1 #LyX 2.2 created this file. For more info see http://www.lyx.org/
5 \save_transient_properties true
6 \origin /systemlyxdir/examples/
8 \use_default_options true
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11 \language_package default
14 \font_roman "default" "default"
15 \font_sans "default" "default"
16 \font_typewriter "default" "default"
17 \font_math "auto" "auto"
18 \font_default_family default
19 \use_non_tex_fonts false
22 \font_sf_scale 100 100
23 \font_tt_scale 100 100
25 \default_output_format pdf2
27 \bibtex_command bibtex
28 \index_command default
29 \paperfontsize default
33 \pdf_bookmarksnumbered false
34 \pdf_bookmarksopen true
35 \pdf_bookmarksopenlevel 1
43 \use_package amsmath 1
44 \use_package amssymb 1
47 \use_package mathdots 1
48 \use_package mathtools 0
50 \use_package stackrel 0
51 \use_package stmaryrd 0
52 \use_package undertilde 0
54 \cite_engine_type default
58 \paperorientation portrait
62 \notefontcolor #0000ff
69 \paragraph_separation indent
70 \paragraph_indentation default
71 \quotes_language english
74 \paperpagestyle default
75 \tracking_changes false
84 \begin_layout Standard
85 \begin_inset Note Note
88 \begin_layout Plain Layout
93 : To be able to view your file as PDF you must have the \SpecialCharNoPassThru LaTeX
98 installed to your \SpecialCharNoPassThru LaTeX
100 If you are using MiK\SpecialCharNoPassThru TeX
101 , you will automatically be asked to install this
102 package when previewing your file, if you are using \SpecialCharNoPassThru TeX
103 Live, use \SpecialCharNoPassThru TeX
108 \begin_layout Plain Layout
113 : If you wish to compile to PDF with plain \SpecialCharNoPassThru LaTeX
114 (instead of pdf\SpecialCharNoPassThru TeX
116 is currently a bug in the Tufte class that causes errors.
117 You can add the class option 'nols' (put this in the
118 \begin_inset Quotes eld
122 \begin_inset Quotes erd
125 field of Document\SpecialChar menuseparator
126 Settings \SpecialChar menuseparator
127 Document Class) to get rid of the errors, but
128 this also removes letterspacing, an important part of the Tufte design.
142 \begin_inset Note Note
145 \begin_layout Plain Layout
146 author of this example file: Jason Waskiewicz
154 \begin_layout Standard
155 \begin_inset CommandInset toc
156 LatexCommand tableofcontents
163 \begin_layout Chapter
164 The Features of the Tufte-book Class
167 \begin_layout Standard
168 In this document, it was endeavored to show some of the features of the
174 In the first chapter, their use is outlined.
175 In the second chapter, their use through a handout that was created in
176 a calculus class is demonstrated.
179 \begin_layout Section
183 \begin_layout Standard
188 class is based on the work of
193 It provides the same functionality as the
197 class with book-specific additions.
198 Tufte's documents consist of a rather narrow column of text and a wide
199 column of margin notes and margin figures.
200 This is to improve readability.
203 \begin_layout Standard
204 The features provided by this format include:
207 \begin_layout Itemize
211 \begin_layout Itemize
212 Ordinary figures in text with captions in margins
215 \begin_layout Itemize
216 Full width figures and text when needed
219 \begin_layout Itemize
220 \begin_inset Quotes eld
224 \begin_inset Quotes erd
230 \begin_layout Itemize
231 Limited layers of sections and subsections
234 \begin_layout Standard
235 In this sample document, some of these features are demonstrated.
236 For a full demonstration, visit the tufte-latex website:
237 \begin_inset Flex URL
240 \begin_layout Plain Layout
242 http://code.google.com/p/tufte-latex
250 \begin_layout Section
254 \begin_layout Standard
256 \begin_inset Quotes eld
260 \begin_inset Quotes erd
263 rather than justified.
264 \begin_inset Flex Sidenote
267 \begin_layout Plain Layout
268 To get justified text, add the option
278 Document\SpecialChar menuseparator
279 Settings\SpecialChar menuseparator
287 Ragged right text is used in most of his works, but the class option
291 is provided to change this.
294 \begin_layout Standard
295 Tufte also formats his pages asymmetrically.
296 This means that the marginalia appear on the right side on each page, whether
298 If you prefer, you can change that and have symmetric layout, as common
299 in traditional book typography, by using the
304 \begin_inset Flex Sidenote
307 \begin_layout Plain Layout
308 To create a symmetric layout, add the option
318 Document\SpecialChar menuseparator
319 Settings\SpecialChar menuseparator
330 \begin_layout Standard
331 Finally, Tufte does not number his chapters or his sections.
332 If you like to refer to sections by number, move the
338 Document\SpecialChar menuseparator
339 Settings\SpecialChar menuseparator
342 to the very right (as done in this document).
343 \begin_inset Flex Marginnote
346 \begin_layout Plain Layout
355 \begin_layout Section
359 \begin_layout Standard
360 Tufte uses ordinary figure floats such as the following:
363 \begin_layout Standard
364 \begin_inset Float figure
369 \begin_layout Plain Layout
370 \begin_inset Box Boxed
380 height_special "totalheight"
385 backgroundcolor "none"
388 \begin_layout Plain Layout
389 Imagine your favorite figure inside this box instead of this boring text.
395 \begin_inset Caption Standard
397 \begin_layout Plain Layout
398 An ordinary figure float.
411 \begin_layout Standard
412 Furthermore, he uses margin figures, as shown in Fig.
417 \begin_inset CommandInset ref
419 reference "fig:margin-figure"
426 \begin_layout Standard
427 \begin_inset VSpace 5theight%
433 \begin_layout Standard
434 \begin_inset Float marginfigure
439 \begin_layout Plain Layout
440 \begin_inset Box Boxed
450 height_special "totalheight"
455 backgroundcolor "none"
458 \begin_layout Plain Layout
459 Imagine your favorite photograph of a squirrel inside this box instead of
466 \begin_inset Caption Standard
468 \begin_layout Plain Layout
470 \begin_inset CommandInset label
472 name "fig:margin-figure"
489 \begin_layout Standard
490 \begin_inset Note Greyedout
493 \begin_layout Plain Layout
498 If you are using margin figures or tables you must use the default float
499 placement option in the document settings under
515 \begin_layout Standard
516 In the same vein, the
520 class allows the use of tables, both in the margins and in the text.
521 The margin tables are recommended for a small set of data to illustrate
523 \begin_inset Quotes eld
526 Look, distance-time data is quadratic when the object is falling.
527 \begin_inset Quotes erd
530 More detailed data such as flame test results and comments should be put
531 in a full-width table instead.
534 \begin_layout Standard
539 provides a full-width figure.
540 This one takes up the entire width of the page, i.
541 \begin_inset space \thinspace{}
550 \begin_inset CommandInset ref
552 reference "fig:full-width-figure"
559 \begin_layout Standard
560 \begin_inset Float figure
565 \begin_layout Plain Layout
566 \begin_inset Box Boxed
576 height_special "totalheight"
581 backgroundcolor "none"
584 \begin_layout Plain Layout
585 Imagine your favorite photograph of a squirrel inside this box instead of
592 \begin_inset VSpace defskip
598 \begin_layout Plain Layout
599 \begin_inset Caption Standard
601 \begin_layout Plain Layout
603 \begin_inset CommandInset label
605 name "fig:full-width-figure"
622 \begin_layout Section
626 \begin_layout Standard
627 One of the most prominent and distinctive features of this style is the
628 extensive use of sidenotes.
629 There is a wide margin to provide ample room for sidenotes and small figures.
630 Any footnotes will automatically be converted to sidenotes.
634 \begin_layout Plain Layout
635 This is a sidenote that was entered using a
644 Alternatively, you can also use the
648 inset directly; you'll find it in the
650 Insert\SpecialChar menuseparator
654 \begin_inset Flex Sidenote
657 \begin_layout Plain Layout
658 This is a sidenote that was entered using a
670 \begin_layout Standard
671 If you like to place ancillary information in the margin without the sidenote
672 mark (the superscript number), you can use the
678 \begin_inset Flex Marginnote
681 \begin_layout Plain Layout
682 This is Tufte's margin note.
683 Notice that there isn't a number preceding the note, and there is no number
684 in the main text where this note was written.
689 The normal margin note will work as well, but it will look rather odd.
690 \begin_inset Marginal
693 \begin_layout Plain Layout
694 This is a normal margin note.
703 \begin_layout Standard
704 \begin_inset Flex NewThought
707 \begin_layout Plain Layout
713 innovation is Tufte's
719 Edit\SpecialChar menuseparator
720 TextStyle\SpecialChar menuseparator
724 It introduces new thoughts by means of small caps, as demonstrated in this
729 \begin_layout Standard
730 The Tufte document classes include two new character styles and some improvement
731 s on existing commands for letterspacing.
734 \begin_layout Standard
735 When setting strings of
736 \begin_inset Flex AllCaps
739 \begin_layout Plain Layout
746 \begin_inset Flex SmallCaps
749 \begin_layout Plain Layout
755 , the letterspacing\threehyphens
756 that is, the spacing between the letters\threehyphens
758 be increased slightly.
759 \begin_inset CommandInset citation
771 Edit\SpecialChar menuseparator
772 TextStyle\SpecialChar menuseparator
775 ) has proper letterspacing for strings of
776 \begin_inset Flex AllCaps
779 \begin_layout Plain Layout
791 Edit\SpecialChar menuseparator
792 TextStyle\SpecialChar menuseparator
795 ) has letterspacing for
796 \begin_inset Flex SmallCaps
799 \begin_layout Plain Layout
800 small capital letters
806 These commands will also automatically convert the case of the text to
807 upper- or lowercase, respectively.
810 \begin_layout Standard
815 shape has also been redefined to include letterspacing.
816 Its case is left as is, however.
817 This allows one to use both uppercase and lowercase letters:
819 The Initial Letters Of The Words In This Sentence Are Capitalized.
822 \begin_layout Standard
827 paragraph environment provides a paragraph layout that stretches across
828 the main text block and the sidenotes area:
831 \begin_layout Full Width
832 Lorem ipsum dolor sit amet, consectetuer adipiscing elit.
833 Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae, felis.
834 Curabitur dictum gravida mauris.
835 Nam arcu libero, nonummy eget, consectetuer id, vulputate a, magna.
836 Donec vehicula augue eu neque.
837 Pellentesque habitant morbi tristique senectus et netus et malesuada fames
840 Cras viverra metus rhoncus sem.
841 Nulla et lectus vestibulum urna fringilla ultrices.
842 Phasellus eu tellus sit amet tortor gravida placerat.
843 Integer sapien est, iaculis in, pretium quis, viverra ac, nunc.
844 Praesent eget sem vel leo ultrices bibendum.
846 Morbi dolor nulla, malesuada eu, pulvinar at, mollis ac, nulla.
847 Curabitur auctor semper nulla.
848 Donec varius orci eget risus.
849 Duis nibh mi, congue eu, accumsan eleifend, sagittis quis, diam.
850 Duis eget orci sit amet orci dignissim rutrum.
853 \begin_layout Section
857 \begin_layout Standard
858 References are placed alongside their citations as sidenotes, as well.
859 This can be accomplished using the normal citation command.
863 \begin_layout Plain Layout
864 The previous section includes a citation.
872 \begin_layout Standard
873 The complete list of references may also be printed automatically by using
876 Insert\SpecialChar menuseparator
877 Lists/TOC\SpecialChar menuseparator
878 Bib\SpecialCharNoPassThru TeX
884 (see the end of this document for an example.) If you do not want to print
885 a bibliography at the end of your document, place the
887 Bib\SpecialCharNoPassThru TeX
893 inset inside a \SpecialCharNoPassThru LyX
894 note and use the \SpecialCharNoPassThru LaTeX
904 \begin_layout Chapter
905 Calculation of Volume: Sections 2.12–2.13
908 \begin_layout Standard
909 Imagine taking a function like
910 \begin_inset Formula $y=\sqrt{x}$
913 and rotating it in 3 dimensions around the x-axis.
914 The resulting shape would look somewhat like a cup (on its side).
915 Interestingly, integration empowers us to do exactly this and to find out
916 how much water that cup could hold.
919 \begin_layout Section
923 \begin_layout Standard
924 \begin_inset Float marginfigure
929 \begin_layout Plain Layout
930 \begin_inset Box Boxed
940 height_special "totalheight"
945 backgroundcolor "none"
948 \begin_layout Plain Layout
949 I had a graph of the square root function here.
955 \begin_inset Caption Standard
957 \begin_layout Plain Layout
958 \begin_inset CommandInset label
960 name "mar:A-graph-of"
965 \begin_inset Formula $f(x)=\sqrt{x}$
981 \begin_layout Standard
982 \begin_inset Float marginfigure
987 \begin_layout Plain Layout
988 \begin_inset Box Boxed
998 height_special "totalheight"
1003 backgroundcolor "none"
1006 \begin_layout Plain Layout
1007 Here I rotated the square root function and then drew a disk on the figure
1008 to illustrate how I would calculate the volume of the figure.
1014 \begin_inset Caption Standard
1016 \begin_layout Plain Layout
1017 \begin_inset CommandInset label
1024 \begin_inset Formula $f(x)=\sqrt{x}$
1027 rotated about the x-axis and with additional remarks for integration.
1040 \begin_layout Standard
1042 \begin_inset CommandInset ref
1044 reference "mar:A-graph-of"
1048 shows the plot of the function
1049 \begin_inset Formula $f(x)=\sqrt{x}.$
1052 Now, imagine that we rotate that function about the x-axis.
1053 The resulting figure would be somewhat like figure
1054 \begin_inset CommandInset ref
1056 reference "mar:rotated"
1061 This is akin to a cup lying on its side.
1062 For the sake of clarity, the artist (me) drew a circle on the end of the
1063 figure to show that it is indeed rotated.
1066 \begin_layout Standard
1067 Now, suppose we wished to find the volume of the figure.
1068 When we integrated the original square root function to find its area,
1069 we imagined a series of rectangles inside the figure.
1071 \begin_inset Formula $h=f(x)$
1075 \begin_inset Formula $dx$
1079 Since height multiplied by width was the area of each rectangle, we summed
1080 these areas and rewrote this as
1081 \begin_inset Formula $\int\, f(x)\, dx$
1084 , or, in this specific case,
1085 \begin_inset Formula $\int\,\sqrt{x}\, dx$
1091 \begin_layout Standard
1092 To find the volume of our rotated figure the prodecure is quite similar.
1093 Begin by rotating each rectangle about the x-axis.
1094 This creates a series of cylinders.
1095 \begin_inset Flex Sidenote
1098 \begin_layout Plain Layout
1099 The text refers to these cylinders as "disks".
1100 This is standard practice in all the Calculus books I checked.
1105 Then, we can find the volume of each cylinder/disk.
1106 The basic formula is:
1109 \begin_layout Standard
1110 \begin_inset Formula
1120 \begin_layout Standard
1123 \begin_inset Formula $h$
1126 is the height of the cylinder (width of the rectangle)
1127 \begin_inset Formula $dx$
1131 The area of each figure is a circle where
1132 \begin_inset Formula $A=\pi r^{2}$
1136 The radius in this case is the function
1137 \begin_inset Formula $f(x)$
1144 \begin_layout Standard
1145 \begin_inset Formula
1155 \begin_layout Standard
1157 In our specific case,
1160 \begin_layout Standard
1161 \begin_inset Formula
1163 A & = & \pi\left(\sqrt{x}\right)^{2}\\
1172 \begin_layout Standard
1173 To calculate the volume of one disk, we have
1176 \begin_layout Standard
1177 \begin_inset Formula
1187 \begin_layout Standard
1189 or, in the general case
1192 \begin_layout Standard
1193 \begin_inset Formula
1203 \begin_layout Standard
1204 To find the volume of the figure between points
1205 \begin_inset Formula $a$
1209 \begin_inset Formula $b$
1212 we sum the volumes by means of integration:
1215 \begin_layout Standard
1216 \begin_inset Formula
1218 \int_{a}^{b}\,\pi f^{2}(x)\, dx
1226 \begin_layout Standard
1228 In the specific example, over the interval
1229 \begin_inset Formula $[0,4]$
1235 \begin_layout Standard
1236 \begin_inset Formula
1238 \int_{0}^{4}\,\pi x\, dx & = & \pi\int_{0}^{4}\, x\, dx\\
1239 & = & \pi\left.\left(\frac{x^{2}}{2}\right)\right|_{0}^{4}\\
1240 & = & \pi\left(\frac{4^{2}}{2}-0\right)\\
1249 \begin_layout Standard
1250 \begin_inset Flex NewThought
1253 \begin_layout Plain Layout
1259 a special hole down the length of the cup we just worked with.
1260 It is made with a quadratic shaped bit.
1261 \begin_inset Flex Sidenote
1264 \begin_layout Plain Layout
1265 I have no idea how I'd do this in real life, but I'm making a point.
1270 I find that the hole the bit makes can be modeled with the function
1271 \begin_inset Formula $g(x)=\frac{x^{2}}{16}$
1275 I would need to subtract the volume of the material removed from the volume
1277 \begin_inset Quotes eld
1281 \begin_inset Quotes erd
1285 Each individual cylinder would become like a
1286 \begin_inset Quotes eld
1290 \begin_inset Quotes erd
1294 To get the area of one washer, I would use the formula
1297 \begin_layout Standard
1298 \begin_inset Float marginfigure
1303 \begin_layout Plain Layout
1304 \begin_inset Box Boxed
1314 height_special "totalheight"
1319 backgroundcolor "none"
1322 \begin_layout Plain Layout
1323 Here I used RLPlot to draw the square root function and the quadratic function.
1324 Then I used Inkscape to shade the area between them.
1330 \begin_inset Caption Standard
1332 \begin_layout Plain Layout
1334 \begin_inset Formula $f(x)$
1338 \begin_inset Formula $g(x)$
1341 and the area left by
1342 \begin_inset Formula $f(x)-g(x)$
1358 \begin_layout Standard
1359 \begin_inset Formula
1361 A_{washer} & = & A_{cup}-A_{drill}\\
1362 & = & \pi f^{2}(x)-\pi g^{2}(x)\\
1363 & = & \pi\left(f^{2}(x)-g^{2}(x)\right)
1371 \begin_layout Standard
1372 The volume of each washer would be
1375 \begin_layout Standard
1376 \begin_inset Formula
1378 V_{washer} & = & A_{washer}\, dx\\
1379 & = & \pi\left(f^{2}(x)-g^{2}(x)\right)\, dx
1387 \begin_layout Standard
1389 Then, by summing the volumes of all the washers between points
1390 \begin_inset Formula $a$
1394 \begin_inset Formula $b$
1397 , the integral is derived:
1400 \begin_layout Standard
1401 \begin_inset Formula
1403 \int_{a}^{b}\,\pi\left(f^{2}(x)-g^{2}(x)\right)\, dx
1411 \begin_layout Standard
1412 In the case of our quadratic drill bit::
1413 \begin_inset Float marginfigure
1418 \begin_layout Plain Layout
1419 \begin_inset Box Boxed
1429 height_special "totalheight"
1434 backgroundcolor "none"
1437 \begin_layout Plain Layout
1438 This was the rotated set of 2 functions.
1444 \begin_inset Caption Standard
1446 \begin_layout Plain Layout
1447 The cup with a quadratic hole drilled down its length
1460 \begin_layout Standard
1461 \begin_inset Formula
1463 \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\\
1464 & = & \pi\left(\int_{0}^{4}\, x\, dx-\int_{0}^{4}\,\frac{x^{4}}{256}\, dx\right)\\
1465 & = & \pi\left(\left.\left(\frac{x^{2}}{2}\right)\right|_{0}^{4}-\left.\left(\frac{x^{5}}{1280}\right)\right|_{0}^{4}\right)\\
1466 & = & \pi\left(\left(\frac{4^{2}}{2}-0\right)-\left(\frac{4^{5}}{1280}-0\right)\right)\\
1467 & = & \pi\left(8-0.8\right)\\
1476 \begin_layout Standard
1480 \begin_layout Section
1484 \begin_layout Itemize
1485 p114: 1, 4, 5, 6, 8, 10, 12, 15
1488 \begin_layout Standard
1489 \begin_inset CommandInset bibtex
1491 bibfiles "biblioExample"