diff --git a/source/activities/act-6-4-1.xml b/source/activities/act-6-4-1.xml index a9ee16321..ec527849a 100644 --- a/source/activities/act-6-4-1.xml +++ b/source/activities/act-6-4-1.xml @@ -206,7 +206,7 @@ Thus, B(h) = 40 - 0.1h. It follows that the total work to life the leaky bucket 100 feet is - W = int_0^{100} (40-0.1h) \, dh = 3500 \text{foot-pounds} + W = \int_0^{100} (40-0.1h) \, dh = 3500 \text{foot-pounds} .

@@ -216,7 +216,7 @@ Given that B(h) = 25 + 15e^{-0.05h} is the weight of the bucket when h feet of rope have been pulled in, it follows that the total work to move the bucket 100 feet is - 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} . In addition, the average force that was exerted on the bucket is precisely the average weight of the bucket, which is diff --git a/source/exercises/ez-1-2.xml b/source/exercises/ez-1-2.xml index f83250918..410d2a46a 100644 --- a/source/exercises/ez-1-2.xml +++ b/source/exercises/ez-1-2.xml @@ -752,19 +752,19 @@ -0.1 - -53.83629174 + -53.04508149 -0.01 - -53.82973418 + -53.76359015 -0.001 - -53.76359015 + -53.82973418 -0.0001 - -53.04508149 + -53.83629174 @@ -773,14 +773,14 @@

and hence - \lim_{h \to 0} AV_{1, 1+h} \approx -53.837 + \lim_{h \to 0} AV_{[1, 1+h]} \approx -53.837 .

  • - Since \lim_{h \to 0} AV_{1, 1+h} \approx -53.837 this tells us that the instantaneous velocity of the bungee jumper at the moment t = 1 is approximately -53.837 ft/sec. + Since \lim_{h \to 0} AV_{[1, 1+h]} \approx -53.837 this tells us that the instantaneous velocity of the bungee jumper at the moment t = 1 is approximately -53.837 ft/sec.

    • diff --git a/source/frontmatter.xml b/source/frontmatter.xml index 19050f70b..de0b6d223 100644 --- a/source/frontmatter.xml +++ b/source/frontmatter.xml @@ -22,8 +22,8 @@ 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 support of free and open textbooks in general, + I'm also grateful to the AIM Open Textbook Initiative, sponsored by the + American Institute of Mathematics, for their support of open textbooks generally and their support of this one in particular.

    @@ -497,7 +497,7 @@

    - The text is available in three different formats: HTML, PDF, and print, each of which is available via links on the landing page at activecalculus.org/. The first two formats are free. If you are going to use the book electronically, the best mode is the HTML. 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 watch this short video from the author. 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 Amazon. + The text is available in three different formats: HTML, PDF, and print, each of which is available via links on the landing page at activecalculus.org/. The first two formats are free. If you are going to use the book electronically, the best mode is the HTML. 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 watch this short video from the author. 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 Amazon.

    @@ -505,7 +505,7 @@

    - 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 (Chapters 1-4, Chapters 5-8) 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 in the back matter. + 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 (Chapters 1-4, Chapters 5-8) in which to record your work on the activities, or you can find free PDFs at the home page for the textbooks (scroll down in the left panel and look for links to download PDF 1-4 and download PDF 5-8) 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 in the back matter.

    @@ -513,7 +513,7 @@

    - At the end of each section, you'll find two types of Exercises. First, there are several anonymous 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 this short video on the HTML version that includes a demonstration). You should use these exercises as a way to test your understanding of basic ideas in the preceding section. If your institution uses , you may also need to log in to a server as directed by your instructor to complete assigned sets as part of your course grade. The exercises included in this text are ungraded and not connected to any individual account. Following the 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- exercises in the back matter. + At the end of each section, you'll find two types of Exercises. First, there are several anonymous 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 this short video on the HTML version that includes a demonstration). You should use these exercises as a way to test your understanding of basic ideas in the preceding section. If your institution uses , you may also need to log in to a server as directed by your instructor to complete assigned sets as part of your course grade. The exercises included in this text are ungraded and not connected to any individual account. Following the 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- exercises in the back matter.

    @@ -529,7 +529,7 @@ Instructors! Read this!

    - This book is different. Before you read further, first read Students! Read this!. + This book is different. Before you read further, first read Students! Read this!. More information for instructors can also be found at the home page for the text, at activecalculus.org generally, and on the instructors page.

    @@ -538,7 +538,7 @@

    - 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 (Chapters 1-4, Chapters 5-8) 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 (Chapters 1-4, Chapters 5-8) or as free PDFs at the home page for the textbooks (scroll down in the left panel and look for links to download PDF 1-4 and download PDF 5-8); many instructors use the PDF to have coursepacks printed for students to purchase from their local bookstore.

    @@ -582,7 +582,7 @@

    - In the back matter of the text, you'll find answers to the Activities and to non- Exercises. Instructors interested in solutions to these should contact the author directly. + In the back matter of the text, you'll find answers to the Activities and to non- Exercises. Instructors interested in solutions to these should contact the author directly.

    @@ -590,7 +590,7 @@

    - The source code for the text can be found on GitHub. If you find errors in the text or have other suggestions, you can file an issue on GitHub, use the Feedback link 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 Open Calculus blog; 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 online video presentation to the MIT Electronic Seminar on Mathematics Education; at about the 17-minute mark, the portion begins where we demonstrate features of and how to use the text. + The source code for the text can be found on GitHub. 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 a blog; you can request to join the Google group via the link at the instructors page. Finally, if you're interested in a video presentation on using the text, you can see this online video presentation to the MIT Electronic Seminar on Mathematics Education; at about the 17-minute mark, the portion begins where we demonstrate features of and how to use the text.