Image adjustments 2026

project.ptx

@@ -4,13 +4,13 @@
     <target name="html" format="html" source="apex.ptx" publication="publication-video.ptx">
       <stringparams key="html.annotation" value="hypothesis"/>
     </target>
-    <target name="html-novideo" format="html" source="apex.ptx" publication="publication-novid.ptx">
+    <target name="html-novideo" format="html" source="apex.ptx" publication="publication-web-novid.ptx">
       <stringparams key="html.annotation" value="hypothesis"/>
     </target>
-    <target name="html-standard" format="html" source="apex-UL-standard.ptx" publication="publication-standard.ptx">
+    <target name="html-standard" format="html" source="apex-UL-standard.ptx" publication="publication-standard-web.ptx">
       <stringparams key="html.annotation" value="hypothesis"/>
     </target>
-    <target name="html-accelerated" format="html" source="apex-UL-accelerated.ptx" publication="publication-accelerated.ptx">
+    <target name="html-accelerated" format="html" source="apex-UL-accelerated.ptx" publication="publication-accelerated-web.ptx">
       <stringparams key="html.annotation" value="hypothesis"/>
     </target>
     <target name="runestone" format="html" source="apex.ptx" publication="publication-runestone.ptx" output-dir="../published/APEX">

ptx/sec_ABC.ptx

@@ -245,7 +245,7 @@
         as shown in <xref ref="fig_abc1"/>.
       </p>
 
-      <figure xml:id="fig_abc1" vshift="3">
+      <figure xml:id="fig_abc1" vshift="2">
         <caption>Graphing an enclosed region in <xref ref="ex_abc1"/></caption>
         <!-- START figures/fig_abc1.tex -->
         <image width="47%">
@@ -403,7 +403,7 @@
         <m>y=-(x-1)^2+3</m> and <m>y=2</m>,
         as shown in <xref ref="fig_abc3"/>.
       </p>
-      <figure xml:id="fig_abc3" vshift="0">
+      <figure xml:id="fig_abc3" vshift="-1">
         <caption>Graphing a region for <xref ref="ex_abc3"/></caption>
         <!-- START figures/fig_abc3.tex -->
         <image width="47%">
@@ -939,8 +939,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            find the area of the shaded region in the given graph.
+            Find the area of the shaded region in the given graph.
           </p>
         </introduction>
 
@@ -1454,8 +1453,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            find the total area enclosed by the functions <m>f</m> and <m>g</m>.
+            Find the total area enclosed by the functions <m>f</m> and <m>g</m>.
           </p>
         </introduction>
   <!-- Exercise 11 -->
@@ -1685,7 +1683,7 @@
       <exercisegroup cols="2" xml:id="exset-area-between-two-ways">
         <introduction>
           <p>
-            In the following exercises, find the area of the enclosed region in two ways:
+            Find the area of the enclosed region in two ways:
           </p>
 
           <p>
@@ -2107,8 +2105,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            find the area of the triangle formed by the given three points.
+            Find the area of the triangle formed by the given three points.
           </p>
         </introduction>
   <!-- Exercise 23 -->

ptx/sec_FTC.ptx

@@ -1039,6 +1039,8 @@
       Let's practice this once more.
     </p>
 
+    <enlarge-page skipsize="2"/>
+
     <example xml:id="ex_ftc12">
       <title>The FTC, Part 1, and the Chain Rule</title>
       <statement>
@@ -1229,7 +1231,7 @@
           as done in <xref ref="fig_ftc6"/>.
         </p>
 
-        <figure xml:id="fig_ftc6" vshift="2">
+        <figure xml:id="fig_ftc6" vshift="0">
           <caption>Sketching the region enclosed by <m>y=x^2+x-5</m> and <m>y=3x-2</m> in <xref ref="ex_ftc6"/></caption>
           <image width="47%">
             <shortdescription>
@@ -1294,7 +1296,7 @@
           </md>
         </p>
       </solution>
-      <solution component="video" vshift="2">
+      <solution component="video" vshift="5">
         <title>Video solution</title>
         <video width="98%" youtube="su2CXdpYPdo" label="vid_int_FTC_ex_4" component="video"/>
       </solution>
@@ -1306,7 +1308,7 @@
       The video example in <xref ref="vid_int_FTC_ex_5"/> illustrates this phenomenon.
     </p>
 
-    <figure xml:id="vid_int_FTC_ex_5" component="video" vshift="-2">
+    <figure xml:id="vid_int_FTC_ex_5" component="video" vshift="2">
       <caption>Finding the area between curves that intersect multiple times</caption>
       <video youtube="Bgji1b7Wdr4" label="vid_int_FTC_ex_5"/>
     </figure>
@@ -1527,7 +1529,7 @@
       </statement>
     </theorem>
 
-    <figure xml:id="vid_int_FTC_MVT_int" component="video" vshift="0">
+    <figure xml:id="vid_int_FTC_MVT_int" component="video" vshift="5">
       <caption>Video presentation of <xref ref="thm_mvt2"/></caption>
       <video youtube="KD90CwK0PJk" label="vid_int_FTC_MVT_int"/>
     </figure>
@@ -1542,7 +1544,7 @@
       we leave it to the reader to see how.
     </p>
 
-    <aside vshift="0">
+    <aside vshift="1">
       <p>
         <xref ref="thm_mvt2"/>
         simply says that there is a rectangle with height <m>f(c)</m> and width <m>b-a</m>,

ptx/sec_Graphical_Numerical.ptx

@@ -1383,6 +1383,7 @@
     <p>
       Let's practice Euler's Method using a few concrete examples.
     </p>
+
     <example xml:id="ex_euler1">
       <title>Using Euler's Method 1</title>
       <statement>
@@ -1407,13 +1408,9 @@
           </md>.
         </p>
         <p>
-          Using Euler's method, we find the approximate <m>y(2) \approx -0.75</m>.
-        </p>
-        <p>
-          To help visualize the Euler's method approximation, these three points
-          (connected by line segments)
-          are plotted along with the analytical solution to the initial value problem in <xref ref="fig_20_01_euler1"/>.
+          Using Euler's method, we find the approximation <m>y(2) \approx -0.75</m>.
         </p>
+
         <figure xml:id="fig_20_01_euler1" vshift="2">
           <caption>Euler's Method approximation to <m>\yp = x + y</m> with <m>y(1) = -1</m> from <xref ref="ex_euler1"/>,
           along with the analytical solution to the initial value problem</caption>
@@ -1452,6 +1449,12 @@
             </latex-image>
           </image>
         </figure>
+
+        <p>
+          To help visualize the Euler's method approximation, these three points
+          (connected by line segments)
+          are plotted along with the analytical solution to the initial value problem in <xref ref="fig_20_01_euler1"/>.
+        </p>
       </solution>
     </example>
 
@@ -1498,7 +1501,7 @@
           along with the points from <xref ref="ex_euler1"/> and the analytic solution,
           are plotted in <xref ref="fig_20_01_euler2"/>.
         </p>
-        <figure xml:id="fig_20_01_euler2" vshift="0">
+        <figure xml:id="fig_20_01_euler2" vshift="3">
           <caption>Euler's Method approximations to <m>\yp = x + y</m> with <m>y(1) = -1</m> from <xref ref="ex_euler1" text="global">Examples</xref>
             and <xref ref="ex_euler2" text="global"/>, along with the analytical solution</caption>
           <image width="47%">
@@ -1642,7 +1645,7 @@
           are plotted in <xref ref="fig_20_01_euler3"/>.
           Notice how well they seem to match the true solution.
         </p>
-        <figure xml:id="fig_20_01_euler3" vshift="2">
+        <figure xml:id="fig_20_01_euler3" vshift="3">
           <caption>Euler's Method approximation to <m>\yp = y(1-y)</m> with <m>y(0) = 0.25</m> from <xref ref="ex_euler3"/>,
           along with the analytical solution</caption>
           <image width="47%">
@@ -1803,8 +1806,7 @@
       <exercisegroup cols="2" xml:id="exset-graphical-numerical-verify-sol">
         <introduction>
           <p>
-            In the following exercises,
-            verify that the given function is a solution to the differential equation or initial value problem.
+            Verify that the given function is a solution to the differential equation or initial value problem.
           </p>
         </introduction>
 
@@ -1879,8 +1881,7 @@
       <exercisegroup cols="2" xml:id="exset-graphical-numerical-verify-particular">
         <introduction>
           <p>
-            In the following exercises,
-            verify that the given function is a solution to the differential equation and find the <m>C</m> 
+            Verify that the given function is a solution to the differential equation and find the <m>C</m> 
             value required to make the function satisfy the initial condition.
           </p>
         </introduction>
@@ -1931,8 +1932,7 @@
       <exercisegroup cols="2" xml:id="exset-graphical-numerical-sketch-slope">
         <introduction>
           <p>
-            In the following exercises,
-            sketch a slope field for the given differential equation.
+            Sketch a slope field for the given differential equation.
             Let <m>x</m> and <m>y</m> range between <m>-2</m> and <m>2</m>.
           </p>
         </introduction>
@@ -2298,8 +2298,7 @@
       <exercisegroup cols="2" xml:id="exset-graphical-numerical-sketch-sol">
         <introduction>
           <p>
-            In the following exercises,
-            sketch the slope field for the differential equation,
+            Sketch the slope field for the differential equation,
             and use it to draw a sketch of the solution to the initial value problem.
           </p>
         </introduction>
@@ -2510,8 +2509,7 @@
       <exercisegroup cols="2" xml:id="exset-graphical-numerical-euler">
         <introduction>
           <p>
-            In the following exercises,
-            use Euler's Method to make a table of values that approximates the solution to the initial value problem on the given interval.
+            Use Euler's Method to make a table of values that approximates the solution to the initial value problem on the given interval.
             Use the specified <m>h</m> or <m>N</m> value.
           </p>
         </introduction>
@@ -2638,8 +2636,7 @@
       <exercisegroup>
         <introduction>
           <p>
-            In the following exercises,
-            use the provided solution <m>y(x)</m> and Euler's Method with the <m>h=0.2</m> and <m>h=0.1</m> to complete the following table.
+            Use the provided solution <m>y(x)</m> and Euler's Method with the <m>h=0.2</m> and <m>h=0.1</m> to complete the following table.
           </p>
           <tabular>
             <col right="minor"/>

ptx/sec_Linear.ptx

@@ -280,7 +280,7 @@
     <p>
       Integrating,
       <md>
-        \ln \mu = \int p(x)\,dx
+        \ln(\mu) = \int p(x)\,dx
       </md>,
       or
       <md>
@@ -776,7 +776,7 @@
       <exercisegroup cols="2" xml:id="exset-ode-linear-general-sol">
         <introduction>
           <p>
-            In the following exercises, Find the general solution to the first order linear differential equation.
+            Find the general solution to the first order linear differential equation.
           </p>
         </introduction>
         <exercise label="ex-ode-linear-general-sol-1">
@@ -879,7 +879,7 @@
       <exercisegroup cols="2" xml:id="exset-ode-linear-particular-sol">
         <introduction>
           <p>
-            In the following exercises, Find the particular solution to the initial value problem.
+            Find the particular solution to the initial value problem.
           </p>
         </introduction>
         <exercise label="ex-ode-linear-particular-sol-1">
@@ -982,8 +982,7 @@
       <exercisegroup cols="2" xml:id="exset-ode-linear-classify">
         <introduction>
           <p>
-            In the following exercises,
-            classify the differential equation as separable,
+            Classify the differential equation as separable,
             first order linear, or both,
             and solve the initial value problem using an appropriate method.
           </p>
@@ -1040,7 +1039,7 @@
       <exercisegroup cols="2" xml:id="exset-ode-linear-slope">
         <introduction>
           <p>
-            In the following exercises, draw a slope field for the differential equation.
+            Draw a slope field for the differential equation.
             Use the slope field to predict the behavior of the solution to the initial value problem for large <m>x</m> values.
             Solve the initial value problem,
             and verify your prediction.

ptx/sec_Modeling.ptx

@@ -793,8 +793,7 @@
       <exercisegroup cols="2" xml:id="exset-ode-modelling">
         <introduction>
           <p>
-            In the following exercises,
-            use the tools in the section to answer the questions presented.
+            Use the tools in the section to answer the questions presented.
           </p>
         </introduction>
         <exercise label="ex-ode-modelling-proportional">

ptx/sec_Separable.ptx

@@ -501,13 +501,13 @@
           The general solution the logistic differential equation is the set containing <m>\displaystyle y = \frac{M}{1 + be^{-kt}}</m> and <m>y=0</m>.
         </p>
       </solution>
-      <solution component="video" vshift="4">
+      <solution component="video" vshift="5">
         <title>Video solution</title>
         <video width="98%" youtube="nLItalqug6A" label="vid-diffeq-separable-example-logistic" component="video"/>
       </solution>
     </example>
 
-    <aside vshift="-1">
+    <aside vshift="1">
       <p>
         Solving for <m>y</m> initially yields the explicit solution <m>\displaystyle y = \frac{AMe^{kt}}{1+Ae^{kt}}</m>.
         Dividing numerator and denominator by <m>Ae^{kt}</m> and defining <m>b = 1/A</m>
@@ -522,8 +522,7 @@
       <exercisegroup cols="2" xml:id="exset-ode-separable-determine">
         <introduction>
           <p>
-            In the following exercises,
-            decide whether the differential equation is separable or not separable.
+            Decide whether the differential equation is separable or not separable.
             If the equation is separable, write it in separated form.
           </p>
         </introduction>
@@ -581,8 +580,7 @@
       <exercisegroup cols="2" xml:id="exset-ode-separable-general-sol">
         <introduction>
           <p>
-            In the following exercises,
-            find the general solution to the separable differential equation.
+            Find the general solution to the separable differential equation.
             Be sure to check for missing constant solutions.
           </p>
         </introduction>
@@ -686,8 +684,7 @@
       <exercisegroup cols="2" xml:id="exset-ode-separable-particular-sol">
         <introduction>
           <p>
-            In the following exercises,
-            find the particular solution to the separable initial value problem.
+            Find the particular solution to the separable initial value problem.
           </p>
         </introduction>
         <exercise label="ex-ode-separable-particular-sol-1">

ptx/sec_alt_series.ptx

@@ -146,7 +146,7 @@
     the sum of the series.
   </p>
 
-  <figure xml:id="fig_alt_series_converge_a" vshift="0">
+  <figure xml:id="fig_alt_series_converge_a" vshift="-1">
     <caption>Illustrating convergence with the Alternating Series Test</caption>
   <!-- START figures/fig_alt_series_converge.tex -->
     <image width="47%">
@@ -994,8 +994,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            an alternating series <m>\ds \sum_{n=i}^\infty a_n</m> is given.
+            An alternating series <m>\ds \sum_{n=i}^\infty a_n</m> is given.
           </p>
 
           <p>
@@ -1588,7 +1587,7 @@
         <introduction>
           <p>
             Let <m>S_n</m> be the <m>n^{ th }</m> partial sum of a series.
-            In the following exercises a convergent alternating series is given and a value of <m>n</m>.
+            A convergent alternating series is given and a value of <m>n</m>.
             Compute <m>S_n</m> and <m>S_{n+1}</m> and use these values to find bounds on the sum of the series.
           </p>
         </introduction>
@@ -1682,8 +1681,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            a convergent alternating series is given along with its sum and a value of <m>\varepsilon</m>.
+            A convergent alternating series is given along with its sum and a value of <m>\varepsilon</m>.
             Use <xref ref="thm_alt_series_approx"/>
             to find <m>n</m> such that the
             <m>n</m>th partial sum of the series is within