Parametric Surface Revision

Old source files/S_mult_ints_double_ints_param_surf.ptx

@@ -167,7 +167,7 @@
       where <m>(s,t)</m> varies over the entire domain of <m>f</m>. Therefore, any familiar surface that we have studied so far can be generated as a parametric surface. But what is more powerful is that there are surfaces that cannot be generated by a single function <m>z = f(x,y)</m> (such as the unit sphere), but that can be represented parametrically. We now consider an important example.
     </p>
 
-    <example xml:id="ex_11_6_Torus">
+    <example xml:id="ex_Torus">
       <statement>
         <p>
           Consider the
@@ -254,7 +254,7 @@
     </example>
 
     <worksheet>
-  <activity workspace="1.5in" xml:id="A_11_6_10">
+  <activity workspace="1.5in" xml:id="act-sphere-param">
       <statement> 
       <p>
         In this activity, we seek a
@@ -417,7 +417,7 @@
 
 
     <worksheet>
-  <activity workspace="1.5in" xml:id="A_11_6_4">
+  <activity workspace="1.5in" xml:id=""cyl-surfacearea">
       <statement> 
         <p>
           Consider the cylinder with radius <m>a</m> and height <m>h</m> defined parametrically by

project.ptx

@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="utf-8"?>
 <project ptx-version="2">
-  <!-- For the conversion to ptx-version="2", I have only tested HTML and instructor targets inintially (20250702). MTK -->
+  <!-- For the conversion to ptx-version="2", I have only tested HTML and instructor targets initially (20250702). MTK -->
   <targets>
     <target name="html" format="html" source="acmv-index.ptx" xsl="acmv-html.xsl" deploy-dir="multi" />
     <target name="instructor" format="html" source="acmv-index.ptx" xsl="acmv-html.xsl" publication="publication-instructor.ptx" deploy-dir="multi-instructor" />

source/C-mvprecalc.ptx

@@ -26,7 +26,7 @@
     More generally, we will need to work with functions and expressions that depend on more than one input or involve outputs more complicated than a single scalar. For instance, when trying to find the optimal price for a product, you will need to consider fixed costs like a building lease, labor costs, and the varying costs of all the materials that are used in the product. Another example would be trying to measure the atmospheric temperature, which will vary over a three-dimensional space and will vary over time of day as well. If we wanted to use wind to help in modeling weather phenomena, we will need new tools since wind has both a direction and a strength associated with it, and thus cannot be measured by a single number. For each of the cases mentioned above, it is not entirely clear how to relate changes in the input variables to changes in the different kinds of outputs. A long-term goal of our work in this book will be to carefully define the relationship between changes of inputs and outputs for many new types of functions.
   </p>
   <p>
-    With our new expanded view of the world around us, we will also need to describe a variety of new examples of mathematical objects that are algebraically nice and exhibit different geometric features. You spent a few math classes to understand and apply to the calculus of one-variable in and one-variable out, we will expand our tools in much less time because of the depth and variety of ideas we have already encountered. Before we look at the calculus of these new kinds of functions, we will need to do a bit of precalculus again.
+    With our new expanded view of the world around us, we will also need to describe a variety of new examples of mathematical objects that are algebraically nice and exhibit different geometric features. Most students took several math classes to understand and apply to the calculus of functions with one-variable in and one-variable out; In this text, we will expand our tools in much less time because of the depth and variety of ideas that you have already encountered. Before we look at the calculus of these new kinds of functions, we will need to do a bit of precalculus again.
   </p>
   </introduction>
   <!-- <xi:include  href="S_Precalc_Ideas.ptx" /> -->

source/C-vvf.ptx

@@ -81,7 +81,7 @@
                 plot2+=text("$f(a)-f(a-h)$",(-0.25,-0.05),color="orange",fontsize=20)
                 plot2
               </sageplot>
-            <description><p>ADD ALT TEXT TO THIS IMAGE</p></description></image>
+            <description><p>A plot of a downward facing parabola with a blue line going between two points on the parabola. The blue line corresponds to more horizontal change than vertical change. The right point on the parabola is labeled <m>P:(a,f(a))</m>. The change in the vertical coordinates between these two points is represented with a vertical segment in yellow and is labeled <m>f(a)-f(a-h)</m>. The change in the horizontal coordinates between two points is represented by a green line segment that is labeled <m>h</m>. </p></description></image>
             <image width="100%" xml:id="img-secline2">
               <sageplot>
                 var('t,x')
@@ -101,7 +101,7 @@
                 plot3+=text("$f(a)-f(a-h)$",(0.10,-0.05),color="orange",fontsize=18)
                 plot3
               </sageplot>
-            <description><p>ADD ALT TEXT TO THIS IMAGE</p></description></image>
+            <description><p>A plot of a downward facing parabola with a blue line going between two points on the parabola. The blue line in this plot is steeper than in the previous plot and the points are closer together on the parabola. The right point on the parabola is labeled <m>P:(a,f(a))</m>. The change in the vertical coordinates between these two points is represented with a vertical segment in yellow and is labeled <m>f(a)-f(a-h)</m>. The change in the horizontal coordinates between two points is represented by a green line segment that is labeled <m>h</m>.</p></description></image>
             <image width="100%" xml:id="img-secline3">
               <sageplot>
                 var('t,x')
@@ -121,7 +121,7 @@
                 plot4+=text("$f(a)-f(a-h)$",(0.20,-0.05),color="orange",fontsize=20)
                 plot4
               </sageplot>
-            <description><p>ADD ALT TEXT TO THIS IMAGE</p></description></image>
+            <description><p>A plot of a downward facing parabola with a blue line going between two points on the parabola. The blue line in this plot is slightly steeper than in the previous plot and the two points are close together on the parabola. The right point on the parabola is labeled <m>P:(a,f(a))</m>. The change in the vertical coordinates between these two points is represented with a vertical segment in yellow and is labeled <m>f(a)-f(a-h)</m>. The change in the horizontal coordinates between two points is represented by a green line segment that is labeled <m>h</m>.</p></description></image>
           </sidebyside>
       <!-- </figure> -->
       <p>
@@ -152,7 +152,11 @@
       <!-- <figure xml:id="Riemannsum1">
         <caption>At left and center, two left Riemann sums for a function <m>f</m> that is sometimes negative; at right, the exact areas bounded by <m>f</m> on the interval <m>[a,d]</m> (image from https://activecalculus.org/single/sec-4-3-definite-integral.html#F-4-3-IncreaseN) </caption> -->
         <image source="images/4_2_NegF">
-          <description><p>ADD ALT TEXT TO THIS IMAGE</p></description></image>
+          <description><p>A sequence of three images shows different Riemann sum converging to the defintie integral. 
+            The left image shows a sinusoidal graph in blue that goes above and below the the horizontal axis. From left to right, points with inputs a, b, c, and d are labeled on a horizontal segment. The blue graph is above the horizontal axis between inputs a nd b and between c and d. The blue graph is below the horizontal axis between b and c. Eleven green rectangles extend vertically from the horizontal axis to the blue graph on the region of inputs from a to d. 
+            The center image shows a sinusoidal graph in blue that goes above and below the the horizontal axis. From left to right, points with inputs a, b, c, and d are labeled on a horizontal segment. The blue graph is above the horizontal axis between inputs a nd b and between c and d. The blue graph is below the horizontal axis between b and c. Twenty two green rectangles extend vertically from the horizontal axis to the blue graph on the region of inputs from a to d. These green rectangles better approximate the area under the blue graph, as compared to the left image.
+            The right image shows a sinusoidal graph in blue that goes above and below the the horizontal axis. From left to right, points with inputs a, b, c, and d are labeled on a horizontal segment. The blue graph is above the horizontal axis between inputs a nd b and between c and d. The blue graph is below the horizontal axis between b and c. The area below the blue curve and above the horizontal axis for inputs from a to b is shaded in blue and labeled <m>A_1</m>. The area above the blue curve and below the horizontal axis for inputs from b to c is shaded in red and labeled <m>A_2</m>. The area below the blue curve and above the horizontal axis for inputs from c to d is shaded in blue and labeled <m>A_3</m>.
+          </p></description></image>
       <!-- </figure> -->
 
       <p>