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    </Task-category>
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<Input>
<Text-field style="Heading 3" layout="Heading 3"><Font italic="false">Example 3.6</Font></Text-field>
</Input>
</Group>
<Group labelreference="L4" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Equation (3.19) can be solved below by finding the matrizant in the manner described above.</Text-field>
</Input>
</Group>
<Group labelreference="L5" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart:</Text-field>
</Input>
</Group>
<Group labelreference="L6" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">with(linalg):with(plots):</Text-field>
</Input>
</Group>
<Group labelreference="L7" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=2;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiTkc2IiIiIw==">IiIj</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L8" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal"> For brevity, only four terms are used for calculating the matrizant in this example.  </Text-field>
</Input>
</Group>
<Group labelreference="L9" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">nvars:=4;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkmbnZhcnNHNiIiIiU=">IiIl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L10" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eq:=1/x*diff(x*diff(c(x),x),x)=phi^2*c(x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjRXFHNiIvKiZJInhHRiQhIiIsJi1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJjR0YkNiNGJ0YnIiIiKiZGJ0YxLUYrNiRGLi1JIiRHRiw2JEYnIiIjRjFGMUYxKiYpSSRwaGlHRiRGOEYxRi5GMQ==">LyomSSJ4RzYiISIiLCYtSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUkiY0dGJTYjRiRGJCIiIiomRiRGLy1GKTYkRihGJEYvRi9GLyomKUkkcGhpR0YlIiIjRi9GLEYv</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L11" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal"> Enter the A matrix (equation 3.22).</Text-field>
</Input>
</Group>
<Group labelreference="L12" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A:=matrix(2,2,[0,1/x,phi^2*x,0]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiQUc2Ii1JJ21hdHJpeEdGJDYjNyQ3JCIiISokSSJ4R0YkISIiNyQqJilJJHBoaUdGJCIiIyIiIkYsRjNGKg==">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y0:=matrix(2,1,[c[1],0]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjWTBHNiItSSdtYXRyaXhHRiQ2IzckNyMmSSJjR0YkNiMiIiI3IyIiIQ==">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L14" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">id:=Matrix(N,N,shape=identity);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjaWRHNiItSSdSVEFCTEVHRiQ2JSIqU0hFXSItSSdNQVRSSVhHRiQ2IzckNyQiIiIiIiE3JEYvRi5JJ01hdHJpeEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJA==">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</Equation></Text-field>
</Output>
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<Group labelreference="L15" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">X1:=matrix(N,N);X2:=matrix(N,N);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjWDFHNiItSSZhcnJheUclKnByb3RlY3RlZEc2JTsiIiIiIiNGKTci">PTYiNiQ7IiIiIiIjRiVFXFtsIQ==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjWDJHNiItSSZhcnJheUclKnByb3RlY3RlZEc2JTsiIiIiIiNGKTci">PTYiNiQ7IiIiIiIjRiVFXFtsIQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L16" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">X1:=map(int,subs(x=x1,evalm(A)),x1=0..x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjWDFHNiItSSdtYXRyaXhHRiQ2IzckNyQiIiFJKWluZmluaXR5RyUqcHJvdGVjdGVkRzckLCQqKCMiIiIiIiNGMSlJJHBoaUdGJEYyRjEpSSJ4R0YkRjJGMUYxRio=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkqbXZlcmJhdGltR0YkNiNRJiUjWDFHRictSSNtb0dGJDYtUSM6PUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZHLUkobWZlbmNlZEdGJDYmLUYjNiMtSSdtdGFibGVHRiQ2Ni1JJG10ckdGJDYnLUkkbXRkR0YkNigtSSNtbkdGJDYkUSIwRidGMy8lKXJvd2FsaWduR1EhRicvJSxjb2x1bW5hbGlnbkdGaG4vJStncm91cGFsaWduR0Zobi8lKHJvd3NwYW5HUSIxRicvJStjb2x1bW5zcGFuR0Zfby1GVjYoLUkjbWlHRiQ2JVEoJmluZmluO0YnLyUnaXRhbGljR1EldHJ1ZUYnL0Y0USdpdGFsaWNGJ0ZmbkZpbkZbb0Zdb0Zgb0ZmbkZpbkZbby1GUzYnLUZWNigtRiM2JS1JJm1mcmFjR0YkNigtRlk2JFEiMUYnRjMtRlk2JFEiMkYnRjMvJS5saW5ldGhpY2tuZXNzR0Zfby8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZgcS8lKWJldmVsbGVkR0Y4LUYwNi1RMSZJbnZpc2libGVUaW1lcztGJ0YzRjZGOUY7Rj1GP0ZBRkMvRkZRJjAuMGVtRicvRklGaXEtRiw2I1FodiomKSUpJnZhcnBoaTtHLUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHNiI2JFEiMjYiLyUsbWF0aHZhcmlhbnRHUSdub3JtYWw2IiIiIiklInhHLUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHNiI2JFEiMjYiLyUsbWF0aHZhcmlhbnRHUSdub3JtYWw2IiIiIkYnRmZuRmluRltvRl1vRmBvRlVGZm5GaW5GW28vJSZhbGlnbkdRJWF4aXNGJy9GZ25RKWJhc2VsaW5lRicvRmpuRmBxL0Zcb1EnfGZybGVmdHxockYnLyUvYWxpZ25tZW50c2NvcGVHRmpvLyUsY29sdW1ud2lkdGhHUSVhdXRvRicvJSZ3aWR0aEdGanIvJStyb3dzcGFjaW5nR1EmMS4wZXhGJy8lLmNvbHVtbnNwYWNpbmdHUSYwLjhlbUYnLyUpcm93bGluZXNHUSVub25lRicvJSxjb2x1bW5saW5lc0dGZXMvJSZmcmFtZUdGZXMvJS1mcmFtZXNwYWNpbmdHUSwwLjRlbX4wLjVleEYnLyUqZXF1YWxyb3dzR0Y4LyUtZXF1YWxjb2x1bW5zR0Y4LyUtZGlzcGxheXN0eWxlR0Y4LyUlc2lkZUdRJnJpZ2h0RicvJTBtaW5sYWJlbHNwYWNpbmdHRmJzRjMvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRic=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L17" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal"> To avoid the singularity, in X1,  integrate from x0 to x and later find the limit as x0 goes to zero.</Text-field>
</Input>
</Group>
<Group labelreference="L18" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">X1:=map(int,subs(x=x1,evalm(A)),x1=x0..x)assuming x&gt;0,x0&gt;=0,x&gt;=x0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjWDFHNiItSSdtYXRyaXhHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IzckNyQiIiEsJi1JI2xuR0YnNiNJI3gwR0YkISIiLUYwNiNJInhHRiQiIiI3JCwkKigjRjciIiNGNylJJHBoaUdGJEY8RjcsJiokKUY2RjxGN0Y3KiQpRjJGPEY3RjNGN0Y3Ri0=">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L19" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">mat := evalm(id + X1) ;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkbWF0RzYiLUknbWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiM3JDckIiIiLCYtSSNsbkdGJzYjSSN4MEdGJCEiIi1GMDYjSSJ4R0YkRi03JCwkKigjRi0iIiNGLSlJJHBoaUdGJEY7Ri0sJiokKUY2RjtGLUYtKiQpRjJGO0YtRjNGLUYtRi0=">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L20" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 2 to nvars do
S:=evalm( subs(x=x1,evalm(A))&amp;*subs(x=x1,evalm(X1)) ):X2:=
map(int,S,x1=x0..x):mat := evalm(mat +X2) :
X1:=evalm(X2):od : </Text-field>
</Input>
</Group>
<Group labelreference="L21" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">evalm(mat)assuming x&gt;0,x0&gt;=0,x&gt;=x0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">[encoded data, 20408 characters]</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L22" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol:=evalm(mat&amp;*Y0);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pkkkc29sRzYiLUknbWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiM3JDcjKiYsKCIiIkYvLUkkaW50R0YnNiQsJCoqI0YvIiIjRi9JI3gxR0YkISIiKUkkcGhpR0YkRjZGLywmKiQpRjdGNkYvRi8qJClJI3gwR0YkRjZGL0Y4Ri9GLy9GNztGQEkieEdGJEYvLUYxNiQqJkY3RjgtRjE2JCooRjlGL0Y3Ri8tRjE2JEYzL0Y3O0ZARjdGL0ZMRi9GQUYvRi8mSSJjR0YkNiNGL0YvNyMqJiwmKihGNUYvRjlGLywmKiQpRkNGNkYvRi9GPkY4Ri9GLy1GMTYkRklGQUYvRi9GTkYv">[encoded data, 6548 characters]</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L23" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">C:=sol[1,1];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiQ0c2IiomLCgiIiJGJy1JJGludEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYkLCQqKiNGJyIiI0YnSSN4MUdGJCEiIilJJHBoaUdGJEYxRicsJiokKUYyRjFGJ0YnKiQpSSN4MEdGJEYxRidGM0YnRicvRjI7RjtJInhHRiRGJy1GKTYkKiZGMkYzLUYpNiQqKEY0RidGMkYnLUYpNiRGLi9GMjtGO0YyRidGR0YnRjxGJ0YnJkkiY0dGJDYjRidGJw==">KiYsKCIiIkYkLUkkaW50RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQsJCoqI0YkIiIjRiRJI3gxR0YqISIiKUkkcGhpR0YqRi9GJCwmKiQpRjBGL0YkRiQqJClJI3gwR0YqRi9GJEYxRiRGJC9GMDtGOUkieEdGKkYkLUYmNiQqJkYwRjEtRiY2JCooRjJGJEYwRiQtRiY2JEYsL0YwO0Y5RjBGJEZFRiRGOkYkRiQmSSJjR0YqNiNGJEYk</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dCdx:=1/x*sol[2,1];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklZENkeEc2IiooSSJ4R0YkISIiLCYqKCMiIiIiIiNGKylJJHBoaUdGJEYsRissJiokKUYmRixGK0YrKiQpSSN4MEdGJEYsRitGJ0YrRistSSRpbnRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2JCooRi1GK0kjeDFHRiRGKy1GNjYkLCQqKkYqRitGPEYnRi1GKywmKiQpRjxGLEYrRitGMkYnRitGKy9GPDtGNEY8RisvRjw7RjRGJkYrRismSSJjR0YkNiNGK0Yr">KihJInhHNiIhIiIsJiooIyIiIiIiI0YpKUkkcGhpR0YkRipGKSwmKiQpRiNGKkYpRikqJClJI3gwR0YkRipGKUYlRilGKS1JJGludEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYkKihGK0YpSSN4MUdGJEYpLUY0NiQsJCoqRihGKUY6RiVGK0YpLCYqJClGOkYqRilGKUYwRiVGKUYpL0Y6O0YyRjpGKS9GOjtGMkYjRilGKSZJImNHRiQ2I0YpRik=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">To find c1 apply the boundary condition at x=1:</Text-field>
</Input>
</Group>
<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc2:=eval(subs(x=1,C))=1 assuming x&gt;0,x0&gt;=0,x&gt;=x0;</Text-field>
</Input>
<Output>
<Text-field style="Warning" layout="Warning">Warning, unable to determine if 0 is between x0 and x1; try to use assumptions or set _EnvAllSolutions to true</Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMyRzYiLyomLDQiIiJGKCooI0YoIiIlRigpSSRwaGlHRiQiIiNGKClJI3gwR0YkRi5GKCEiIioqI0YoRi5GKEYsRigtSSNsbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRjBGKEYvRihGKComRipGKEYsRihGKCoqI0YoIiM7RigpRi1GK0YoKUYwRitGKEY0RihGKCooIyIiJiIja0YoRj5GKEY/RihGMSoqI0YoIiIpRihGPkYoRjRGKEYvRihGKComI0YoRkNGKEY+RihGKCooRjxGKEY+RihGL0YoRihGKCZJImNHRiQ2I0YoRihGKA==">LyomLDQiIiJGJSooI0YlIiIlRiUpSSRwaGlHNiIiIiNGJSlJI3gwR0YrRixGJSEiIioqI0YlRixGJUYpRiUtSSNsbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGKzYjRi5GJUYtRiVGJSomRidGJUYpRiVGJSoqI0YlIiM7RiUpRipGKEYlKUYuRihGJUYyRiVGJSooIyIiJiIja0YlRjxGJUY9RiVGLyoqI0YlIiIpRiVGPEYlRjJGJUYtRiVGJSomI0YlRkFGJUY8RiVGJSooRjpGJUY8RiVGLUYlRiVGJSZJImNHRis2I0YlRiVGJQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L27" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">c[1]:=solve(bc2,c[1]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJImNHNiI2IyIiIiwkKiYiI2tGJyw0RipGJyooIiM7RicpSSRwaGlHRiUiIiNGJylJI3gwR0YlRjBGJyEiIioqIiNLRidGLkYnLUkjbG5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2I0YyRidGMUYnRicqJkYtRidGLkYnRicqKiIiJUYnKUYvRj5GJylGMkY+RidGNkYnRicqKCIiJkYnRj9GJ0ZARidGMyoqIiIpRidGP0YnRjZGJ0YxRidGJyokRj9GJ0YnKihGPkYnRj9GJ0YxRidGJ0YzRic=">LCQqJiIjayIiIiw0RiRGJSooIiM7RiUpSSRwaGlHNiIiIiNGJSlJI3gwR0YrRixGJSEiIioqIiNLRiVGKUYlLUkjbG5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRis2I0YuRiVGLUYlRiUqJkYoRiVGKUYlRiUqKiIiJUYlKUYqRjpGJSlGLkY6RiVGMkYlRiUqKCIiJkYlRjtGJUY8RiVGLyoqIiIpRiVGO0YlRjJGJUYtRiVGJSokRjtGJUYlKihGOkYlRjtGJUYtRiVGJUYvRiU=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">C:=eval(C);</Text-field>
</Input>
<Output>
<Text-field style="Warning" layout="Warning">Warning, unable to determine if 0 is between x0 and x; try to use assumptions or set _EnvAllSolutions to true</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, unable to determine if 0 is between x0 and x1; try to use assumptions or set _EnvAllSolutions to true</Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiQ0c2IiwkKigiI2siIiIsKEYoRigtSSRpbnRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2JCwkKiojRigiIiNGKEkjeDFHRiQhIiIpSSRwaGlHRiRGM0YoLCYqJClGNEYzRihGKCokKUkjeDBHRiRGM0YoRjVGKEYoL0Y0O0Y9SSJ4R0YkRigtRis2JComRjRGNS1GKzYkKihGNkYoRjRGKC1GKzYkRjAvRjQ7Rj1GNEYoRklGKEY+RihGKCw0RidGKCooIiM7RihGNkYoRjxGKEY1KioiI0tGKEY2RigtSSNsbkdGLDYjRj1GKEY8RihGKComRk1GKEY2RihGKCoqIiIlRigpRjdGVUYoKUY9RlVGKEZQRihGKCooIiImRihGVkYoRldGKEY1KioiIilGKEZWRihGUEYoRjxGKEYoKiRGVkYoRigqKEZVRihGVkYoRjxGKEYoRjVGKA==">LCQqKCIjayIiIiwoRiVGJS1JJGludEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkLCQqKiNGJSIiI0YlSSN4MUdGLCEiIilJJHBoaUdGLEYxRiUsJiokKUYyRjFGJUYlKiQpSSN4MEdGLEYxRiVGM0YlRiUvRjI7RjtJInhHRixGJS1GKDYkKiZGMkYzLUYoNiQqKEY0RiVGMkYlLUYoNiRGLi9GMjtGO0YyRiVGR0YlRjxGJUYlLDRGJEYlKigiIztGJUY0RiVGOkYlRjMqKiIjS0YlRjRGJS1JI2xuR0YpNiNGO0YlRjpGJUYlKiZGS0YlRjRGJUYlKioiIiVGJSlGNUZTRiUpRjtGU0YlRk5GJUYlKigiIiZGJUZURiVGVUYlRjMqKiIiKUYlRlRGJUZORiVGOkYlRiUqJEZURiVGJSooRlNGJUZURiVGOkYlRiVGM0Yl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L29" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal"> Now apply the limit command fo<Font style="Text">r x0<Font executable="true">.</Font></Font></Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" linebreak="space" spaceabove="0" rightmargin="0" bullet="none" firstindent="0" bulletsuffix="" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"></Text-field>
</Input>
<Output>
<Text-field style="Warning" layout="Warning">Warning, premature end of input, use &lt;Shift&gt; + &lt;Enter&gt; to avoid this message.</Text-field>
</Output>
</Group>
<Group labelreference="L30" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">C:=limit(C,x0=0);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiQ0c2IiomLCgiI2siIiIqKCIjO0YoKUkkcGhpR0YkIiIjRigpSSJ4R0YkRi1GKEYoKiYpRiwiIiVGKClGL0YyRihGKEYoLChGJ0YoKiZGKkYoRitGKEYoKiRGMUYoRighIiI=">KiYsKCIjayIiIiooIiM7RiUpSSRwaGlHNiIiIiNGJSlJInhHRipGK0YlRiUqJilGKSIiJUYlKUYtRjBGJUYlRiUsKEYkRiUqJkYnRiVGKEYlRiUqJEYvRiVGJSEiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L31" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">Divide both numerator and denominator by 64.  (Note when different values of 'nvars' are used, this number has to be changed accordingly.)</Text-field>
</Input>
</Group>
<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">n1:=numer(C)/64;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjbjFHNiIsKCIiIkYmKigjRiYiIiVGJilJJHBoaUdGJCIiI0YmKUkieEdGJEYsRiZGJiooI0YmIiNrRiYpRitGKUYmKUYuRilGJkYm">LCgiIiJGIyooI0YjIiIlRiMpSSRwaGlHNiIiIiNGIylJInhHRilGKkYjRiMqKCNGIyIja0YjKUYoRiZGIylGLEYmRiNGIw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L33" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">d1:=denom(C)/64;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjZDFHNiIsKCIiIkYmKiYjRiYiIiVGJilJJHBoaUdGJCIiI0YmRiYqJiNGJiIja0YmKUYrRilGJkYm">LCgiIiJGIyomI0YjIiIlRiMpSSRwaGlHNiIiIiNGI0YjKiYjRiMiI2tGIylGKEYmRiNGIw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L34" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">C:=n1/d1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiQ0c2IiomLCgiIiJGJyooI0YnIiIlRicpSSRwaGlHRiQiIiNGJylJInhHRiRGLUYnRicqKCNGJyIja0YnKUYsRipGJylGL0YqRidGJ0YnLChGJ0YnKiZGKUYnRitGJ0YnKiZGMUYnRjNGJ0YnISIi">KiYsKCIiIkYkKigjRiQiIiVGJClJJHBoaUc2IiIiI0YkKUkieEdGKkYrRiRGJCooI0YkIiNrRiQpRilGJ0YkKUYtRidGJEYkRiQsKEYkRiQqJkYmRiRGKEYkRiQqJkYvRiRGMUYkRiQhIiI=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L35" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal"> One can verify that both the numerator and the denominator of C are modified Bessel functions of the order zero by using Maple.</Text-field>
</Input>
</Group>
<Group labelreference="L36" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">series(BesselI(0,phi*x),x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KytJInhHNiIiIiIiIiEsJComI0YlIiIlRiUpSSRwaGlHRiQiIiNGJUYlRi0sJComI0YlIiNrRiUpRixGKkYlRiVGKi1JIk9HJSpwcm90ZWN0ZWRHNiNGJSIiJw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L37" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">series(BesselI(0,phi),phi);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">KytJJHBoaUc2IiIiIiIiISNGJSIiJSIiIyNGJSIja0YoLUkiT0clKnByb3RlY3RlZEc2I0YlIiIn</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L38" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal"><Font style="Text">Next, plots can be obtained by substituting the parameters for the Thiele modulus </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEpJnZhcnBoaTtGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjI=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEpJnZhcnBoaTtGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjI=</Equation><Font style="Text"> .</Font></Text-field>
</Input>
</Group>
<Group labelreference="L39" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pars:=[0.1,1,2,10];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklcGFyc0c2IjcmJCIiIiEiIkYnIiIjIiM1">NyYkIiIiISIiRiQiIiMiIzU=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L49" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">clr:=[red,green,blue,brown];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkY2xyRzYiNyZJJHJlZEdGJEkmZ3JlZW5HRiRJJWJsdWVHRiRJJmJyb3duR0Yk">NyZJJHJlZEc2IkkmZ3JlZW5HRiRJJWJsdWVHRiRJJmJyb3duR0Yk</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L40" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to 4 do p[i]:=plot(subs(phi=pars[i],C),x=0..1,color=clr[i]):od:</Text-field>
</Input>
</Group>
<Group labelreference="L41" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pt[1]:=textplot([0.1,evalf(subs({x=0.1,phi=pars[1]},C)),'phi=pars[1]'], align=below):
pt[2]:=textplot([0.4,evalf(subs({x=.4,phi=pars[2]},C)),'phi=pars[2]'],align=below):
pt[3]:=textplot([0.5,evalf(subs({x=.5,phi=pars[3]},C)),'phi=pars[3]'],align=below):
pt[4]:=textplot([0.8,evalf(subs({x=0.8,phi=pars[4]},C)),'phi=pars[4]'],align=below):</Text-field>
</Input>
</Group>
<Group labelreference="L51" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display({seq(p[i],i=1..4),seq(pt[i],i=1..4)},axes=boxed,thickness=3,title=&quot;Figure Exp. 3.1.8.&quot;,labels=[x,&quot;C&quot;]);</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, 20856 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L46" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">For  higher values of <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NjY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NjY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy</Equation>, more terms (nvars) in the matrizant series solution are needed for higher accurance.</Text-field>
</Input>
</Group>
<Group labelreference="L44" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L45" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
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</Worksheet>