1 #LyX 2.3 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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15 \font_sans "default" "default"
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19 \use_non_tex_fonts false
22 \font_sf_scale 100 100
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25 \use_dash_ligatures false
27 \default_output_format pdf2
29 \bibtex_command bibtex
30 \index_command default
31 \paperfontsize default
35 \pdf_bookmarksnumbered false
36 \pdf_bookmarksopen true
37 \pdf_bookmarksopenlevel 1
45 \use_package amsmath 1
46 \use_package amssymb 1
49 \use_package mathdots 1
50 \use_package mathtools 1
52 \use_package stackrel 1
53 \use_package stmaryrd 1
54 \use_package undertilde 1
56 \cite_engine_type default
60 \paperorientation portrait
64 \notefontcolor #0000ff
71 \paragraph_separation indent
72 \paragraph_indentation default
74 \math_numbering_side default
78 \paperpagestyle default
79 \tracking_changes false
89 \begin_layout Standard
90 \begin_inset Note Note
93 \begin_layout Plain Layout
98 : To be able to view your file as PDF you must have the \SpecialChar LaTeX
103 installed to your \SpecialChar LaTeX
105 If you are using MiK\SpecialChar TeX
106 , you will automatically be asked to install this package
107 when previewing your file, if you are using \SpecialChar TeX
108 Live, use \SpecialChar TeX
109 Live's package manager.
112 \begin_layout Plain Layout
117 : If you wish to compile to PDF with plain \SpecialChar LaTeX
118 (instead of pdf\SpecialChar TeX
119 ), there is currently
120 a bug in the Tufte class that causes errors.
121 You can add the class option 'nols' (put this in the
122 \begin_inset Quotes eld
126 \begin_inset Quotes erd
129 field of Document\SpecialChar menuseparator
130 Settings \SpecialChar menuseparator
131 Document Class) to get rid of the errors, but
132 this also removes letterspacing, an important part of the Tufte design.
146 \begin_inset Note Note
149 \begin_layout Plain Layout
150 author of this example file: Jason Waskiewicz
158 \begin_layout Standard
159 \begin_inset CommandInset toc
160 LatexCommand tableofcontents
167 \begin_layout Chapter
168 The Features of the Tufte-book Class
171 \begin_layout Standard
172 In this document, it was endeavored to show some of the features of the
178 In the first chapter, their use is outlined.
179 In the second chapter, their use through a handout that was created in
180 a calculus class is demonstrated.
183 \begin_layout Section
187 \begin_layout Standard
192 class is based on the work of
197 It provides the same functionality as the
201 class with book-specific additions.
202 Tufte's documents consist of a rather narrow column of text and a wide
203 column of margin notes and margin figures.
204 This is to improve readability.
207 \begin_layout Standard
208 The features provided by this format include:
211 \begin_layout Itemize
215 \begin_layout Itemize
216 Ordinary figures in text with captions in margins
219 \begin_layout Itemize
220 Full width figures and text when needed
223 \begin_layout Itemize
224 \begin_inset Quotes eld
228 \begin_inset Quotes erd
234 \begin_layout Itemize
235 Limited layers of sections and subsections
238 \begin_layout Standard
239 In this sample document, some of these features are demonstrated.
240 For a full demonstration, visit the tufte-latex website:
241 \begin_inset Flex URL
244 \begin_layout Plain Layout
246 https://tufte-latex.github.io/tufte-latex/
254 \begin_layout Section
258 \begin_layout Standard
260 \begin_inset Quotes eld
264 \begin_inset Quotes erd
267 rather than justified.
268 \begin_inset Flex Sidenote
271 \begin_layout Plain Layout
272 To get justified text, add the option
282 Document\SpecialChar menuseparator
283 Settings\SpecialChar menuseparator
291 Ragged right text is used in most of his works, but the class option
295 is provided to change this.
298 \begin_layout Standard
299 Tufte also formats his pages asymmetrically.
300 This means that the marginalia appear on the right side on each page, whether
302 If you prefer, you can change that and have symmetric layout, as common
303 in traditional book typography, by using the
308 \begin_inset Flex Sidenote
311 \begin_layout Plain Layout
312 To create a symmetric layout, add the option
322 Document\SpecialChar menuseparator
323 Settings\SpecialChar menuseparator
334 \begin_layout Standard
335 Finally, Tufte does not number his chapters or his sections.
336 If you like to refer to sections by number, move the
342 Document\SpecialChar menuseparator
343 Settings\SpecialChar menuseparator
346 to the very right (as done in this document).
347 \begin_inset Flex Marginnote
350 \begin_layout Plain Layout
359 \begin_layout Section
363 \begin_layout Standard
364 Tufte uses ordinary figure floats such as the following:
367 \begin_layout Standard
368 \begin_inset Float figure
373 \begin_layout Plain Layout
374 \begin_inset Box Boxed
384 height_special "totalheight"
389 backgroundcolor "none"
392 \begin_layout Plain Layout
393 Imagine your favorite figure inside this box instead of this boring text.
399 \begin_inset Caption Standard
401 \begin_layout Plain Layout
402 An ordinary figure float.
415 \begin_layout Standard
416 Furthermore, he uses margin figures, as shown in Fig.
421 \begin_inset CommandInset ref
423 reference "fig:margin-figure"
430 \begin_layout Standard
431 \begin_inset VSpace 5theight%
437 \begin_layout Standard
438 \begin_inset Float marginfigure
443 \begin_layout Plain Layout
444 \begin_inset Box Boxed
454 height_special "totalheight"
459 backgroundcolor "none"
462 \begin_layout Plain Layout
463 Imagine your favorite photograph of a squirrel inside this box instead of
470 \begin_inset Caption Standard
472 \begin_layout Plain Layout
474 \begin_inset CommandInset label
476 name "fig:margin-figure"
493 \begin_layout Standard
494 \begin_inset Note Greyedout
497 \begin_layout Plain Layout
502 If you are using margin figures or tables you must use the default float
503 placement option in the document settings under
519 \begin_layout Standard
520 In the same vein, the
524 class allows the use of tables, both in the margins and in the text.
525 The margin tables are recommended for a small set of data to illustrate
527 \begin_inset Quotes eld
530 Look, distance-time data is quadratic when the object is falling.
531 \begin_inset Quotes erd
534 More detailed data such as flame test results and comments should be put
535 in a full-width table instead.
538 \begin_layout Standard
543 provides a full-width figure.
544 This one takes up the entire width of the page, i.
545 \begin_inset space \thinspace{}
554 \begin_inset CommandInset ref
556 reference "fig:full-width-figure"
563 \begin_layout Standard
564 \begin_inset Float figure
569 \begin_layout Plain Layout
570 \begin_inset Box Boxed
580 height_special "totalheight"
585 backgroundcolor "none"
588 \begin_layout Plain Layout
589 Imagine your favorite photograph of a squirrel inside this box instead of
596 \begin_inset VSpace defskip
602 \begin_layout Plain Layout
603 \begin_inset Caption Standard
605 \begin_layout Plain Layout
607 \begin_inset CommandInset label
609 name "fig:full-width-figure"
626 \begin_layout Section
630 \begin_layout Standard
631 One of the most prominent and distinctive features of this style is the
632 extensive use of sidenotes.
633 There is a wide margin to provide ample room for sidenotes and small figures.
634 Any footnotes will automatically be converted to sidenotes.
638 \begin_layout Plain Layout
639 This is a sidenote that was entered using a
648 Alternatively, you can also use the
652 inset directly; you'll find it in the
654 Insert\SpecialChar menuseparator
658 \begin_inset Flex Sidenote
661 \begin_layout Plain Layout
662 This is a sidenote that was entered using a
674 \begin_layout Standard
675 If you like to place ancillary information in the margin without the sidenote
676 mark (the superscript number), you can use the
682 \begin_inset Flex Marginnote
685 \begin_layout Plain Layout
686 This is Tufte's margin note.
687 Notice that there isn't a number preceding the note, and there is no number
688 in the main text where this note was written.
693 The normal margin note will work as well, but it will look rather odd.
694 \begin_inset Marginal
697 \begin_layout Plain Layout
698 This is a normal margin note.
707 \begin_layout Standard
708 \begin_inset Flex NewThought
711 \begin_layout Plain Layout
717 innovation is Tufte's
723 Edit\SpecialChar menuseparator
724 TextStyle\SpecialChar menuseparator
728 It introduces new thoughts by means of small caps, as demonstrated in this
733 \begin_layout Standard
734 The Tufte document classes include two new character styles and some improvement
735 s on existing commands for letterspacing.
738 \begin_layout Standard
739 When setting strings of
740 \begin_inset Flex AllCaps
743 \begin_layout Plain Layout
750 \begin_inset Flex SmallCaps
753 \begin_layout Plain Layout
759 , the letterspacing—that is, the spacing between the letters—should be increased
761 \begin_inset CommandInset citation
774 Edit\SpecialChar menuseparator
775 TextStyle\SpecialChar menuseparator
778 ) has proper letterspacing for strings of
779 \begin_inset Flex AllCaps
782 \begin_layout Plain Layout
794 Edit\SpecialChar menuseparator
795 TextStyle\SpecialChar menuseparator
798 ) has letterspacing for
799 \begin_inset Flex SmallCaps
802 \begin_layout Plain Layout
803 small capital letters
809 These commands will also automatically convert the case of the text to
810 upper- or lowercase, respectively.
813 \begin_layout Standard
818 shape has also been redefined to include letterspacing.
819 Its case is left as is, however.
820 This allows one to use both uppercase and lowercase letters:
822 The Initial Letters Of The Words In This Sentence Are Capitalized.
825 \begin_layout Standard
830 paragraph environment provides a paragraph layout that stretches across
831 the main text block and the sidenotes area:
834 \begin_layout Full Width
835 Lorem ipsum dolor sit amet, consectetuer adipiscing elit.
836 Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae, felis.
837 Curabitur dictum gravida mauris.
838 Nam arcu libero, nonummy eget, consectetuer id, vulputate a, magna.
839 Donec vehicula augue eu neque.
840 Pellentesque habitant morbi tristique senectus et netus et malesuada fames
843 Cras viverra metus rhoncus sem.
844 Nulla et lectus vestibulum urna fringilla ultrices.
845 Phasellus eu tellus sit amet tortor gravida placerat.
846 Integer sapien est, iaculis in, pretium quis, viverra ac, nunc.
847 Praesent eget sem vel leo ultrices bibendum.
849 Morbi dolor nulla, malesuada eu, pulvinar at, mollis ac, nulla.
850 Curabitur auctor semper nulla.
851 Donec varius orci eget risus.
852 Duis nibh mi, congue eu, accumsan eleifend, sagittis quis, diam.
853 Duis eget orci sit amet orci dignissim rutrum.
856 \begin_layout Section
860 \begin_layout Standard
861 References are placed alongside their citations as sidenotes, as well.
862 This can be accomplished using the normal citation command.
866 \begin_layout Plain Layout
867 The previous section includes a citation.
875 \begin_layout Standard
876 The complete list of references may also be printed automatically by using
879 Insert\SpecialChar menuseparator
880 Lists/TOC\SpecialChar menuseparator
888 (see the end of this document for an example.) If you do not want to print
889 a bibliography at the end of your document, place the
898 inset inside a \SpecialChar LyX
899 note and use the \SpecialChar LaTeX
909 \begin_layout Chapter
910 Calculation of Volume: Sections 2.12–2.13
913 \begin_layout Standard
914 Imagine taking a function like
915 \begin_inset Formula $y=\sqrt{x}$
918 and rotating it in 3 dimensions around the x-axis.
919 The resulting shape would look somewhat like a cup (on its side).
920 Interestingly, integration empowers us to do exactly this and to find out
921 how much water that cup could hold.
924 \begin_layout Section
928 \begin_layout Standard
929 \begin_inset Float marginfigure
934 \begin_layout Plain Layout
935 \begin_inset Box Boxed
945 height_special "totalheight"
950 backgroundcolor "none"
953 \begin_layout Plain Layout
954 I had a graph of the square root function here.
960 \begin_inset Caption Standard
962 \begin_layout Plain Layout
963 \begin_inset CommandInset label
965 name "mar:A-graph-of"
970 \begin_inset Formula $f(x)=\sqrt{x}$
986 \begin_layout Standard
987 \begin_inset Float marginfigure
992 \begin_layout Plain Layout
993 \begin_inset Box Boxed
1003 height_special "totalheight"
1008 backgroundcolor "none"
1011 \begin_layout Plain Layout
1012 Here I rotated the square root function and then drew a disk on the figure
1013 to illustrate how I would calculate the volume of the figure.
1019 \begin_inset Caption Standard
1021 \begin_layout Plain Layout
1022 \begin_inset CommandInset label
1029 \begin_inset Formula $f(x)=\sqrt{x}$
1032 rotated about the x-axis and with additional remarks for integration.
1045 \begin_layout Standard
1047 \begin_inset CommandInset ref
1049 reference "mar:A-graph-of"
1053 shows the plot of the function
1054 \begin_inset Formula $f(x)=\sqrt{x}.$
1057 Now, imagine that we rotate that function about the x-axis.
1058 The resulting figure would be somewhat like figure
1059 \begin_inset CommandInset ref
1061 reference "mar:rotated"
1066 This is akin to a cup lying on its side.
1067 For the sake of clarity, the artist (me) drew a circle on the end of the
1068 figure to show that it is indeed rotated.
1071 \begin_layout Standard
1072 Now, suppose we wished to find the volume of the figure.
1073 When we integrated the original square root function to find its area,
1074 we imagined a series of rectangles inside the figure.
1076 \begin_inset Formula $h=f(x)$
1080 \begin_inset Formula $dx$
1084 Since height multiplied by width was the area of each rectangle, we summed
1085 these areas and rewrote this as
1086 \begin_inset Formula $\int\,f(x)\,dx$
1089 , or, in this specific case,
1090 \begin_inset Formula $\int\,\sqrt{x}\,dx$
1096 \begin_layout Standard
1097 To find the volume of our rotated figure the prodecure is quite similar.
1098 Begin by rotating each rectangle about the x-axis.
1099 This creates a series of cylinders.
1100 \begin_inset Flex Sidenote
1103 \begin_layout Plain Layout
1104 The text refers to these cylinders as "disks".
1105 This is standard practice in all the Calculus books I checked.
1110 Then, we can find the volume of each cylinder/disk.
1111 The basic formula is:
1114 \begin_layout Standard
1115 \begin_inset Formula
1125 \begin_layout Standard
1128 \begin_inset Formula $h$
1131 is the height of the cylinder (width of the rectangle)
1132 \begin_inset Formula $dx$
1136 The area of each figure is a circle where
1137 \begin_inset Formula $A=\pi r^{2}$
1141 The radius in this case is the function
1142 \begin_inset Formula $f(x)$
1149 \begin_layout Standard
1150 \begin_inset Formula
1160 \begin_layout Standard
1162 In our specific case,
1165 \begin_layout Standard
1166 \begin_inset Formula
1168 A & = & \pi\left(\sqrt{x}\right)^{2}\\
1177 \begin_layout Standard
1178 To calculate the volume of one disk, we have
1181 \begin_layout Standard
1182 \begin_inset Formula
1192 \begin_layout Standard
1194 or, in the general case
1197 \begin_layout Standard
1198 \begin_inset Formula
1208 \begin_layout Standard
1209 To find the volume of the figure between points
1210 \begin_inset Formula $a$
1214 \begin_inset Formula $b$
1217 we sum the volumes by means of integration:
1220 \begin_layout Standard
1221 \begin_inset Formula
1223 \int_{a}^{b}\,\pi f^{2}(x)\,dx
1231 \begin_layout Standard
1233 In the specific example, over the interval
1234 \begin_inset Formula $[0,4]$
1240 \begin_layout Standard
1241 \begin_inset Formula
1243 \int_{0}^{4}\,\pi x\,dx & = & \pi\int_{0}^{4}\,x\,dx\\
1244 & = & \pi\left.\left(\frac{x^{2}}{2}\right)\right|_{0}^{4}\\
1245 & = & \pi\left(\frac{4^{2}}{2}-0\right)\\
1254 \begin_layout Standard
1255 \begin_inset Flex NewThought
1258 \begin_layout Plain Layout
1264 a special hole down the length of the cup we just worked with.
1265 It is made with a quadratic shaped bit.
1266 \begin_inset Flex Sidenote
1269 \begin_layout Plain Layout
1270 I have no idea how I'd do this in real life, but I'm making a point.
1275 I find that the hole the bit makes can be modeled with the function
1276 \begin_inset Formula $g(x)=\frac{x^{2}}{16}$
1280 I would need to subtract the volume of the material removed from the volume
1282 \begin_inset Quotes eld
1286 \begin_inset Quotes erd
1290 Each individual cylinder would become like a
1291 \begin_inset Quotes eld
1295 \begin_inset Quotes erd
1299 To get the area of one washer, I would use the formula
1302 \begin_layout Standard
1303 \begin_inset Float marginfigure
1308 \begin_layout Plain Layout
1309 \begin_inset Box Boxed
1319 height_special "totalheight"
1324 backgroundcolor "none"
1327 \begin_layout Plain Layout
1328 Here I used RLPlot to draw the square root function and the quadratic function.
1329 Then I used Inkscape to shade the area between them.
1335 \begin_inset Caption Standard
1337 \begin_layout Plain Layout
1339 \begin_inset Formula $f(x)$
1343 \begin_inset Formula $g(x)$
1346 and the area left by
1347 \begin_inset Formula $f(x)-g(x)$
1363 \begin_layout Standard
1364 \begin_inset Formula
1366 A_{washer} & = & A_{cup}-A_{drill}\\
1367 & = & \pi f^{2}(x)-\pi g^{2}(x)\\
1368 & = & \pi\left(f^{2}(x)-g^{2}(x)\right)
1376 \begin_layout Standard
1377 The volume of each washer would be
1380 \begin_layout Standard
1381 \begin_inset Formula
1383 V_{washer} & = & A_{washer}\,dx\\
1384 & = & \pi\left(f^{2}(x)-g^{2}(x)\right)\,dx
1392 \begin_layout Standard
1394 Then, by summing the volumes of all the washers between points
1395 \begin_inset Formula $a$
1399 \begin_inset Formula $b$
1402 , the integral is derived:
1405 \begin_layout Standard
1406 \begin_inset Formula
1408 \int_{a}^{b}\,\pi\left(f^{2}(x)-g^{2}(x)\right)\,dx
1416 \begin_layout Standard
1417 In the case of our quadratic drill bit::
1418 \begin_inset Float marginfigure
1423 \begin_layout Plain Layout
1424 \begin_inset Box Boxed
1434 height_special "totalheight"
1439 backgroundcolor "none"
1442 \begin_layout Plain Layout
1443 This was the rotated set of 2 functions.
1449 \begin_inset Caption Standard
1451 \begin_layout Plain Layout
1452 The cup with a quadratic hole drilled down its length
1465 \begin_layout Standard
1466 \begin_inset Formula
1468 \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\\
1469 & = & \pi\left(\int_{0}^{4}\,x\,dx-\int_{0}^{4}\,\frac{x^{4}}{256}\,dx\right)\\
1470 & = & \pi\left(\left.\left(\frac{x^{2}}{2}\right)\right|_{0}^{4}-\left.\left(\frac{x^{5}}{1280}\right)\right|_{0}^{4}\right)\\
1471 & = & \pi\left(\left(\frac{4^{2}}{2}-0\right)-\left(\frac{4^{5}}{1280}-0\right)\right)\\
1472 & = & \pi\left(8-0.8\right)\\
1481 \begin_layout Standard
1485 \begin_layout Section
1489 \begin_layout Itemize
1490 p114: 1, 4, 5, 6, 8, 10, 12, 15
1493 \begin_layout Standard
1494 \begin_inset CommandInset bibtex
1496 bibfiles "biblioExample"