyRjUsJEYrRi0=">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</Equation></Text-field>
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<Input>
<Text-field style="Text" layout="Normal">Use b1 to find b.</Text-field>
</Input>
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<Group labelreference="L14" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">b:=matrix(N,1);for i to N do b[i,1]:=-b1[i];od:evalm(b);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiYkc2Ii1JJmFycmF5RyUqcHJvdGVjdGVkRzYlOyIiIiIiJDtGKkYqNyI=">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</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUknbWF0cml4RzYiNiM3JTcjKiZJJHRhdUdGJCEiIiwmIiIiRiwtSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IywkKiYiIiNGLEkidEdGJEYsRixGLEYsNyMiIiFGNw==">PTYiNiQ7IiIiIiIkO0YmRiZFXFtsJDYkIiIjRiYiIiE2JEYnRiZGLDYkRiZGJiomSSR0YXVHRiMhIiIsJkYmRiYtSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiM2IywkKiZGK0YmSSJ0R0YjRiZGJkYmRiY=</Equation></Text-field>
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<Group labelreference="L43" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">In this case the forcing function vector b depends on time, which means we will need to use </Text-field>
<Text-field style="Text" layout="Normal" alignment="centred"><Image height="52" width="324" zoomable="false">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<Drawing-Root>LSUlUk9PVEc2Jy0lKUJPVU5EU19YRzYjJCIiISEiIi0lKUJPVU5EU19ZR0YnLSUtQk9VTkRTX1dJRFRIRzYjJCIlU0tGKi0lLkJPVU5EU19IRUlHSFRHNiMkIiQ/JkYqLSUpQ0hJTERSRU5HNiI=</Drawing-Root></Image></Text-field>
<Text-field style="Text" layout="Normal">to find the solution vector.  Next, find the matrix exponential of A.</Text-field>
</Input>
</Group>
<Group labelreference="L44" drawlabel="true">
<Text-field selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="0" rightmargin="0" bullet="none" firstindent="0" bulletsuffix="" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="centred" initial="0" spacebelow="0"></Text-field>
</Group>
<Group labelreference="L15" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">mat:=exponential(A,t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkbWF0RzYiLUknbWF0cml4R0YkNiM3JTclLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJCooLCYiIiJGMyomJkkia0dGJDYjRjNGM0kkdGF1R0YkRjNGM0YzRjghIiJJInRHRiRGM0Y5IiIhRjs3JSwkKihGNUYzLCYtRis2IywkKigsJkYzRjMqJiZGNjYjIiIjRjNGOEYzRjNGM0Y4RjlGOkYzRjlGOUYqRjNGMywmRkZGOUY1RjNGOUY5RkBGOzclKiYsKiomRjVGM0ZARjNGOSomRipGM0ZGRjNGMyomLUYrNiMsJComRjhGOUY6RjNGOUYzRkZGM0Y5KiZGUEYzRjVGM0YzRjNGSUY5LCZGQEY5RlBGM0ZQ">[encoded data, 11196 characters]</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L45" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Specify the initial conditions.</Text-field>
</Input>
</Group>
<Group labelreference="L16" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal262">Y0:=matrix(3,1,[0,0,0]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjWTBHNiItSSdtYXRyaXhHRiQ2IzclNyMiIiFGKUYp">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkqbXZlcmJhdGltR0YkNiNRJiUjWTBHRictSSNtb0dGJDYtUSM6PUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZHLUkobWZlbmNlZEdGJDYmLUYjNiMtSSdtdGFibGVHRiQ2Ny1JJG10ckdGJDYmLUkkbXRkR0YkNigtSSNtbkdGJDYkUSIwRidGMy8lKXJvd2FsaWduR1EhRicvJSxjb2x1bW5hbGlnbkdGaG4vJStncm91cGFsaWduR0Zobi8lKHJvd3NwYW5HUSIxRicvJStjb2x1bW5zcGFuR0Zfb0ZmbkZpbkZbb0ZSRlIvJSZhbGlnbkdRJWF4aXNGJy9GZ25RKWJhc2VsaW5lRicvRmpuUSZyaWdodEYnL0Zcb1EnfGZybGVmdHxockYnLyUvYWxpZ25tZW50c2NvcGVHUSV0cnVlRicvJSxjb2x1bW53aWR0aEdRJWF1dG9GJy8lJndpZHRoR0ZgcC8lK3Jvd3NwYWNpbmdHUSYxLjBleEYnLyUuY29sdW1uc3BhY2luZ0dRJjAuOGVtRicvJSlyb3dsaW5lc0dRJW5vbmVGJy8lLGNvbHVtbmxpbmVzR0ZbcS8lJmZyYW1lR0ZbcS8lLWZyYW1lc3BhY2luZ0dRLDAuNGVtfjAuNWV4RicvJSplcXVhbHJvd3NHRjgvJS1lcXVhbGNvbHVtbnNHRjgvJS1kaXNwbGF5c3R5bGVHRjgvJSVzaWRlR0Zoby8lMG1pbmxhYmVsc3BhY2luZ0dGaHBGMy8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L46" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Since \317\204 is a parameter in the system of governing equations, we use t1 as the dummy integration variable in </Font></Text-field>
<Text-field style="Text" layout="Normal" alignment="centred"><Image height="44" width="378" zoomable="false">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<Drawing-Root>LSUlUk9PVEc2Jy0lKUJPVU5EU19YRzYjJCIiISEiIi0lKUJPVU5EU19ZRzYjJCIjNUYqLSUtQk9VTkRTX1dJRFRIRzYjJCIlIXkkRiotJS5CT1VORFNfSEVJR0hURzYjJCIkUyVGKi0lKUNISUxEUkVORzYi</Drawing-Root></Image>.</Text-field>
<Text-field style="Text" layout="Normal">We will need to generate a <Font bold="true">b</Font> vector that depends on time,  Call this vector <Font bold="true">b</Font>2.</Text-field>
</Input>
</Group>
<Group labelreference="L17" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">b2:=subs(t=t1,evalm(b));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjYjJHNiItSSdtYXRyaXhHRiQ2IzclNyMqJkkkdGF1R0YkISIiLCYiIiJGLi1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjLCQqJiIiI0YuSSN0MUdGJEYuRi5GLkYuNyMiIiFGOQ==">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L47" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The matrix exponential under the integral sign the the above equation is obtained next and named mat2.</Text-field>
</Input>
</Group>
<Group labelreference="L18" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">mat2:=subs(t=t-t1,evalm(mat)):</Text-field>
</Input>
</Group>
<Group labelreference="L19" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">mat3:=evalm(mat2&amp;*b2):</Text-field>
</Input>
</Group>
<Group labelreference="L20" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">mat4:=map(int,mat3,t1=0..t):</Text-field>
</Input>
</Group>
<Group labelreference="L21" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol:=evalm(mat&amp;*Y0+mat4):</Text-field>
</Input>
</Group>
<Group labelreference="L48" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The solution is not printed for brevity.  Store the concentration expressions Ca, Cb, and Cc.</Text-field>
</Input>
</Group>
<Group labelreference="L22" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ca:=sol[1,1];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L23" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">cb:=sol[2,1]:</Text-field>
</Input>
</Group>
<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">cc:=sol[3,1]:</Text-field>
</Input>
</Group>
<Group labelreference="L49" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Again cb and cc are not printed for brevity.  Next, numerical values for the rate constants (k1 and k2) and the time constant \317\204 are specified and substituted in the expressions for Ca, Cb, and Cc:</Font></Text-field>
</Input>
</Group>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal262">pars:={tau=1,k[1]=1,k[2]=1/4};</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklcGFyc0c2IjwlLyZJImtHRiQ2IyIiIkYqL0kkdGF1R0YkRiovJkYoNiMiIiMjRioiIiU=">PCUvJkkia0c2IjYjIiIiRigvSSR0YXVHRiZGKC8mRiU2IyIiIyNGKCIiJQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Ca:=simplify(subs(pars,ca));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjQ2FHNiIsJCooIyIiIiIiJUYoLCpGKEYoKiYiIiRGKC1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjLCQqJiIiI0YoSSJ0R0YkRihGKEYoISIiKihGNUYoRi1GKCktSSRjb3NHRi82I0Y2RjVGKEYoKipGNUYoRi1GKC1JJHNpbkdGL0Y8RihGOkYoRjdGKC1GLjYjLCRGNEY3RihGNw==">LCQqKCMiIiIiIiVGJSwqRiVGJSomIiIkRiUtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkKiYiIiNGJUkidEdGL0YlRiVGJSEiIiooRjNGJUYqRiUpLUkkY29zR0YsNiNGNEYzRiVGJSoqRjNGJUYqRiUtSSRzaW5HRixGOkYlRjhGJUY1RiUtRis2IywkRjJGNUYlRjU=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L27" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Cb:=simplify(subs(pars,cb));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjQ2JHNiIsJCooIyIiIiIlTjhGKC1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjLCQqJiIiI0YoSSJ0R0YkRighIiJGKCwsKioiIyEqRigtRis2IywkRjFGKEYoLUkkc2luR0YsNiNGM0YoLUkkY29zR0YsRj1GKEYoIiRYJUY0KiYiJCV5RigtRis2IywkKiYjIiIkIiIlRihGM0YoRihGKEYoKiYiJEgoRihGOEYoRjQqKCIkIVJGKEY4RigpRj5GMkYoRihGKEY0">LCQqKCMiIiIiJU44RiUtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkKiYiIiNGJUkidEdGLEYlISIiRiUsLCoqIiMhKkYlLUYoNiMsJEYvRiVGJS1JJHNpbkdGKTYjRjFGJS1JJGNvc0dGKUY7RiVGJSIkWCVGMiomIiQleUYlLUYoNiMsJComIyIiJCIiJUYlRjFGJUYlRiVGJSomIiRIKEYlRjZGJUYyKigiJCFSRiVGNkYlKUY8RjBGJUYlRiVGMg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Cc:=simplify(subs(pars,cc));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjQ2NHNiIsJCooIyIiIiIlU2BGKC1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjLCQqJiIiI0YoSSJ0R0YkRighIiJGKCwuKiYiJS9LRigtRis2I0YzRihGKCoqIiR1IkYoLUYrNiMsJEYxRihGKC1JJHNpbkdGLEY5RigtSSRjb3NHRixGOUYoRigiJFglRigqJiIlT0pGKC1GKzYjLCQqJiMiIiQiIiVGKEYzRihGKEYoRjQqJiIkYiZGKEY8RihGNCooIiNVRihGPEYoKUZBRjJGKEYoRihGNA==">LCQqKCMiIiIiJVNgRiUtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkKiYiIiNGJUkidEdGLEYlISIiRiUsLiomIiUvS0YlLUYoNiNGMUYlRiUqKiIkdSJGJS1GKDYjLCRGL0YlRiUtSSRzaW5HRilGN0YlLUkkY29zR0YpRjdGJUYlIiRYJUYlKiYiJU9KRiUtRig2IywkKiYjIiIkIiIlRiVGMUYlRiVGJUYyKiYiJGImRiVGOkYlRjIqKCIjVUYlRjpGJSlGP0YwRiVGJUYlRjI=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L50" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Next, plot the concentration profiles.  Specify the time you want to use to plot the results.</Text-field>
</Input>
</Group>
<Group labelreference="L29" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">tf:=20;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjdGZHNiIiIz8=">IiM/</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L30" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal262">p1:=plot(Ca,t=0..tf,thickness=4,color=red,linestyle=1,labels=[&quot;t(min)&quot;,&quot;Ca(mol/1)&quot;],labeldirections=[HORIZONTAL,VERTICAL],title=&quot;Figure Exp. 2.4.1 Concentration of species A as a function of time.&quot;,axes=boxed);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="[encoded data, 11144 characters]">[encoded data, 11116 characters]</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L53" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pt1:=textplot([10,0.1,{tau=1.0*Unit(min),k[1]=1.0*Unit(min^(-1)),k[2]=0.25*Unit(min^(-1))}]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkcHQxRzYiLUkvSU5URVJGQUNFX1BMT1RHRiQ2Iy1JJVRFWFRHRiQ2JDckJCIjNSIiISQiIiIhIiI8JS9JJHRhdUdGJCwkKiYkRi1GMUYwLUklVW5pdEdGJDYjSSRtaW5HRiRGMEYwLyZJImtHRiQ2I0YwLCQqJkY3RjAtRjk2IyokRjtGMUYwRjAvJkY+NiMiIiMsJComJCIjRCEiI0YwRkJGMEYw">LSUlUExPVEc2Iy1JJVRFWFRHNiI2JDckJCIjNSIiISQiIiIhIiI8JS9JJHRhdUdGJywkKiYkRitGL0YuLUklVW5pdEdGJzYjSSRtaW5HRidGLkYuLyZJImtHRic2I0YuLCQqJkY1Ri4tRjc2IyokRjlGL0YuRi4vJkY8NiMiIiMsJComJCIjRCEiI0YuRkBGLkYu</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L54" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display([p1,pt1]);</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, 35556 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L31" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal262">p2:=plot(Cb,t=0..tf,thickness=4,color=green,linestyle=1,labels=[&quot;t(min)&quot;,&quot;Cb(mol/1)&quot;],labeldirections=[HORIZONTAL,VERTICAL],title=&quot;Figure Exp. 2.4.2 Concentration of species B as a function of time.&quot;,axes=boxed);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="[encoded data, 9128 characters]">[encoded data, 9104 characters]</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L56" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pt1:=textplot([10,0.1,[tau=1.0*Unit(min),k[1]=1.0*Unit(min^(-1)),k[2]=0.25*Unit(min^(-1))]]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkcHQxRzYiLUkvSU5URVJGQUNFX1BMT1RHRiQ2Iy1JJVRFWFRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2JDckJCIjNSIiISQiIiIhIiI3JS9JJHRhdUdGJCwkKiYkRjBGNEYzLUklVW5pdEdGJDYjSSRtaW5HRiRGM0YzLyZJImtHRiQ2I0YzLCQqJkY6RjMtRjw2IyokRj5GNEYzRjMvJkZBNiMiIiMsJComJCIjRCEiI0YzRkVGM0Yz">LSUlUExPVEc2Iy1JJVRFWFRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JDckJCIjNSIiISQiIiIhIiI3JS9JJHRhdUdGKiwkKiYkRi5GMkYxLUklVW5pdEdGKjYjSSRtaW5HRipGMUYxLyZJImtHRio2I0YxLCQqJkY4RjEtRjo2IyokRjxGMkYxRjEvJkY/NiMiIiMsJComJCIjRCEiI0YxRkNGMUYx</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L57" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display([p2,pt1]);</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, 33680 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal262">p3:=plot(Cc,t=0..tf,thickness=4,color=gold,linestyle=1,labels=[&quot;t(min)&quot;,&quot;Cc(mol/1)&quot;],labeldirections=[HORIZONTAL,VERTICAL],title=&quot;Figure 2.4.3 Concentration of species C as a function of time.&quot;,axes=boxed);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="[encoded data, 7932 characters]">[encoded data, 7904 characters]</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L61" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pt3:=textplot([10,0.02,[tau=1.0*Unit(min),k[1]=1.0*Unit(min^(-1)),k[2]=0.25*Unit(min^(-1))]]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkcHQzRzYiLUkvSU5URVJGQUNFX1BMT1RHRiQ2Iy1JJVRFWFRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2JDckJCIjNSIiISQiIiMhIiM3JS9JJHRhdUdGJCwkKiYkRjAhIiIiIiItSSVVbml0R0YkNiNJJG1pbkdGJEY8RjwvJkkia0dGJDYjRjwsJComRjpGPC1GPjYjKiRGQEY7RjxGPC8mRkM2I0YzLCQqJiQiI0RGNEY8RkdGPEY8">LSUlUExPVEc2Iy1JJVRFWFRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JDckJCIjNSIiISQiIiMhIiM3JS9JJHRhdUdGKiwkKiYkRi4hIiIiIiItSSVVbml0R0YqNiNJJG1pbkdGKkY6RjovJkkia0dGKjYjRjosJComRjhGOi1GPDYjKiRGPkY5RjpGOi8mRkE2I0YxLCQqJiQiI0RGMkY6RkVGOkY6</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L60" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display([p3,pt3]);</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, 32536 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L52" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">We observe that all the concentrations start from zero and after about six minutes oscillate at almost a steady state value.</Text-field>
</Input>
</Group>
<Group labelreference="L51" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
</Worksheet>