1 #LyX 1.6.5svn created this file. For more info see http://www.lyx.org/
6 \use_default_options true
11 \font_typewriter default
12 \font_default_family default
19 \paperfontsize default
28 \paperorientation portrait
31 \paragraph_separation indent
33 \quotes_language english
36 \paperpagestyle default
37 \tracking_changes false
51 \begin_inset Note Note
54 \begin_layout Plain Layout
55 author of this example file: Jason Waskiewicz
63 \begin_layout Standard
64 \begin_inset CommandInset toc
65 LatexCommand tableofcontents
73 The Features of the Tufte-book Class
76 \begin_layout Standard
77 In this document, it was endeavored to show some of the features of the
83 In the first chapter, their use is outlined.
84 In the second chapter, their use through a handout that was created in
85 a calculus class is demonstrated.
92 \begin_layout Standard
97 class is based on the work of
102 It provides the same functionality as the
106 class with book-specific additions.
107 Tufte's documents consist of a rather narrow column of text and a wide
108 column of margin notes and margin figures.
109 This is to improve readability.
112 \begin_layout Standard
113 The features provided by this format include:
116 \begin_layout Itemize
120 \begin_layout Itemize
121 Ordinary figures in text with captions in margins
124 \begin_layout Itemize
125 Full width figures and text when needed
128 \begin_layout Itemize
129 \begin_inset Quotes eld
133 \begin_inset Quotes erd
139 \begin_layout Itemize
140 Limited layers of sections and subsections
143 \begin_layout Standard
144 In this sample document, some of these features are demonstrated.
145 For a full demonstration, visit the tufte-latex website:
146 \begin_inset Flex URL
149 \begin_layout Plain Layout
151 http://code.google.com/p/tufte-latex
159 \begin_layout Section
163 \begin_layout Standard
165 \begin_inset Quotes eld
169 \begin_inset Quotes erd
172 rather than justified.
173 \begin_inset Flex Sidenote
176 \begin_layout Plain Layout
177 To get justified text, add the option
187 Document\SpecialChar \menuseparator
188 Settings\SpecialChar \menuseparator
196 Ragged right text is used in most of his works, but the class option
200 is provided to change this.
203 \begin_layout Standard
204 Tufte also formats his pages asymmetrically.
205 This means that the marginalia appear on the right side on each page, whether
207 If you prefer, you can change that and have symmetric layout, as common
208 in traditional book typography, by using the
213 \begin_inset Flex Sidenote
216 \begin_layout Plain Layout
217 To create a symmetric layout, add the option
227 Document\SpecialChar \menuseparator
228 Settings\SpecialChar \menuseparator
239 \begin_layout Standard
240 Finally, Tufte does not number his chapters or his sections.
241 If you like to refer to sections by number, move the
247 Document\SpecialChar \menuseparator
248 Settings\SpecialChar \menuseparator
251 to the very right (as done in this document).
252 \begin_inset Flex Marginnote
255 \begin_layout Plain Layout
264 \begin_layout Section
268 \begin_layout Standard
269 Tufte uses ordinary figure floats such as the following:
272 \begin_layout Standard
273 \begin_inset Float figure
278 \begin_layout Plain Layout
279 \begin_inset Box Boxed
288 height_special "totalheight"
291 \begin_layout Plain Layout
292 Imagine your favorite figure inside this box instead of this boring text.
300 \begin_layout Plain Layout
301 An ordinary figure float.
314 \begin_layout Standard
315 Furthermore, he uses margin figures, as shown in Fig.
320 \begin_inset CommandInset ref
322 reference "fig:margin-figure"
329 \begin_layout Standard
330 \begin_inset Float marginfigure
335 \begin_layout Plain Layout
336 \begin_inset Box Boxed
345 height_special "totalheight"
348 \begin_layout Plain Layout
349 Imagine your favorite photograph of a squirrel inside this box instead of
358 \begin_layout Plain Layout
360 \begin_inset CommandInset label
362 name "fig:margin-figure"
379 \begin_layout Standard
380 In the same vein, the
384 class allows the use of tables, both in the margins and in the text.
385 The margin tables are recommended for a small set of data to illustrate
387 \begin_inset Quotes eld
390 Look, distance-time data is quadratic when the object is falling.
391 \begin_inset Quotes erd
394 More detailed data such as flame test results and comments should be put
395 in a full-width table instead.
398 \begin_layout Standard
403 provides a full-width figure.
404 This one takes up the entire width of the page, i.
405 \begin_inset space \thinspace{}
414 \begin_inset CommandInset ref
416 reference "fig:full-width-figure"
423 \begin_layout Standard
424 \begin_inset Float figure
429 \begin_layout Plain Layout
430 \begin_inset Box Boxed
439 height_special "totalheight"
442 \begin_layout Plain Layout
443 Imagine your favorite photograph of a squirrel inside this box instead of
450 \begin_inset VSpace defskip
456 \begin_layout Plain Layout
459 \begin_layout Plain Layout
461 \begin_inset CommandInset label
463 name "fig:full-width-figure"
480 \begin_layout Section
484 \begin_layout Standard
485 One of the most prominent and distinctive features of this style is the
486 extensive use of sidenotes.
487 There is a wide margin to provide ample room for sidenotes and small figures.
488 Any footnotes will automatically be converted to sidenotes.
492 \begin_layout Plain Layout
493 This is a sidenote that was entered using a
502 Alternatively, you can also use the
506 inset directly; you'll find it in the
508 Insert\SpecialChar \menuseparator
512 \begin_inset Flex Sidenote
515 \begin_layout Plain Layout
516 This is a sidenote that was entered using a
528 \begin_layout Standard
529 If you like to place ancillary information in the margin without the sidenote
530 mark (the superscript number), you can use the
536 \begin_inset Flex Marginnote
539 \begin_layout Plain Layout
540 This is Tufte's margin note.
541 Notice that there isn't a number preceding the note, and there is no number
542 in the main text where this note was written.
547 The normal margin note will work as well, but it will look rather odd.
548 \begin_inset Marginal
551 \begin_layout Plain Layout
552 This is a normal margin note.
561 \begin_layout Standard
562 \begin_inset Flex NewThought
565 \begin_layout Plain Layout
571 innovation is Tufte's
577 Edit\SpecialChar \menuseparator
578 TextStyle\SpecialChar \menuseparator
582 It introduces new thoughts by means of small caps, as demonstrated in this
587 \begin_layout Standard
588 The Tufte document classes include two new character styles and some improvement
589 s on existing commands for letterspacing.
592 \begin_layout Standard
593 When setting strings of
594 \begin_inset Flex AllCaps
597 \begin_layout Plain Layout
604 \begin_inset Flex SmallCaps
607 \begin_layout Plain Layout
613 , the letterspacing---that is, the spacing between the letters---should
614 be increased slightly.
615 \begin_inset CommandInset citation
627 Edit\SpecialChar \menuseparator
628 TextStyle\SpecialChar \menuseparator
631 ) has proper letterspacing for strings of
632 \begin_inset Flex AllCaps
635 \begin_layout Plain Layout
647 Edit\SpecialChar \menuseparator
648 TextStyle\SpecialChar \menuseparator
651 ) has letterspacing for
652 \begin_inset Flex SmallCaps
655 \begin_layout Plain Layout
656 small capital letters
662 These commands will also automatically convert the case of the text to
663 upper- or lowercase, respectively.
666 \begin_layout Standard
671 shape has also been redefined to include letterspacing.
672 Its case is left as is, however.
673 This allows one to use both uppercase and lowercase letters:
675 The Initial Letters Of The Words In This Sentence Are Capitalized.
678 \begin_layout Standard
683 paragraph environment provides a paragraph layout that stretches across
684 the main text block and the sidenotes area:
687 \begin_layout Full Width
688 Lorem ipsum dolor sit amet, consectetuer adipiscing elit.
689 Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae, felis.
690 Curabitur dictum gravida mauris.
691 Nam arcu libero, nonummy eget, consectetuer id, vulputate a, magna.
692 Donec vehicula augue eu neque.
693 Pellentesque habitant morbi tristique senectus et netus et malesuada fames
696 Cras viverra metus rhoncus sem.
697 Nulla et lectus vestibulum urna fringilla ultrices.
698 Phasellus eu tellus sit amet tortor gravida placerat.
699 Integer sapien est, iaculis in, pretium quis, viverra ac, nunc.
700 Praesent eget sem vel leo ultrices bibendum.
702 Morbi dolor nulla, malesuada eu, pulvinar at, mollis ac, nulla.
703 Curabitur auctor semper nulla.
704 Donec varius orci eget risus.
705 Duis nibh mi, congue eu, accumsan eleifend, sagittis quis, diam.
706 Duis eget orci sit amet orci dignissim rutrum.
709 \begin_layout Section
713 \begin_layout Standard
714 References are placed alongside their citations as sidenotes, as well.
715 This can be accomplished using the normal citation command.
719 \begin_layout Plain Layout
720 The previous section includes a citation.
728 \begin_layout Standard
729 The complete list of references may also be printed automatically by using
732 Insert\SpecialChar \menuseparator
733 Lists/TOC\SpecialChar \menuseparator
740 (see the end of this document for an example.) If you do not want to print
741 a bibliography at the end of your document, place the
749 inset inside a LyX note and use the LaTeX command
758 \begin_layout Chapter
759 Calculation of Volume: Sections 2.12–2.13
762 \begin_layout Abstract
763 Imagine taking a function like
764 \begin_inset Formula $y=\sqrt{x}$
767 and rotating it in 3 dimensions around the x-axis.
768 The resulting shape would look somewhat like a cup (on its side).
769 Interestingly, integration empowers us to do exactly this and to find out
770 how much water that cup could hold.
773 \begin_layout Section
777 \begin_layout Standard
778 \begin_inset Float marginfigure
783 \begin_layout Plain Layout
784 \begin_inset Box Boxed
793 height_special "totalheight"
796 \begin_layout Plain Layout
797 I had a graph of the square root function here.
805 \begin_layout Plain Layout
806 \begin_inset CommandInset label
808 name "mar:A-graph-of"
813 \begin_inset Formula $f(x)=\sqrt{x}$
829 \begin_layout Standard
830 \begin_inset Float marginfigure
835 \begin_layout Plain Layout
836 \begin_inset Box Boxed
845 height_special "totalheight"
848 \begin_layout Plain Layout
849 Here I rotated the square root function and then drew a disk on the figure
850 to illustrate how I would calculate the volume of the figure.
858 \begin_layout Plain Layout
859 \begin_inset CommandInset label
866 \begin_inset Formula $f(x)=\sqrt{x}$
869 rotated about the x-axis and with additional remarks for integration.
882 \begin_layout Standard
884 \begin_inset CommandInset ref
886 reference "mar:A-graph-of"
890 shows the plot of the function
891 \begin_inset Formula $f(x)=\sqrt{x}.$
894 Now, imagine that we rotate that function about the x-axis.
895 The resulting figure would be somewhat like figure
896 \begin_inset CommandInset ref
898 reference "mar:rotated"
903 This is akin to a cup lying on its side.
904 For the sake of clarity, the artist (me) drew a circle on the end of the
905 figure to show that it is indeed rotated.
908 \begin_layout Standard
909 Now, suppose we wished to find the volume of the figure.
910 When we integrated the original square root function to find its area,
911 we imagined a series of rectangles inside the figure.
913 \begin_inset Formula $h=f(x)$
917 \begin_inset Formula $dx$
921 Since height multiplied by width was the area of each rectangle, we summed
922 these areas and rewrote this as
923 \begin_inset Formula $\int\, f(x)\, dx$
926 , or, in this specific case,
927 \begin_inset Formula $\int\,\sqrt{x}\, dx$
933 \begin_layout Standard
934 To find the volume of our rotated figure the prodecure is quite similar.
935 Begin by rotating each rectangle about the x-axis.
936 This creates a series of cylinders.
937 \begin_inset Flex Sidenote
940 \begin_layout Plain Layout
941 The text refers to these cylinders as "disks".
942 This is standard practice in all the Calculus books I checked.
947 Then, we can find the volume of each cylinder/disk.
948 The basic formula is:
951 \begin_layout Standard
952 \begin_inset Formula \[
960 \begin_layout Standard
963 \begin_inset Formula $h$
966 is the height of the cylinder (width of the rectangle)
967 \begin_inset Formula $dx$
971 The area of each figure is a circle where
972 \begin_inset Formula $A=\pi r^{2}$
976 The radius in this case is the function
977 \begin_inset Formula $f(x)$
984 \begin_layout Standard
985 \begin_inset Formula \[
993 \begin_layout Standard
995 In our specific case,
998 \begin_layout Standard
999 \begin_inset Formula \begin{eqnarray*}
1000 A & = & \pi\left(\sqrt{x}\right)^{2}\\
1001 & = & \pi x\end{eqnarray*}
1008 \begin_layout Standard
1009 To calculate the volume of one disk, we have
1012 \begin_layout Standard
1013 \begin_inset Formula \[
1021 \begin_layout Standard
1023 or, in the general case
1026 \begin_layout Standard
1027 \begin_inset Formula \[
1028 V=\pi f^{2}(x)\, dx\]
1035 \begin_layout Standard
1036 To find the volume of the figure between points
1037 \begin_inset Formula $a$
1041 \begin_inset Formula $b$
1044 we sum the volumes by means of integration:
1047 \begin_layout Standard
1048 \begin_inset Formula \begin{equation}
1049 \int_{a}^{b}\,\pi f^{2}(x)\, dx\end{equation}
1056 \begin_layout Standard
1058 In the specific example, over the interval
1059 \begin_inset Formula $[0,4]$
1065 \begin_layout Standard
1066 \begin_inset Formula \begin{eqnarray*}
1067 \int_{0}^{4}\,\pi x\, dx & = & \pi\int_{0}^{4}\, x\, dx\\
1068 & = & \pi\left.\left(\frac{x^{2}}{2}\right)\right|_{0}^{4}\\
1069 & = & \pi\left(\frac{4^{2}}{2}-0\right)\\
1070 & = & 8\pi\end{eqnarray*}
1077 \begin_layout Standard
1078 \begin_inset Flex NewThought
1081 \begin_layout Plain Layout
1087 a special hole down the length of the cup we just worked with.
1088 It is made with a quadratic shaped bit.
1089 \begin_inset Flex Sidenote
1092 \begin_layout Plain Layout
1093 I have no idea how I'd do this in real life, but I'm making a point.
1098 I find that the hole the bit makes can be modeled with the function
1099 \begin_inset Formula $g(x)=\frac{x^{2}}{16}$
1103 I would need to subtract the volume of the material removed from the volume
1105 \begin_inset Quotes eld
1109 \begin_inset Quotes erd
1113 Each individual cylinder would become like a
1114 \begin_inset Quotes eld
1118 \begin_inset Quotes erd
1122 To get the area of one washer, I would use the formula
1125 \begin_layout Standard
1126 \begin_inset Float marginfigure
1131 \begin_layout Plain Layout
1132 \begin_inset Box Boxed
1141 height_special "totalheight"
1144 \begin_layout Plain Layout
1145 Here I used RLPlot to draw the square root function and the quadratic function.
1146 Then I used Inkscape to shade the area between them.
1152 \begin_inset Caption
1154 \begin_layout Plain Layout
1156 \begin_inset Formula $f(x)$
1160 \begin_inset Formula $g(x)$
1163 and the area left by
1164 \begin_inset Formula $f(x)-g(x)$
1180 \begin_layout Standard
1181 \begin_inset Formula \begin{eqnarray*}
1182 A_{washer} & = & A_{cup}-A_{drill}\\
1183 & = & \pi f^{2}(x)-\pi g^{2}(x)\\
1184 & = & \pi\left(f^{2}(x)-g^{2}(x)\right)\end{eqnarray*}
1191 \begin_layout Standard
1192 The volume of each washer would be
1195 \begin_layout Standard
1196 \begin_inset Formula \begin{eqnarray*}
1197 V_{washer} & = & A_{washer}\, dx\\
1198 & = & \pi\left(f^{2}(x)-g^{2}(x)\right)\, dx\end{eqnarray*}
1205 \begin_layout Standard
1207 Then, by summing the volumes of all the washers between points
1208 \begin_inset Formula $a$
1212 \begin_inset Formula $b$
1215 , the integral is derived:
1218 \begin_layout Standard
1219 \begin_inset Formula \begin{equation}
1220 \int_{a}^{b}\,\pi\left(f^{2}(x)-g^{2}(x)\right)\, dx\end{equation}
1227 \begin_layout Standard
1228 In the case of our quadratic drill bit::
1229 \begin_inset Float marginfigure
1234 \begin_layout Plain Layout
1235 \begin_inset Box Boxed
1244 height_special "totalheight"
1247 \begin_layout Plain Layout
1248 This was the rotated set of 2 functions.
1254 \begin_inset Caption
1256 \begin_layout Plain Layout
1257 The cup with a quadratic hole drilled down its length
1270 \begin_layout Standard
1271 \begin_inset Formula \begin{eqnarray*}
1272 \int_{0}^{4}\,\pi\left(\left(\sqrt{x}\right)^{2}-\left(\frac{x^{2}}{16}\right)\right)\, dx & = & \pi\int_{0}^{4}\,\left(x-\frac{x^{4}}{256}\right)\, dx\\
1273 & = & \pi\left(\int_{0}^{4}\, x\, dx-\int_{0}^{4}\,\frac{x^{4}}{256}\, dx\right)\\
1274 & = & \pi\left(\left.\left(\frac{x^{2}}{2}\right)\right|_{0}^{4}-\left.\left(\frac{x^{5}}{1280}\right)\right|_{0}^{4}\right)\\
1275 & = & \pi\left(\left(\frac{4^{2}}{2}-0\right)-\left(\frac{4^{5}}{1280}-0\right)\right)\\
1276 & = & \pi\left(8-0.8\right)\\
1277 & = & 7.2\pi\end{eqnarray*}
1284 \begin_layout Standard
1288 \begin_layout Section
1292 \begin_layout Itemize
1293 p114: 1, 4, 5, 6, 8, 10, 12, 15
1296 \begin_layout Standard
1297 \begin_inset CommandInset bibtex
1299 bibfiles "biblioExample"
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