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 a photograph of a squirrel stretched out on its side in this box.
475 One of the bugs in my layout is that this only works with pictures, not
476 with frames around minipages, the way it's set up here.
484 \begin_layout Plain Layout
487 \begin_layout Plain Layout
489 \begin_inset CommandInset label
491 name "fig:full-width-figure"
508 \begin_layout Section
512 \begin_layout Standard
513 One of the most prominent and distinctive features of this style is the
514 extensive use of sidenotes.
515 There is a wide margin to provide ample room for sidenotes and small figures.
516 Any footnotes will automatically be converted to sidenotes.
520 \begin_layout Plain Layout
521 This is a sidenote that was entered using a
530 Alternatively, you can also use the
534 inset directly; you'll find it in the
536 Insert\SpecialChar \menuseparator
540 \begin_inset Flex Sidenote
543 \begin_layout Plain Layout
544 This is a sidenote that was entered using a
556 \begin_layout Standard
557 If you like to place ancillary information in the margin without the sidenote
558 mark (the superscript number), you can use the
564 \begin_inset Flex Marginnote
567 \begin_layout Plain Layout
568 This is Tufte's margin note.
569 Notice that there isn't a number preceding the note, and there is no number
570 in the main text where this note was written.
575 The normal margin note will work as well, but it will look rather odd.
576 \begin_inset Marginal
579 \begin_layout Plain Layout
580 This is a normal margin note.
589 \begin_layout Standard
590 \begin_inset Flex NewThought
593 \begin_layout Plain Layout
599 innovation is Tufte's
605 Edit\SpecialChar \menuseparator
606 TextStyle\SpecialChar \menuseparator
610 It introduces new thoughts by means of small caps, as demonstrated in this
615 \begin_layout Standard
616 The Tufte document classes include two new character styles and some improvement
617 s on existing commands for letterspacing.
620 \begin_layout Standard
621 When setting strings of
622 \begin_inset Flex AllCaps
625 \begin_layout Plain Layout
632 \begin_inset Flex SmallCaps
635 \begin_layout Plain Layout
641 , the letterspacing---that is, the spacing between the letters---should
642 be increased slightly.
643 \begin_inset CommandInset citation
655 Edit\SpecialChar \menuseparator
656 TextStyle\SpecialChar \menuseparator
659 ) has proper letterspacing for strings of
660 \begin_inset Flex AllCaps
663 \begin_layout Plain Layout
675 Edit\SpecialChar \menuseparator
676 TextStyle\SpecialChar \menuseparator
679 ) has letterspacing for
680 \begin_inset Flex SmallCaps
683 \begin_layout Plain Layout
684 small capital letters
690 These commands will also automatically convert the case of the text to
691 upper- or lowercase, respectively.
694 \begin_layout Standard
699 shape has also been redefined to include letterspacing.
700 Its case is left as is, however.
701 This allows one to use both uppercase and lowercase letters:
703 The Initial Letters Of The Words In This Sentence Are Capitalized.
706 \begin_layout Standard
711 paragraph environment provides a paragraph layout that stretches across
712 the main text block and the sidenotes area:
715 \begin_layout Full Width
716 Lorem ipsum dolor sit amet, consectetuer adipiscing elit.
717 Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae, felis.
718 Curabitur dictum gravida mauris.
719 Nam arcu libero, nonummy eget, consectetuer id, vulputate a, magna.
720 Donec vehicula augue eu neque.
721 Pellentesque habitant morbi tristique senectus et netus et malesuada fames
724 Cras viverra metus rhoncus sem.
725 Nulla et lectus vestibulum urna fringilla ultrices.
726 Phasellus eu tellus sit amet tortor gravida placerat.
727 Integer sapien est, iaculis in, pretium quis, viverra ac, nunc.
728 Praesent eget sem vel leo ultrices bibendum.
730 Morbi dolor nulla, malesuada eu, pulvinar at, mollis ac, nulla.
731 Curabitur auctor semper nulla.
732 Donec varius orci eget risus.
733 Duis nibh mi, congue eu, accumsan eleifend, sagittis quis, diam.
734 Duis eget orci sit amet orci dignissim rutrum.
737 \begin_layout Section
741 \begin_layout Standard
742 References are placed alongside their citations as sidenotes, as well.
743 This can be accomplished using the normal citation command.
747 \begin_layout Plain Layout
748 The previous section includes a citation.
756 \begin_layout Standard
757 The complete list of references may also be printed automatically by using
760 Insert\SpecialChar \menuseparator
761 Lists/TOC\SpecialChar \menuseparator
768 (see the end of this document for an example.) If you do not want to print
769 a bibliography at the end of your document, place the
777 inset inside a LyX note and use the LaTeX command
786 \begin_layout Chapter
787 Calculation of Volume: Sections 2.12--2.13
790 \begin_layout Abstract
791 Imagine taking a function like
792 \begin_inset Formula $y=\sqrt{x}$
795 and rotating it in 3 dimensions around the x-axis.
796 The resulting shape would look somewhat like a cup (on its side).
797 Interestingly, integration empowers us to do exactly this and to find out
798 how much water that cup could hold.
801 \begin_layout Section
805 \begin_layout Standard
806 \begin_inset Float marginfigure
811 \begin_layout Plain Layout
812 \begin_inset Box Boxed
821 height_special "totalheight"
824 \begin_layout Plain Layout
825 I had a graph of the square root function here.
833 \begin_layout Plain Layout
834 \begin_inset CommandInset label
836 name "mar:A-graph-of"
841 \begin_inset Formula $f(x)=\sqrt{x}$
857 \begin_layout Standard
858 \begin_inset Float marginfigure
863 \begin_layout Plain Layout
864 \begin_inset Box Boxed
873 height_special "totalheight"
876 \begin_layout Plain Layout
877 Here I rotated the square root function and then drew a disk on the figure
878 to illustrate how I would calculate the volume of the figure.
886 \begin_layout Plain Layout
887 \begin_inset CommandInset label
894 \begin_inset Formula $f(x)=\sqrt{x}$
897 rotated about the x-axis and with additional remarks for integration.
910 \begin_layout Standard
912 \begin_inset CommandInset ref
914 reference "mar:A-graph-of"
918 shows the plot of the function
919 \begin_inset Formula $f(x)=\sqrt{x}.$
922 Now, imagine that we rotate that function about the x-axis.
923 The resulting figure would be somewhat like figure
924 \begin_inset CommandInset ref
926 reference "mar:rotated"
931 This is akin to a cup lying on its side.
932 For the sake of clarity, the artist (me) drew a circle on the end of the
933 figure to show that it is indeed rotated.
936 \begin_layout Standard
937 Now, suppose we wished to find the volume of the figure.
938 When we integrated the original square root function to find its area,
939 we imagined a series of rectangles inside the figure.
941 \begin_inset Formula $h=f(x)$
945 \begin_inset Formula $dx$
949 Since height multiplied by width was the area of each rectangle, we summed
950 these areas and rewrote this as
951 \begin_inset Formula $\int\, f(x)\, dx$
954 , or, in this specific case,
955 \begin_inset Formula $\int\,\sqrt{x}\, dx$
961 \begin_layout Standard
962 To find the volume of our rotated figure the prodecure is quite similar.
963 Begin by rotating each rectangle about the x-axis.
964 This creates a series of cylinders.
965 \begin_inset Flex Sidenote
968 \begin_layout Plain Layout
969 The text refers to these cylinders as "disks".
970 This is standard practice in all the Calculus books I checked.
975 Then, we can find the volume of each cylinder/disk.
976 The basic formula is:
979 \begin_layout Standard
980 \begin_inset Formula \[
988 \begin_layout Standard
991 \begin_inset Formula $h$
994 is the height of the cylinder (width of the rectangle)
995 \begin_inset Formula $dx$
999 The area of each figure is a circle where
1000 \begin_inset Formula $A=\pi r^{2}$
1004 The radius in this case is the function
1005 \begin_inset Formula $f(x)$
1012 \begin_layout Standard
1013 \begin_inset Formula \[
1021 \begin_layout Standard
1023 In our specific case,
1026 \begin_layout Standard
1027 \begin_inset Formula \begin{eqnarray*}
1028 A & = & \pi\left(\sqrt{x}\right)^{2}\\
1029 & = & \pi x\end{eqnarray*}
1036 \begin_layout Standard
1037 To calculate the volume of one disk, we have
1040 \begin_layout Standard
1041 \begin_inset Formula \[
1049 \begin_layout Standard
1051 or, in the general case
1054 \begin_layout Standard
1055 \begin_inset Formula \[
1056 V=\pi f^{2}(x)\, dx\]
1063 \begin_layout Standard
1064 To find the volume of the figure between points
1065 \begin_inset Formula $a$
1069 \begin_inset Formula $b$
1072 we sum the volumes by means of integration:
1075 \begin_layout Standard
1076 \begin_inset Formula \begin{equation}
1077 \int_{a}^{b}\,\pi f^{2}(x)\, dx\end{equation}
1084 \begin_layout Standard
1086 In the specific example, over the interval
1087 \begin_inset Formula $[0,4]$
1093 \begin_layout Standard
1094 \begin_inset Formula \begin{eqnarray*}
1095 \int_{0}^{4}\,\pi x\, dx & = & \pi\int_{0}^{4}\, x\, dx\\
1096 & = & \pi\left.\left(\frac{x^{2}}{2}\right)\right|_{0}^{4}\\
1097 & = & \pi\left(\frac{4^{2}}{2}-0\right)\\
1098 & = & 8\pi\end{eqnarray*}
1105 \begin_layout Standard
1106 \begin_inset Flex NewThought
1109 \begin_layout Plain Layout
1115 a special hole down the length of the cup we just worked with.
1116 It is made with a quadratic shaped bit.
1117 \begin_inset Flex Sidenote
1120 \begin_layout Plain Layout
1121 I have no idea how I'd do this in real life, but I'm making a point.
1126 I find that the hole the bit makes can be modeled with the function
1127 \begin_inset Formula $g(x)=\frac{x^{2}}{16}$
1131 I would need to subtract the volume of the material removed from the volume
1133 \begin_inset Quotes eld
1137 \begin_inset Quotes erd
1141 Each individual cylinder would become like a
1142 \begin_inset Quotes eld
1146 \begin_inset Quotes erd
1150 To get the area of one washer, I would use the formula
1153 \begin_layout Standard
1154 \begin_inset Float marginfigure
1159 \begin_layout Plain Layout
1160 \begin_inset Box Boxed
1169 height_special "totalheight"
1172 \begin_layout Plain Layout
1173 Here I used RLPlot to draw the square root function and the quadratic function.
1174 Then I used Inkscape to shade the area between them.
1180 \begin_inset Caption
1182 \begin_layout Plain Layout
1184 \begin_inset Formula $f(x)$
1188 \begin_inset Formula $g(x)$
1191 and the area left by
1192 \begin_inset Formula $f(x)-g(x)$
1208 \begin_layout Standard
1209 \begin_inset Formula \begin{eqnarray*}
1210 A_{washer} & = & A_{cup}-A_{drill}\\
1211 & = & \pi f^{2}(x)-\pi g^{2}(x)\\
1212 & = & \pi\left(f^{2}(x)-g^{2}(x)\right)\end{eqnarray*}
1219 \begin_layout Standard
1220 The volume of each washer would be
1223 \begin_layout Standard
1224 \begin_inset Formula \begin{eqnarray*}
1225 V_{washer} & = & A_{washer}\, dx\\
1226 & = & \pi\left(f^{2}(x)-g^{2}(x)\right)\, dx\end{eqnarray*}
1233 \begin_layout Standard
1235 Then, by summing the volumes of all the washers between points
1236 \begin_inset Formula $a$
1240 \begin_inset Formula $b$
1243 , the integral is derived:
1246 \begin_layout Standard
1247 \begin_inset Formula \begin{equation}
1248 \int_{a}^{b}\,\pi\left(f^{2}(x)-g^{2}(x)\right)\, dx\end{equation}
1255 \begin_layout Standard
1256 In the case of our quadratic drill bit::
1257 \begin_inset Float marginfigure
1262 \begin_layout Plain Layout
1263 \begin_inset Box Boxed
1272 height_special "totalheight"
1275 \begin_layout Plain Layout
1276 This was the rotated set of 2 functions.
1282 \begin_inset Caption
1284 \begin_layout Plain Layout
1285 The cup with a quadratic hole drilled down its length
1298 \begin_layout Standard
1299 \begin_inset Formula \begin{eqnarray*}
1300 \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\\
1301 & = & \pi\left(\int_{0}^{4}\, x\, dx-\int_{0}^{4}\,\frac{x^{4}}{256}\, dx\right)\\
1302 & = & \pi\left(\left.\left(\frac{x^{2}}{2}\right)\right|_{0}^{4}-\left.\left(\frac{x^{5}}{1280}\right)\right|_{0}^{4}\right)\\
1303 & = & \pi\left(\left(\frac{4^{2}}{2}-0\right)-\left(\frac{4^{5}}{1280}-0\right)\right)\\
1304 & = & \pi\left(8-0.8\right)\\
1305 & = & 7.2\pi\end{eqnarray*}
1312 \begin_layout Standard
1316 \begin_layout Section
1320 \begin_layout Itemize
1321 p114: 1, 4, 5, 6, 8, 10, 12, 15
1324 \begin_layout Standard
1325 \begin_inset CommandInset bibtex
1327 bibfiles "biblioExample"
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