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Merge pull request #333 from mattboelkins/S24-edits
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minor changes to some frontmatter things, plus a few answer/solution …
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mattboelkins authored Aug 16, 2024
2 parents bf9b773 + d69be5c commit 9aacd2b
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4 changes: 2 additions & 2 deletions source/activities/act-6-4-1.xml
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Thus, <m>B(h) = 40 - 0.1h</m>.
It follows that the total work to life the leaky bucket 100 feet is
<me permid="GOO">
W = int_0^{100} (40-0.1h) \, dh = 3500 \text{foot-pounds}
W = \int_0^{100} (40-0.1h) \, dh = 3500 \text{foot-pounds}
</me>.
</p>
</li>
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Given that <m>B(h) = 25 + 15e^{-0.05h}</m> is the weight of the bucket when <m>h</m> feet of rope have been pulled in,
it follows that the total work to move the bucket 100 feet is
<me permid="mVX">
W = \int_0^{100} (25 + 5e^{-0.05h})\, dh \approx 2597.98 \text{ foot-pounds}
W = \int_0^{100} (25 + 15e^{-0.05h})\, dh \approx 2797.98 \text{ foot-pounds}
</me>.
In addition,
the average force that was exerted on the bucket is precisely the average weight of the bucket, which is
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12 changes: 6 additions & 6 deletions source/exercises/ez-1-2.xml
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</row>
<row>
<cell><m>-0.1</m></cell>
<cell><m>-53.83629174</m></cell>
<cell><m>-53.04508149</m></cell>
</row>
<row>
<cell><m>-0.01</m></cell>
<cell><m>-53.82973418</m></cell>
<cell><m>-53.76359015</m></cell>
</row>
<row>
<cell><m>-0.001</m></cell>
<cell><m>-53.76359015</m></cell>
<cell><m>-53.82973418</m></cell>
</row>
<row>
<cell><m>-0.0001</m></cell>
<cell><m>-53.04508149</m></cell>
<cell><m>-53.83629174</m></cell>
</row>
</tabular>

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<p permid="EhH">
and hence
<me permid="YKs">
\lim_{h \to 0} AV_{1, 1+h} \approx -53.837
\lim_{h \to 0} AV_{[1, 1+h]} \approx -53.837
</me>.
</p>
</li>

<li permid="PMf">
<p permid="koQ">
Since <m>\lim_{h \to 0} AV_{1, 1+h} \approx -53.837</m> this tells us that the instantaneous velocity of the bungee jumper at the moment <m>t = 1</m> is approximately <m>-53.837</m> ft/sec.
Since <m>\lim_{h \to 0} AV_{[1, 1+h]} \approx -53.837</m> this tells us that the instantaneous velocity of the bungee jumper at the moment <m>t = 1</m> is approximately <m>-53.837</m> ft/sec.
</p>
</li>
</ol>
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18 changes: 9 additions & 9 deletions source/frontmatter.xml
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during which I wrote most of the material for the first four chapters.
For the sabbatical leave, I am indebted to Grand Valley State University for its support of the project,
as well as to my colleagues in the Department of Mathematics and the College of Liberal Arts and Sciences for their endorsement of the project.
I'm also grateful to the American Institute of Mathematics
for their <url href="https://aimath.org/textbooks/" visual="aimath.org/textbooks/">support of free and open textbooks in general</url>,
I'm also grateful to the <url href="https://textbooks.aimath.org/" visual="https://textbooks.aimath.org/">AIM Open Textbook Initiative</url>, sponsored by the
American Institute of Mathematics, for their support of open textbooks generally
and their support of this one in particular.
</p>

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</p>

<p permid="TVG">
The text is available in three different formats: HTML, PDF, and print, each of which is available via links on the landing page at <url href="https://activecalculus.org/" visual="">activecalculus.org/</url>. The first two formats are free. If you are going to use the book electronically, the best mode is the <url href="https://activecalculus.org/single/" visual="activecalculus.org/single">HTML</url>. The HTML version looks great in any browser, including on a smartphone, and the links are much easier to navigate in HTML than in PDF. Some particular direct suggestions about using the HTML follow among the next few paragraphs; alternatively, you can <url href="https://gvsu.edu/s/14i" visual="gvsu.edu/s/14i">watch this short video from the author</url>. It is also wise to download and save the PDF, since you can use the PDF offline, while the HTML version requires an internet connection. A print copy costs about $21 via <url href="https://gvsu.edu/s/14n" visual="gvsu.edu/s/14n">Amazon</url>.
The text is available in three different formats: HTML, PDF, and print, each of which is available via links on the landing page at <url href="https://activecalculus.org/" visual="">activecalculus.org/</url>. The first two formats are free. If you are going to use the book electronically, the best mode is the <url href="https://activecalculus.org/single/" visual="activecalculus.org/single">HTML</url>. The HTML version looks great in any browser, including on a smartphone, and the links are much easier to navigate in HTML than in PDF. Some particular direct suggestions about using the HTML follow among the next few paragraphs; alternatively, you can <url href="https://gvsu.edu/s/14i" visual="gvsu.edu/s/14i">watch this short video from the author</url>. It is also wise to download and save the PDF, since you can use the PDF offline, while the HTML version requires an internet connection. A print copy costs about $25 via <url href="https://gvsu.edu/s/14n" visual="gvsu.edu/s/14n">Amazon</url>.
</p>

<p permid="AcP">
This book is intended to be read sequentially and engaged with, much more than to be used as a lookup reference. For example, each section begins with a short introduction and a Preview Activity; you should read the short introduction and complete the Preview Activity prior to class. Your instructor may require you to do this. Most Preview Activities can be completed in 15-20 minutes and are intended to be accessible based on the understanding you have from preceding sections. There are not answers provided to Preview Activities, as these are designed simply to get you thinking about ideas that will be helpful in work on upcoming new material.
</p>

<p permid="gjY">
As you use the book, think of it as a workbook, not a worked-book. There is a great deal of scholarship that shows people learn better when they interactively engage and struggle with ideas themselves, rather than passively watch others. Thus, instead of reading worked examples or watching an instructor complete examples, you will engage with Activities that prompt you to grapple with concepts and develop deep understanding. You should expect to spend time in class working with peers on Activities and getting feedback from them and from your instructor. You can purchase a separate Activities Workbook from Amazon (<url href="https://gvsu.edu/s/14l" visual="gvsu.edu/s/14l">Chapters 1-4</url>, <url href="https://gvsu.edu/s/14m" visual="gvsu.edu/s/14m">Chapters 5-8</url>) in which to record your work on the activities, or you can ask your instructor for a copy of the PDF file that has only the activities along with room to record your work. Your goal should be to do all of the activities in the relevant sections of the text and keep a careful record of your work. You can find answers to the activities <xref ref="activities-answers">in the back matter</xref>.
As you use the book, think of it as a workbook, not a worked-book. There is a great deal of scholarship that shows people learn better when they interactively engage and struggle with ideas themselves, rather than passively watch others. Thus, instead of reading worked examples or watching an instructor complete examples, you will engage with Activities that prompt you to grapple with concepts and develop deep understanding. You should expect to spend time in class working with peers on Activities and getting feedback from them and from your instructor. You can purchase a separate Activities Workbook from Amazon (<url href="https://gvsu.edu/s/14l" visual="gvsu.edu/s/14l">Chapters 1-4</url>, <url href="https://gvsu.edu/s/14m" visual="gvsu.edu/s/14m">Chapters 5-8</url>) in which to record your work on the activities, or you can find free PDFs at <url href="https://activecalculus.org/acs/" visual="https://activecalculus.org/acs/">the home page for the textbooks</url> (scroll down in the left panel and look for links to <q>download PDF 1-4</q> and <q>download PDF 5-8</q>) that have only the activities along with room to record your work. Your goal should be to do all of the activities in the relevant sections of the text and keep a careful record of your work. You can find answers to the activities <xref ref="activities-answers" text="custom">in the back matter</xref>.
</p>

<p permid="Mrh">
Each section concludes with a Summary. Reading the Summary after you have read the section and worked the Activities is a good way to find a short list of key ideas that are most essential to take from the section. A good study habit is to write similar summaries in your own words.
</p>

<p permid="syq">
At the end of each section, you'll find two types of Exercises. First, there are several anonymous <webwork /> exercises. These are online, interactive exercises that allow you to submit answers for immediate feedback with unlimited attempts without penalty; to submit answers, you have to be using the HTML version of the text (see <url href="https://gvsu.edu/s/14i" visual="gvsu.edu/s/14i">this short video</url> on the HTML version that includes a <webwork /> demonstration). You should use these exercises as a way to test your understanding of basic ideas in the preceding section. If your institution uses <webwork />, you may also need to log in to a server as directed by your instructor to complete assigned <webwork /> sets as part of your course grade. The <webwork /> exercises included in this text are ungraded and not connected to any individual account. Following the <webwork /> exercises there are 3-4 additional challenging exercises that are designed to encourage you to connect ideas, investigate new situations, and write about your understanding. There are answers to most of the non-<webwork /> exercises <xref ref="exercises-answers">in the back matter</xref>.
At the end of each section, you'll find two types of Exercises. First, there are several anonymous <webwork /> exercises. These are online, interactive exercises that allow you to submit answers for immediate feedback with unlimited attempts without penalty; to submit answers, you have to be using the HTML version of the text (see <url href="https://gvsu.edu/s/14i" visual="gvsu.edu/s/14i">this short video</url> on the HTML version that includes a <webwork /> demonstration). You should use these exercises as a way to test your understanding of basic ideas in the preceding section. If your institution uses <webwork />, you may also need to log in to a server as directed by your instructor to complete assigned <webwork /> sets as part of your course grade. The <webwork /> exercises included in this text are ungraded and not connected to any individual account. Following the <webwork /> exercises there are 3-4 additional challenging exercises that are designed to encourage you to connect ideas, investigate new situations, and write about your understanding. There are answers to most of the non-<webwork /> exercises <xref ref="exercises-answers" text="custom">in the back matter</xref>.
</p>

<p permid="YFz">
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<preface xml:id="preface-for-instructors" permid="Sgt">
<title>Instructors! Read this!</title>
<p permid="kTR">
This book is different. Before you read further, first read <xref ref="preface-for-students" text="custom"><q>Students! Read this!</q></xref>.
This book is different. Before you read further, first read <xref ref="preface-for-students" text="custom"><q>Students! Read this!</q></xref>. More information for instructors can also be found at <url href="https://activecalculus.org/acs/" visual="https://activecalculus.org/acs/">the home page for the text</url>, at <url href="https://activecalculus.org/" visual="https://activecalculus.org/">activecalculus.org generally</url>, and on the <url href="https://activecalculus.org/instructors/" visual="https://activecalculus.org/instructors/">instructors page</url>.
</p>

<p permid="Rba">
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<p permid="xij">
Among the three formats (HTML, PDF, print), the HTML is optimal for display in class if you have a suitable projector. The HTML is also best for navigation, as links to internal and external references are much more obvious. We recommend saving a downloaded version of the PDF format as a backup in the event you don't have internet access. It's a good idea for each student to have a printed version of the Activities Workbook, which is available on Amazon (<url href="https://gvsu.edu/s/14l" visual="gvsu.edu/s/14l">Chapters 1-4</url>, <url href="https://gvsu.edu/s/14m" visual="gvsu.edu/s/14m">Chapters 5-8</url>) or as a PDF document by direct request to the author (boelkinm at gvsu dot edu); many instructors use the PDF to have coursepacks printed for students to purchase from their local bookstore.
Among the three formats (HTML, PDF, print), the HTML is optimal for display in class if you have a suitable projector. The HTML is also best for navigation, as links to internal and external references are much more obvious. We recommend saving a downloaded version of the PDF format as a backup in the event you don't have internet access. It's a good idea for each student to have a printed version of the Activities Workbook, which is available on Amazon (<url href="https://gvsu.edu/s/14l" visual="gvsu.edu/s/14l">Chapters 1-4</url>, <url href="https://gvsu.edu/s/14m" visual="gvsu.edu/s/14m">Chapters 5-8</url>) or as free PDFs at <url href="https://activecalculus.org/acs/" visual="https://activecalculus.org/acs/">the home page for the textbooks</url> (scroll down in the left panel and look for links to <q>download PDF 1-4</q> and <q>download PDF 5-8</q>); many instructors use the PDF to have coursepacks printed for students to purchase from their local bookstore.
</p>

<p permid="dps">
Expand Down Expand Up @@ -582,15 +582,15 @@
</p>

<p permid="VKT">
In the back matter of the text, you'll find answers to the <xref ref="activities-answers" text="custom">Activities</xref> and to <xref ref="exercises-answers">non-<webwork /> Exercises</xref>. Instructors interested in solutions to these should contact the author directly.
In the back matter of the text, you'll find answers to the <xref ref="activities-answers" text="custom">Activities</xref> and to <xref ref="exercises-answers" text="custom">non-<webwork /> Exercises</xref>. Instructors interested in solutions to these should contact the author directly.
</p>

<p permid="BSc">
You and your students can find additional resources in the <url href="https://www.youtube.com/playlist?list=PL9bIjQJDwfGuXQHuS5Jkmum_CFILoCZX-" visual="gvsu.edu/s/pG">GVSU Math 201 YouTube Channel</url> and <url href="https://www.youtube.com/playlist?list=PL9bIjQJDwfGtewW75Nw7PnGNSkfqwAm3v" visual="gvsu.edu/s/Nb">GVSU Math 202 YouTube Channel</url> where there are short video tutorials for every section of the text. Math 201 (GVSU's Calculus I) corresponds to Chapters 1-4 and Math 202 (GVSU's Calculus II) to Chapters 5-8.
</p>

<p permid="hZl">
The <pretext /> source code for the text can be found on <url href="https://github.com/active-calculus/active-calculus-single-mbx" visual="github.com/active-calculus/active-calculus-single-mbx">GitHub</url>. If you find errors in the text or have other suggestions, you can file an issue on GitHub, use the <url href="https://gvsu.edu/s/0vK" visual="gvsu.edu/s/0vK">Feedback link</url> in the HTML version (found at the bottom left in the main menu), or email the author directly. To engage with instructors who use the text, we maintain both an email list and the <url href="https://opencalculus.wordpress.com/" visual="opencalculus.wordpress.com">Open Calculus blog</url>; you can request that your address be added to the email list by contacting the author. Finally, if you're interested in a video presentation on using the text, you can see this <url href="https://math.mit.edu/seminars/esme/videos/2018-10-02_Boelkins.mp4" visual="math.mit.edu/seminars/esme/videos/2018-10-02_Boelkins.mp4">online video presentation</url> to the <url href="https://math.mit.edu/seminars/esme/" visual="math.mit.edu/seminars/esme/">MIT Electronic Seminar on Mathematics Education</url>; at about the 17-minute mark, the portion begins where we demonstrate features of and how to use the text.
The <pretext /> source code for the text can be found on <url href="https://github.com/active-calculus/active-calculus-single-mbx" visual="github.com/active-calculus/active-calculus-single-mbx">GitHub</url>. If you find errors in the text or have other suggestions, you can file an issue on GitHub or email the author directly. To engage with instructors who use the text, we maintain a Google group and <url href="https://activecalculus.org/blog/" visual="activecalculus.org/blog">a blog</url>; you can request to join the Google group via the link at <url href="https://activecalculus.org/instructors/" visual="https://activecalculus.org/instructors/"> the instructors page</url>. Finally, if you're interested in a video presentation on using the text, you can see this <url href="https://math.mit.edu/seminars/esme/videos/2018-10-02_Boelkins.mp4" visual="math.mit.edu/seminars/esme/videos/2018-10-02_Boelkins.mp4">online video presentation</url> to the <url href="https://math.mit.edu/seminars/esme/" visual="math.mit.edu/seminars/esme/">MIT Electronic Seminar on Mathematics Education</url>; at about the 17-minute mark, the portion begins where we demonstrate features of and how to use the text.
</p>

<p permid="Ogu">
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