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
45 \begin_layout Standard
46 \begin_inset Note Note
49 \begin_layout Plain Layout
56 Insert\SpecialChar \menuseparator
65 Document\SpecialChar \menuseparator
68 menu cannot be used for tufte document classes!
82 \begin_inset Note Note
85 \begin_layout Plain Layout
86 author of this example file: Jason Waskiewicz
94 \begin_layout Standard
95 \begin_inset CommandInset toc
96 LatexCommand tableofcontents
103 \begin_layout Chapter
104 The Features of the Tufte-book Class
107 \begin_layout Standard
108 In this document, it was endeavored to show some of the features of the
114 In the first chapter, their use is outlined.
115 In the second chapter, their use through a handout that was created in
116 a calculus class is demonstrated.
119 \begin_layout Section
123 \begin_layout Standard
128 class is based on the work of
133 It provides the same functionality as the
137 class with book-specific additions.
138 Tufte's documents consist of a rather narrow column of text and a wide
139 column of margin notes and margin figures.
140 This is to improve readability.
143 \begin_layout Standard
144 The features provided by this format include:
147 \begin_layout Itemize
151 \begin_layout Itemize
152 Ordinary figures in text with captions in margins
155 \begin_layout Itemize
156 Full width figures and text when needed
159 \begin_layout Itemize
160 \begin_inset Quotes eld
164 \begin_inset Quotes erd
170 \begin_layout Itemize
171 Limited layers of sections and subsections
174 \begin_layout Standard
175 In this sample document, some of these features are demonstrated.
176 For a full demonstration, visit the tufte-latex website:
177 \begin_inset Flex URL
180 \begin_layout Plain Layout
182 http://code.google.com/p/tufte-latex
190 \begin_layout Section
194 \begin_layout Standard
196 \begin_inset Quotes eld
200 \begin_inset Quotes erd
203 rather than justified.
204 \begin_inset Flex Sidenote
207 \begin_layout Plain Layout
208 To get justified text, add the option
218 Document\SpecialChar \menuseparator
219 Settings\SpecialChar \menuseparator
227 Ragged right text is used in most of his works, but the class option
231 is provided to change this.
234 \begin_layout Standard
235 Tufte also formats his pages asymmetrically.
236 This means that the marginalia appear on the right side on each page, whether
238 If you prefer, you can change that and have symmetric layout, as common
239 in traditional book typography, by using the
244 \begin_inset Flex Sidenote
247 \begin_layout Plain Layout
248 To create a symmetric layout, add the option
258 Document\SpecialChar \menuseparator
259 Settings\SpecialChar \menuseparator
270 \begin_layout Standard
271 Finally, Tufte does not number his chapters or his sections.
272 If you like to refer to sections by number, move the
278 Document\SpecialChar \menuseparator
279 Settings\SpecialChar \menuseparator
282 to the very right (as done in this document).
283 \begin_inset Flex Marginnote
286 \begin_layout Plain Layout
295 \begin_layout Section
299 \begin_layout Standard
300 Tufte uses ordinary figure floats such as the following:
303 \begin_layout Standard
304 \begin_inset Float figure
309 \begin_layout Plain Layout
310 \begin_inset Box Boxed
319 height_special "totalheight"
322 \begin_layout Plain Layout
323 Imagine your favorite figure inside this box instead of this boring text.
331 \begin_layout Plain Layout
332 An ordinary figure float.
345 \begin_layout Standard
346 Furthermore, he uses margin figures, as shown in Fig.
351 \begin_inset CommandInset ref
353 reference "fig:margin-figure"
360 \begin_layout Standard
361 \begin_inset Float marginfigure
366 \begin_layout Plain Layout
367 \begin_inset Box Boxed
376 height_special "totalheight"
379 \begin_layout Plain Layout
380 Imagine your favorite photograph of a squirrel inside this box instead of
389 \begin_layout Plain Layout
391 \begin_inset CommandInset label
393 name "fig:margin-figure"
410 \begin_layout Standard
411 In the same vein, the
415 class allows the use of tables, both in the margins and in the text.
416 The margin tables are recommended for a small set of data to illustrate
418 \begin_inset Quotes eld
421 Look, distance-time data is quadratic when the object is falling.
422 \begin_inset Quotes erd
425 More detailed data such as flame test results and comments should be put
426 in a full-width table instead.
429 \begin_layout Standard
434 provides a full-width figure.
435 This one takes up the entire width of the page, i.
436 \begin_inset space \thinspace{}
445 \begin_inset CommandInset ref
447 reference "fig:full-width-figure"
454 \begin_layout Standard
455 \begin_inset Float figure
460 \begin_layout Plain Layout
461 \begin_inset Box Boxed
470 height_special "totalheight"
473 \begin_layout Plain Layout
474 Imagine your favorite photograph of a squirrel inside this box instead of
481 \begin_inset VSpace defskip
487 \begin_layout Plain Layout
490 \begin_layout Plain Layout
492 \begin_inset CommandInset label
494 name "fig:full-width-figure"
511 \begin_layout Section
515 \begin_layout Standard
516 One of the most prominent and distinctive features of this style is the
517 extensive use of sidenotes.
518 There is a wide margin to provide ample room for sidenotes and small figures.
519 Any footnotes will automatically be converted to sidenotes.
523 \begin_layout Plain Layout
524 This is a sidenote that was entered using a
533 Alternatively, you can also use the
537 inset directly; you'll find it in the
539 Insert\SpecialChar \menuseparator
543 \begin_inset Flex Sidenote
546 \begin_layout Plain Layout
547 This is a sidenote that was entered using a
559 \begin_layout Standard
560 If you like to place ancillary information in the margin without the sidenote
561 mark (the superscript number), you can use the
567 \begin_inset Flex Marginnote
570 \begin_layout Plain Layout
571 This is Tufte's margin note.
572 Notice that there isn't a number preceding the note, and there is no number
573 in the main text where this note was written.
578 The normal margin note will work as well, but it will look rather odd.
579 \begin_inset Marginal
582 \begin_layout Plain Layout
583 This is a normal margin note.
592 \begin_layout Standard
593 \begin_inset Flex NewThought
596 \begin_layout Plain Layout
602 innovation is Tufte's
608 Edit\SpecialChar \menuseparator
609 TextStyle\SpecialChar \menuseparator
613 It introduces new thoughts by means of small caps, as demonstrated in this
618 \begin_layout Standard
619 The Tufte document classes include two new character styles and some improvement
620 s on existing commands for letterspacing.
623 \begin_layout Standard
624 When setting strings of
625 \begin_inset Flex AllCaps
628 \begin_layout Plain Layout
635 \begin_inset Flex SmallCaps
638 \begin_layout Plain Layout
644 , the letterspacing---that is, the spacing between the letters---should
645 be increased slightly.
646 \begin_inset CommandInset citation
658 Edit\SpecialChar \menuseparator
659 TextStyle\SpecialChar \menuseparator
662 ) has proper letterspacing for strings of
663 \begin_inset Flex AllCaps
666 \begin_layout Plain Layout
678 Edit\SpecialChar \menuseparator
679 TextStyle\SpecialChar \menuseparator
682 ) has letterspacing for
683 \begin_inset Flex SmallCaps
686 \begin_layout Plain Layout
687 small capital letters
693 These commands will also automatically convert the case of the text to
694 upper- or lowercase, respectively.
697 \begin_layout Standard
702 shape has also been redefined to include letterspacing.
703 Its case is left as is, however.
704 This allows one to use both uppercase and lowercase letters:
706 The Initial Letters Of The Words In This Sentence Are Capitalized.
709 \begin_layout Standard
714 paragraph environment provides a paragraph layout that stretches across
715 the main text block and the sidenotes area:
718 \begin_layout Full Width
719 Lorem ipsum dolor sit amet, consectetuer adipiscing elit.
720 Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae, felis.
721 Curabitur dictum gravida mauris.
722 Nam arcu libero, nonummy eget, consectetuer id, vulputate a, magna.
723 Donec vehicula augue eu neque.
724 Pellentesque habitant morbi tristique senectus et netus et malesuada fames
727 Cras viverra metus rhoncus sem.
728 Nulla et lectus vestibulum urna fringilla ultrices.
729 Phasellus eu tellus sit amet tortor gravida placerat.
730 Integer sapien est, iaculis in, pretium quis, viverra ac, nunc.
731 Praesent eget sem vel leo ultrices bibendum.
733 Morbi dolor nulla, malesuada eu, pulvinar at, mollis ac, nulla.
734 Curabitur auctor semper nulla.
735 Donec varius orci eget risus.
736 Duis nibh mi, congue eu, accumsan eleifend, sagittis quis, diam.
737 Duis eget orci sit amet orci dignissim rutrum.
740 \begin_layout Section
744 \begin_layout Standard
745 References are placed alongside their citations as sidenotes, as well.
746 This can be accomplished using the normal citation command.
750 \begin_layout Plain Layout
751 The previous section includes a citation.
759 \begin_layout Standard
760 The complete list of references may also be printed automatically by using
763 Insert\SpecialChar \menuseparator
764 Lists/TOC\SpecialChar \menuseparator
771 (see the end of this document for an example.) If you do not want to print
772 a bibliography at the end of your document, place the
780 inset inside a LyX note and use the LaTeX command
789 \begin_layout Chapter
790 Calculation of Volume: Sections 2.12--2.13
793 \begin_layout Abstract
794 Imagine taking a function like
795 \begin_inset Formula $y=\sqrt{x}$
798 and rotating it in 3 dimensions around the x-axis.
799 The resulting shape would look somewhat like a cup (on its side).
800 Interestingly, integration empowers us to do exactly this and to find out
801 how much water that cup could hold.
804 \begin_layout Section
808 \begin_layout Standard
809 \begin_inset Float marginfigure
814 \begin_layout Plain Layout
815 \begin_inset Box Boxed
824 height_special "totalheight"
827 \begin_layout Plain Layout
828 I had a graph of the square root function here.
836 \begin_layout Plain Layout
837 \begin_inset CommandInset label
839 name "mar:A-graph-of"
844 \begin_inset Formula $f(x)=\sqrt{x}$
860 \begin_layout Standard
861 \begin_inset Float marginfigure
866 \begin_layout Plain Layout
867 \begin_inset Box Boxed
876 height_special "totalheight"
879 \begin_layout Plain Layout
880 Here I rotated the square root function and then drew a disk on the figure
881 to illustrate how I would calculate the volume of the figure.
889 \begin_layout Plain Layout
890 \begin_inset CommandInset label
897 \begin_inset Formula $f(x)=\sqrt{x}$
900 rotated about the x-axis and with additional remarks for integration.
913 \begin_layout Standard
915 \begin_inset CommandInset ref
917 reference "mar:A-graph-of"
921 shows the plot of the function
922 \begin_inset Formula $f(x)=\sqrt{x}.$
925 Now, imagine that we rotate that function about the x-axis.
926 The resulting figure would be somewhat like figure
927 \begin_inset CommandInset ref
929 reference "mar:rotated"
934 This is akin to a cup lying on its side.
935 For the sake of clarity, the artist (me) drew a circle on the end of the
936 figure to show that it is indeed rotated.
939 \begin_layout Standard
940 Now, suppose we wished to find the volume of the figure.
941 When we integrated the original square root function to find its area,
942 we imagined a series of rectangles inside the figure.
944 \begin_inset Formula $h=f(x)$
948 \begin_inset Formula $dx$
952 Since height multiplied by width was the area of each rectangle, we summed
953 these areas and rewrote this as
954 \begin_inset Formula $\int\, f(x)\, dx$
957 , or, in this specific case,
958 \begin_inset Formula $\int\,\sqrt{x}\, dx$
964 \begin_layout Standard
965 To find the volume of our rotated figure the prodecure is quite similar.
966 Begin by rotating each rectangle about the x-axis.
967 This creates a series of cylinders.
968 \begin_inset Flex Sidenote
971 \begin_layout Plain Layout
972 The text refers to these cylinders as "disks".
973 This is standard practice in all the Calculus books I checked.
978 Then, we can find the volume of each cylinder/disk.
979 The basic formula is:
982 \begin_layout Standard
983 \begin_inset Formula \[
991 \begin_layout Standard
994 \begin_inset Formula $h$
997 is the height of the cylinder (width of the rectangle)
998 \begin_inset Formula $dx$
1002 The area of each figure is a circle where
1003 \begin_inset Formula $A=\pi r^{2}$
1007 The radius in this case is the function
1008 \begin_inset Formula $f(x)$
1015 \begin_layout Standard
1016 \begin_inset Formula \[
1024 \begin_layout Standard
1026 In our specific case,
1029 \begin_layout Standard
1030 \begin_inset Formula \begin{eqnarray*}
1031 A & = & \pi\left(\sqrt{x}\right)^{2}\\
1032 & = & \pi x\end{eqnarray*}
1039 \begin_layout Standard
1040 To calculate the volume of one disk, we have
1043 \begin_layout Standard
1044 \begin_inset Formula \[
1052 \begin_layout Standard
1054 or, in the general case
1057 \begin_layout Standard
1058 \begin_inset Formula \[
1059 V=\pi f^{2}(x)\, dx\]
1066 \begin_layout Standard
1067 To find the volume of the figure between points
1068 \begin_inset Formula $a$
1072 \begin_inset Formula $b$
1075 we sum the volumes by means of integration:
1078 \begin_layout Standard
1079 \begin_inset Formula \begin{equation}
1080 \int_{a}^{b}\,\pi f^{2}(x)\, dx\end{equation}
1087 \begin_layout Standard
1089 In the specific example, over the interval
1090 \begin_inset Formula $[0,4]$
1096 \begin_layout Standard
1097 \begin_inset Formula \begin{eqnarray*}
1098 \int_{0}^{4}\,\pi x\, dx & = & \pi\int_{0}^{4}\, x\, dx\\
1099 & = & \pi\left.\left(\frac{x^{2}}{2}\right)\right|_{0}^{4}\\
1100 & = & \pi\left(\frac{4^{2}}{2}-0\right)\\
1101 & = & 8\pi\end{eqnarray*}
1108 \begin_layout Standard
1109 \begin_inset Flex NewThought
1112 \begin_layout Plain Layout
1118 a special hole down the length of the cup we just worked with.
1119 It is made with a quadratic shaped bit.
1120 \begin_inset Flex Sidenote
1123 \begin_layout Plain Layout
1124 I have no idea how I'd do this in real life, but I'm making a point.
1129 I find that the hole the bit makes can be modeled with the function
1130 \begin_inset Formula $g(x)=\frac{x^{2}}{16}$
1134 I would need to subtract the volume of the material removed from the volume
1136 \begin_inset Quotes eld
1140 \begin_inset Quotes erd
1144 Each individual cylinder would become like a
1145 \begin_inset Quotes eld
1149 \begin_inset Quotes erd
1153 To get the area of one washer, I would use the formula
1156 \begin_layout Standard
1157 \begin_inset Float marginfigure
1162 \begin_layout Plain Layout
1163 \begin_inset Box Boxed
1172 height_special "totalheight"
1175 \begin_layout Plain Layout
1176 Here I used RLPlot to draw the square root function and the quadratic function.
1177 Then I used Inkscape to shade the area between them.
1183 \begin_inset Caption
1185 \begin_layout Plain Layout
1187 \begin_inset Formula $f(x)$
1191 \begin_inset Formula $g(x)$
1194 and the area left by
1195 \begin_inset Formula $f(x)-g(x)$
1211 \begin_layout Standard
1212 \begin_inset Formula \begin{eqnarray*}
1213 A_{washer} & = & A_{cup}-A_{drill}\\
1214 & = & \pi f^{2}(x)-\pi g^{2}(x)\\
1215 & = & \pi\left(f^{2}(x)-g^{2}(x)\right)\end{eqnarray*}
1222 \begin_layout Standard
1223 The volume of each washer would be
1226 \begin_layout Standard
1227 \begin_inset Formula \begin{eqnarray*}
1228 V_{washer} & = & A_{washer}\, dx\\
1229 & = & \pi\left(f^{2}(x)-g^{2}(x)\right)\, dx\end{eqnarray*}
1236 \begin_layout Standard
1238 Then, by summing the volumes of all the washers between points
1239 \begin_inset Formula $a$
1243 \begin_inset Formula $b$
1246 , the integral is derived:
1249 \begin_layout Standard
1250 \begin_inset Formula \begin{equation}
1251 \int_{a}^{b}\,\pi\left(f^{2}(x)-g^{2}(x)\right)\, dx\end{equation}
1258 \begin_layout Standard
1259 In the case of our quadratic drill bit::
1260 \begin_inset Float marginfigure
1265 \begin_layout Plain Layout
1266 \begin_inset Box Boxed
1275 height_special "totalheight"
1278 \begin_layout Plain Layout
1279 This was the rotated set of 2 functions.
1285 \begin_inset Caption
1287 \begin_layout Plain Layout
1288 The cup with a quadratic hole drilled down its length
1301 \begin_layout Standard
1302 \begin_inset Formula \begin{eqnarray*}
1303 \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\\
1304 & = & \pi\left(\int_{0}^{4}\, x\, dx-\int_{0}^{4}\,\frac{x^{4}}{256}\, dx\right)\\
1305 & = & \pi\left(\left.\left(\frac{x^{2}}{2}\right)\right|_{0}^{4}-\left.\left(\frac{x^{5}}{1280}\right)\right|_{0}^{4}\right)\\
1306 & = & \pi\left(\left(\frac{4^{2}}{2}-0\right)-\left(\frac{4^{5}}{1280}-0\right)\right)\\
1307 & = & \pi\left(8-0.8\right)\\
1308 & = & 7.2\pi\end{eqnarray*}
1315 \begin_layout Standard
1319 \begin_layout Section
1323 \begin_layout Itemize
1324 p114: 1, 4, 5, 6, 8, 10, 12, 15
1327 \begin_layout Standard
1328 \begin_inset CommandInset bibtex
1330 bibfiles "biblioExample"
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