1 #LyX 2.0 created this file. For more info see http://www.lyx.org/
6 \use_default_options true
7 \maintain_unincluded_children false
9 \language_package default
14 \font_typewriter default
15 \font_default_family default
16 \use_non_tex_fonts false
23 \default_output_format default
25 \bibtex_command default
26 \index_command default
27 \paperfontsize default
31 \pdf_bookmarksnumbered false
32 \pdf_bookmarksopen true
33 \pdf_bookmarksopenlevel 1
48 \paperorientation portrait
51 \notefontcolor #0000ff
58 \paragraph_separation indent
59 \paragraph_indentation default
60 \quotes_language english
63 \paperpagestyle default
64 \tracking_changes false
73 \begin_layout Standard
74 \begin_inset Note Note
77 \begin_layout Plain Layout
82 : To be able to view your file as PDF you must have the LaTeX-package
86 installed to your LaTeX system.
87 If you are using MiKTeX, you will automatically be asked to install this
88 package when previewing your file, if you are using TeXLive, use TeXLive's
103 \begin_inset Note Note
106 \begin_layout Plain Layout
107 author of this example file: Jason Waskiewicz
115 \begin_layout Standard
116 \begin_inset CommandInset toc
117 LatexCommand tableofcontents
124 \begin_layout Chapter
125 The Features of the Tufte-book Class
128 \begin_layout Standard
129 In this document, it was endeavored to show some of the features of the
135 In the first chapter, their use is outlined.
136 In the second chapter, their use through a handout that was created in
137 a calculus class is demonstrated.
140 \begin_layout Section
144 \begin_layout Standard
149 class is based on the work of
154 It provides the same functionality as the
158 class with book-specific additions.
159 Tufte's documents consist of a rather narrow column of text and a wide
160 column of margin notes and margin figures.
161 This is to improve readability.
164 \begin_layout Standard
165 The features provided by this format include:
168 \begin_layout Itemize
172 \begin_layout Itemize
173 Ordinary figures in text with captions in margins
176 \begin_layout Itemize
177 Full width figures and text when needed
180 \begin_layout Itemize
181 \begin_inset Quotes eld
185 \begin_inset Quotes erd
191 \begin_layout Itemize
192 Limited layers of sections and subsections
195 \begin_layout Standard
196 In this sample document, some of these features are demonstrated.
197 For a full demonstration, visit the tufte-latex website:
198 \begin_inset Flex URL
201 \begin_layout Plain Layout
203 http://code.google.com/p/tufte-latex
211 \begin_layout Section
215 \begin_layout Standard
217 \begin_inset Quotes eld
221 \begin_inset Quotes erd
224 rather than justified.
225 \begin_inset Flex Sidenote
228 \begin_layout Plain Layout
229 To get justified text, add the option
239 Document\SpecialChar \menuseparator
240 Settings\SpecialChar \menuseparator
248 Ragged right text is used in most of his works, but the class option
252 is provided to change this.
255 \begin_layout Standard
256 Tufte also formats his pages asymmetrically.
257 This means that the marginalia appear on the right side on each page, whether
259 If you prefer, you can change that and have symmetric layout, as common
260 in traditional book typography, by using the
265 \begin_inset Flex Sidenote
268 \begin_layout Plain Layout
269 To create a symmetric layout, add the option
279 Document\SpecialChar \menuseparator
280 Settings\SpecialChar \menuseparator
291 \begin_layout Standard
292 Finally, Tufte does not number his chapters or his sections.
293 If you like to refer to sections by number, move the
299 Document\SpecialChar \menuseparator
300 Settings\SpecialChar \menuseparator
303 to the very right (as done in this document).
304 \begin_inset Flex Marginnote
307 \begin_layout Plain Layout
316 \begin_layout Section
320 \begin_layout Standard
321 Tufte uses ordinary figure floats such as the following:
324 \begin_layout Standard
325 \begin_inset Float figure
330 \begin_layout Plain Layout
331 \begin_inset Box Boxed
341 height_special "totalheight"
344 \begin_layout Plain Layout
345 Imagine your favorite figure inside this box instead of this boring text.
353 \begin_layout Plain Layout
354 An ordinary figure float.
367 \begin_layout Standard
368 Furthermore, he uses margin figures, as shown in Fig.
373 \begin_inset CommandInset ref
375 reference "fig:margin-figure"
382 \begin_layout Standard
383 \begin_inset VSpace 5theight%
389 \begin_layout Standard
390 \begin_inset Float marginfigure
395 \begin_layout Plain Layout
396 \begin_inset Box Boxed
406 height_special "totalheight"
409 \begin_layout Plain Layout
410 Imagine your favorite photograph of a squirrel inside this box instead of
419 \begin_layout Plain Layout
421 \begin_inset CommandInset label
423 name "fig:margin-figure"
440 \begin_layout Standard
441 \begin_inset Note Greyedout
444 \begin_layout Plain Layout
449 If you are using margin figures or tables you must use the default float
450 placement option in the document settings under
466 \begin_layout Standard
467 In the same vein, the
471 class allows the use of tables, both in the margins and in the text.
472 The margin tables are recommended for a small set of data to illustrate
474 \begin_inset Quotes eld
477 Look, distance-time data is quadratic when the object is falling.
478 \begin_inset Quotes erd
481 More detailed data such as flame test results and comments should be put
482 in a full-width table instead.
485 \begin_layout Standard
490 provides a full-width figure.
491 This one takes up the entire width of the page, i.
492 \begin_inset space \thinspace{}
501 \begin_inset CommandInset ref
503 reference "fig:full-width-figure"
510 \begin_layout Standard
511 \begin_inset Float figure
516 \begin_layout Plain Layout
517 \begin_inset Box Boxed
527 height_special "totalheight"
530 \begin_layout Plain Layout
531 Imagine your favorite photograph of a squirrel inside this box instead of
538 \begin_inset VSpace defskip
544 \begin_layout Plain Layout
547 \begin_layout Plain Layout
549 \begin_inset CommandInset label
551 name "fig:full-width-figure"
568 \begin_layout Section
572 \begin_layout Standard
573 One of the most prominent and distinctive features of this style is the
574 extensive use of sidenotes.
575 There is a wide margin to provide ample room for sidenotes and small figures.
576 Any footnotes will automatically be converted to sidenotes.
580 \begin_layout Plain Layout
581 This is a sidenote that was entered using a
590 Alternatively, you can also use the
594 inset directly; you'll find it in the
596 Insert\SpecialChar \menuseparator
600 \begin_inset Flex Sidenote
603 \begin_layout Plain Layout
604 This is a sidenote that was entered using a
616 \begin_layout Standard
617 If you like to place ancillary information in the margin without the sidenote
618 mark (the superscript number), you can use the
624 \begin_inset Flex Marginnote
627 \begin_layout Plain Layout
628 This is Tufte's margin note.
629 Notice that there isn't a number preceding the note, and there is no number
630 in the main text where this note was written.
635 The normal margin note will work as well, but it will look rather odd.
636 \begin_inset Marginal
639 \begin_layout Plain Layout
640 This is a normal margin note.
649 \begin_layout Standard
650 \begin_inset Flex NewThought
653 \begin_layout Plain Layout
659 innovation is Tufte's
665 Edit\SpecialChar \menuseparator
666 TextStyle\SpecialChar \menuseparator
670 It introduces new thoughts by means of small caps, as demonstrated in this
675 \begin_layout Standard
676 The Tufte document classes include two new character styles and some improvement
677 s on existing commands for letterspacing.
680 \begin_layout Standard
681 When setting strings of
682 \begin_inset Flex AllCaps
685 \begin_layout Plain Layout
692 \begin_inset Flex SmallCaps
695 \begin_layout Plain Layout
701 , the letterspacing---that is, the spacing between the letters---should
702 be increased slightly.
703 \begin_inset CommandInset citation
715 Edit\SpecialChar \menuseparator
716 TextStyle\SpecialChar \menuseparator
719 ) has proper letterspacing for strings of
720 \begin_inset Flex AllCaps
723 \begin_layout Plain Layout
735 Edit\SpecialChar \menuseparator
736 TextStyle\SpecialChar \menuseparator
739 ) has letterspacing for
740 \begin_inset Flex SmallCaps
743 \begin_layout Plain Layout
744 small capital letters
750 These commands will also automatically convert the case of the text to
751 upper- or lowercase, respectively.
754 \begin_layout Standard
759 shape has also been redefined to include letterspacing.
760 Its case is left as is, however.
761 This allows one to use both uppercase and lowercase letters:
763 The Initial Letters Of The Words In This Sentence Are Capitalized.
766 \begin_layout Standard
771 paragraph environment provides a paragraph layout that stretches across
772 the main text block and the sidenotes area:
775 \begin_layout Full Width
776 Lorem ipsum dolor sit amet, consectetuer adipiscing elit.
777 Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae, felis.
778 Curabitur dictum gravida mauris.
779 Nam arcu libero, nonummy eget, consectetuer id, vulputate a, magna.
780 Donec vehicula augue eu neque.
781 Pellentesque habitant morbi tristique senectus et netus et malesuada fames
784 Cras viverra metus rhoncus sem.
785 Nulla et lectus vestibulum urna fringilla ultrices.
786 Phasellus eu tellus sit amet tortor gravida placerat.
787 Integer sapien est, iaculis in, pretium quis, viverra ac, nunc.
788 Praesent eget sem vel leo ultrices bibendum.
790 Morbi dolor nulla, malesuada eu, pulvinar at, mollis ac, nulla.
791 Curabitur auctor semper nulla.
792 Donec varius orci eget risus.
793 Duis nibh mi, congue eu, accumsan eleifend, sagittis quis, diam.
794 Duis eget orci sit amet orci dignissim rutrum.
797 \begin_layout Section
801 \begin_layout Standard
802 References are placed alongside their citations as sidenotes, as well.
803 This can be accomplished using the normal citation command.
807 \begin_layout Plain Layout
808 The previous section includes a citation.
816 \begin_layout Standard
817 The complete list of references may also be printed automatically by using
820 Insert\SpecialChar \menuseparator
821 Lists/TOC\SpecialChar \menuseparator
828 (see the end of this document for an example.) If you do not want to print
829 a bibliography at the end of your document, place the
837 inset inside a LyX note and use the LaTeX command
846 \begin_layout Chapter
847 Calculation of Volume: Sections 2.12–2.13
850 \begin_layout Standard
851 Imagine taking a function like
852 \begin_inset Formula $y=\sqrt{x}$
855 and rotating it in 3 dimensions around the x-axis.
856 The resulting shape would look somewhat like a cup (on its side).
857 Interestingly, integration empowers us to do exactly this and to find out
858 how much water that cup could hold.
861 \begin_layout Section
865 \begin_layout Standard
866 \begin_inset Float marginfigure
871 \begin_layout Plain Layout
872 \begin_inset Box Boxed
882 height_special "totalheight"
885 \begin_layout Plain Layout
886 I had a graph of the square root function here.
894 \begin_layout Plain Layout
895 \begin_inset CommandInset label
897 name "mar:A-graph-of"
902 \begin_inset Formula $f(x)=\sqrt{x}$
918 \begin_layout Standard
919 \begin_inset Float marginfigure
924 \begin_layout Plain Layout
925 \begin_inset Box Boxed
935 height_special "totalheight"
938 \begin_layout Plain Layout
939 Here I rotated the square root function and then drew a disk on the figure
940 to illustrate how I would calculate the volume of the figure.
948 \begin_layout Plain Layout
949 \begin_inset CommandInset label
956 \begin_inset Formula $f(x)=\sqrt{x}$
959 rotated about the x-axis and with additional remarks for integration.
972 \begin_layout Standard
974 \begin_inset CommandInset ref
976 reference "mar:A-graph-of"
980 shows the plot of the function
981 \begin_inset Formula $f(x)=\sqrt{x}.$
984 Now, imagine that we rotate that function about the x-axis.
985 The resulting figure would be somewhat like figure
986 \begin_inset CommandInset ref
988 reference "mar:rotated"
993 This is akin to a cup lying on its side.
994 For the sake of clarity, the artist (me) drew a circle on the end of the
995 figure to show that it is indeed rotated.
998 \begin_layout Standard
999 Now, suppose we wished to find the volume of the figure.
1000 When we integrated the original square root function to find its area,
1001 we imagined a series of rectangles inside the figure.
1003 \begin_inset Formula $h=f(x)$
1007 \begin_inset Formula $dx$
1011 Since height multiplied by width was the area of each rectangle, we summed
1012 these areas and rewrote this as
1013 \begin_inset Formula $\int\, f(x)\, dx$
1016 , or, in this specific case,
1017 \begin_inset Formula $\int\,\sqrt{x}\, dx$
1023 \begin_layout Standard
1024 To find the volume of our rotated figure the prodecure is quite similar.
1025 Begin by rotating each rectangle about the x-axis.
1026 This creates a series of cylinders.
1027 \begin_inset Flex Sidenote
1030 \begin_layout Plain Layout
1031 The text refers to these cylinders as "disks".
1032 This is standard practice in all the Calculus books I checked.
1037 Then, we can find the volume of each cylinder/disk.
1038 The basic formula is:
1041 \begin_layout Standard
1042 \begin_inset Formula
1052 \begin_layout Standard
1055 \begin_inset Formula $h$
1058 is the height of the cylinder (width of the rectangle)
1059 \begin_inset Formula $dx$
1063 The area of each figure is a circle where
1064 \begin_inset Formula $A=\pi r^{2}$
1068 The radius in this case is the function
1069 \begin_inset Formula $f(x)$
1076 \begin_layout Standard
1077 \begin_inset Formula
1087 \begin_layout Standard
1089 In our specific case,
1092 \begin_layout Standard
1093 \begin_inset Formula
1095 A & = & \pi\left(\sqrt{x}\right)^{2}\\
1104 \begin_layout Standard
1105 To calculate the volume of one disk, we have
1108 \begin_layout Standard
1109 \begin_inset Formula
1119 \begin_layout Standard
1121 or, in the general case
1124 \begin_layout Standard
1125 \begin_inset Formula
1135 \begin_layout Standard
1136 To find the volume of the figure between points
1137 \begin_inset Formula $a$
1141 \begin_inset Formula $b$
1144 we sum the volumes by means of integration:
1147 \begin_layout Standard
1148 \begin_inset Formula
1150 \int_{a}^{b}\,\pi f^{2}(x)\, dx
1158 \begin_layout Standard
1160 In the specific example, over the interval
1161 \begin_inset Formula $[0,4]$
1167 \begin_layout Standard
1168 \begin_inset Formula
1170 \int_{0}^{4}\,\pi x\, dx & = & \pi\int_{0}^{4}\, x\, dx\\
1171 & = & \pi\left.\left(\frac{x^{2}}{2}\right)\right|_{0}^{4}\\
1172 & = & \pi\left(\frac{4^{2}}{2}-0\right)\\
1181 \begin_layout Standard
1182 \begin_inset Flex NewThought
1185 \begin_layout Plain Layout
1191 a special hole down the length of the cup we just worked with.
1192 It is made with a quadratic shaped bit.
1193 \begin_inset Flex Sidenote
1196 \begin_layout Plain Layout
1197 I have no idea how I'd do this in real life, but I'm making a point.
1202 I find that the hole the bit makes can be modeled with the function
1203 \begin_inset Formula $g(x)=\frac{x^{2}}{16}$
1207 I would need to subtract the volume of the material removed from the volume
1209 \begin_inset Quotes eld
1213 \begin_inset Quotes erd
1217 Each individual cylinder would become like a
1218 \begin_inset Quotes eld
1222 \begin_inset Quotes erd
1226 To get the area of one washer, I would use the formula
1229 \begin_layout Standard
1230 \begin_inset Float marginfigure
1235 \begin_layout Plain Layout
1236 \begin_inset Box Boxed
1246 height_special "totalheight"
1249 \begin_layout Plain Layout
1250 Here I used RLPlot to draw the square root function and the quadratic function.
1251 Then I used Inkscape to shade the area between them.
1257 \begin_inset Caption
1259 \begin_layout Plain Layout
1261 \begin_inset Formula $f(x)$
1265 \begin_inset Formula $g(x)$
1268 and the area left by
1269 \begin_inset Formula $f(x)-g(x)$
1285 \begin_layout Standard
1286 \begin_inset Formula
1288 A_{washer} & = & A_{cup}-A_{drill}\\
1289 & = & \pi f^{2}(x)-\pi g^{2}(x)\\
1290 & = & \pi\left(f^{2}(x)-g^{2}(x)\right)
1298 \begin_layout Standard
1299 The volume of each washer would be
1302 \begin_layout Standard
1303 \begin_inset Formula
1305 V_{washer} & = & A_{washer}\, dx\\
1306 & = & \pi\left(f^{2}(x)-g^{2}(x)\right)\, dx
1314 \begin_layout Standard
1316 Then, by summing the volumes of all the washers between points
1317 \begin_inset Formula $a$
1321 \begin_inset Formula $b$
1324 , the integral is derived:
1327 \begin_layout Standard
1328 \begin_inset Formula
1330 \int_{a}^{b}\,\pi\left(f^{2}(x)-g^{2}(x)\right)\, dx
1338 \begin_layout Standard
1339 In the case of our quadratic drill bit::
1340 \begin_inset Float marginfigure
1345 \begin_layout Plain Layout
1346 \begin_inset Box Boxed
1356 height_special "totalheight"
1359 \begin_layout Plain Layout
1360 This was the rotated set of 2 functions.
1366 \begin_inset Caption
1368 \begin_layout Plain Layout
1369 The cup with a quadratic hole drilled down its length
1382 \begin_layout Standard
1383 \begin_inset Formula
1385 \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\\
1386 & = & \pi\left(\int_{0}^{4}\, x\, dx-\int_{0}^{4}\,\frac{x^{4}}{256}\, dx\right)\\
1387 & = & \pi\left(\left.\left(\frac{x^{2}}{2}\right)\right|_{0}^{4}-\left.\left(\frac{x^{5}}{1280}\right)\right|_{0}^{4}\right)\\
1388 & = & \pi\left(\left(\frac{4^{2}}{2}-0\right)-\left(\frac{4^{5}}{1280}-0\right)\right)\\
1389 & = & \pi\left(8-0.8\right)\\
1398 \begin_layout Standard
1402 \begin_layout Section
1406 \begin_layout Itemize
1407 p114: 1, 4, 5, 6, 8, 10, 12, 15
1410 \begin_layout Standard
1411 \begin_inset CommandInset bibtex
1413 bibfiles "biblioExample"