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
9 \maintain_unincluded_children false
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 \SpecialChar LaTeX
98 installed to your \SpecialChar LaTeX
100 If you are using MiK\SpecialChar TeX
101 , you will automatically be asked to install this package
102 when previewing your file, if you are using \SpecialChar TeX
103 Live, use \SpecialChar TeX
104 Live's package manager.
107 \begin_layout Plain Layout
112 : If you wish to compile to PDF with plain \SpecialChar LaTeX
113 (instead of pdf\SpecialChar TeX
114 ), there is currently
115 a bug in the Tufte class that causes errors.
116 You can add the class option 'nols' (put this in the
117 \begin_inset Quotes eld
121 \begin_inset Quotes erd
124 field of Document\SpecialChar menuseparator
125 Settings \SpecialChar menuseparator
126 Document Class) to get rid of the errors, but
127 this also removes letterspacing, an important part of the Tufte design.
141 \begin_inset Note Note
144 \begin_layout Plain Layout
145 author of this example file: Jason Waskiewicz
153 \begin_layout Standard
154 \begin_inset CommandInset toc
155 LatexCommand tableofcontents
162 \begin_layout Chapter
163 The Features of the Tufte-book Class
166 \begin_layout Standard
167 In this document, it was endeavored to show some of the features of the
173 In the first chapter, their use is outlined.
174 In the second chapter, their use through a handout that was created in
175 a calculus class is demonstrated.
178 \begin_layout Section
182 \begin_layout Standard
187 class is based on the work of
192 It provides the same functionality as the
196 class with book-specific additions.
197 Tufte's documents consist of a rather narrow column of text and a wide
198 column of margin notes and margin figures.
199 This is to improve readability.
202 \begin_layout Standard
203 The features provided by this format include:
206 \begin_layout Itemize
210 \begin_layout Itemize
211 Ordinary figures in text with captions in margins
214 \begin_layout Itemize
215 Full width figures and text when needed
218 \begin_layout Itemize
219 \begin_inset Quotes eld
223 \begin_inset Quotes erd
229 \begin_layout Itemize
230 Limited layers of sections and subsections
233 \begin_layout Standard
234 In this sample document, some of these features are demonstrated.
235 For a full demonstration, visit the tufte-latex website:
236 \begin_inset Flex URL
239 \begin_layout Plain Layout
241 https://tufte-latex.github.io/tufte-latex/
249 \begin_layout Section
253 \begin_layout Standard
255 \begin_inset Quotes eld
259 \begin_inset Quotes erd
262 rather than justified.
263 \begin_inset Flex Sidenote
266 \begin_layout Plain Layout
267 To get justified text, add the option
277 Document\SpecialChar menuseparator
278 Settings\SpecialChar menuseparator
286 Ragged right text is used in most of his works, but the class option
290 is provided to change this.
293 \begin_layout Standard
294 Tufte also formats his pages asymmetrically.
295 This means that the marginalia appear on the right side on each page, whether
297 If you prefer, you can change that and have symmetric layout, as common
298 in traditional book typography, by using the
303 \begin_inset Flex Sidenote
306 \begin_layout Plain Layout
307 To create a symmetric layout, add the option
317 Document\SpecialChar menuseparator
318 Settings\SpecialChar menuseparator
329 \begin_layout Standard
330 Finally, Tufte does not number his chapters or his sections.
331 If you like to refer to sections by number, move the
337 Document\SpecialChar menuseparator
338 Settings\SpecialChar menuseparator
341 to the very right (as done in this document).
342 \begin_inset Flex Marginnote
345 \begin_layout Plain Layout
354 \begin_layout Section
358 \begin_layout Standard
359 Tufte uses ordinary figure floats such as the following:
362 \begin_layout Standard
363 \begin_inset Float figure
368 \begin_layout Plain Layout
369 \begin_inset Box Boxed
379 height_special "totalheight"
384 backgroundcolor "none"
387 \begin_layout Plain Layout
388 Imagine your favorite figure inside this box instead of this boring text.
394 \begin_inset Caption Standard
396 \begin_layout Plain Layout
397 An ordinary figure float.
410 \begin_layout Standard
411 Furthermore, he uses margin figures, as shown in Fig.
416 \begin_inset CommandInset ref
418 reference "fig:margin-figure"
425 \begin_layout Standard
426 \begin_inset VSpace 5theight%
432 \begin_layout Standard
433 \begin_inset Float marginfigure
438 \begin_layout Plain Layout
439 \begin_inset Box Boxed
449 height_special "totalheight"
454 backgroundcolor "none"
457 \begin_layout Plain Layout
458 Imagine your favorite photograph of a squirrel inside this box instead of
465 \begin_inset Caption Standard
467 \begin_layout Plain Layout
469 \begin_inset CommandInset label
471 name "fig:margin-figure"
488 \begin_layout Standard
489 \begin_inset Note Greyedout
492 \begin_layout Plain Layout
497 If you are using margin figures or tables you must use the default float
498 placement option in the document settings under
514 \begin_layout Standard
515 In the same vein, the
519 class allows the use of tables, both in the margins and in the text.
520 The margin tables are recommended for a small set of data to illustrate
522 \begin_inset Quotes eld
525 Look, distance-time data is quadratic when the object is falling.
526 \begin_inset Quotes erd
529 More detailed data such as flame test results and comments should be put
530 in a full-width table instead.
533 \begin_layout Standard
538 provides a full-width figure.
539 This one takes up the entire width of the page, i.
540 \begin_inset space \thinspace{}
549 \begin_inset CommandInset ref
551 reference "fig:full-width-figure"
558 \begin_layout Standard
559 \begin_inset Float figure
564 \begin_layout Plain Layout
565 \begin_inset Box Boxed
575 height_special "totalheight"
580 backgroundcolor "none"
583 \begin_layout Plain Layout
584 Imagine your favorite photograph of a squirrel inside this box instead of
591 \begin_inset VSpace defskip
597 \begin_layout Plain Layout
598 \begin_inset Caption Standard
600 \begin_layout Plain Layout
602 \begin_inset CommandInset label
604 name "fig:full-width-figure"
621 \begin_layout Section
625 \begin_layout Standard
626 One of the most prominent and distinctive features of this style is the
627 extensive use of sidenotes.
628 There is a wide margin to provide ample room for sidenotes and small figures.
629 Any footnotes will automatically be converted to sidenotes.
633 \begin_layout Plain Layout
634 This is a sidenote that was entered using a
643 Alternatively, you can also use the
647 inset directly; you'll find it in the
649 Insert\SpecialChar menuseparator
653 \begin_inset Flex Sidenote
656 \begin_layout Plain Layout
657 This is a sidenote that was entered using a
669 \begin_layout Standard
670 If you like to place ancillary information in the margin without the sidenote
671 mark (the superscript number), you can use the
677 \begin_inset Flex Marginnote
680 \begin_layout Plain Layout
681 This is Tufte's margin note.
682 Notice that there isn't a number preceding the note, and there is no number
683 in the main text where this note was written.
688 The normal margin note will work as well, but it will look rather odd.
689 \begin_inset Marginal
692 \begin_layout Plain Layout
693 This is a normal margin note.
702 \begin_layout Standard
703 \begin_inset Flex NewThought
706 \begin_layout Plain Layout
712 innovation is Tufte's
718 Edit\SpecialChar menuseparator
719 TextStyle\SpecialChar menuseparator
723 It introduces new thoughts by means of small caps, as demonstrated in this
728 \begin_layout Standard
729 The Tufte document classes include two new character styles and some improvement
730 s on existing commands for letterspacing.
733 \begin_layout Standard
734 When setting strings of
735 \begin_inset Flex AllCaps
738 \begin_layout Plain Layout
745 \begin_inset Flex SmallCaps
748 \begin_layout Plain Layout
754 , the letterspacing—that is, the spacing between the letters—should be increased
756 \begin_inset CommandInset citation
768 Edit\SpecialChar menuseparator
769 TextStyle\SpecialChar menuseparator
772 ) has proper letterspacing for strings of
773 \begin_inset Flex AllCaps
776 \begin_layout Plain Layout
788 Edit\SpecialChar menuseparator
789 TextStyle\SpecialChar menuseparator
792 ) has letterspacing for
793 \begin_inset Flex SmallCaps
796 \begin_layout Plain Layout
797 small capital letters
803 These commands will also automatically convert the case of the text to
804 upper- or lowercase, respectively.
807 \begin_layout Standard
812 shape has also been redefined to include letterspacing.
813 Its case is left as is, however.
814 This allows one to use both uppercase and lowercase letters:
816 The Initial Letters Of The Words In This Sentence Are Capitalized.
819 \begin_layout Standard
824 paragraph environment provides a paragraph layout that stretches across
825 the main text block and the sidenotes area:
828 \begin_layout Full Width
829 Lorem ipsum dolor sit amet, consectetuer adipiscing elit.
830 Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae, felis.
831 Curabitur dictum gravida mauris.
832 Nam arcu libero, nonummy eget, consectetuer id, vulputate a, magna.
833 Donec vehicula augue eu neque.
834 Pellentesque habitant morbi tristique senectus et netus et malesuada fames
837 Cras viverra metus rhoncus sem.
838 Nulla et lectus vestibulum urna fringilla ultrices.
839 Phasellus eu tellus sit amet tortor gravida placerat.
840 Integer sapien est, iaculis in, pretium quis, viverra ac, nunc.
841 Praesent eget sem vel leo ultrices bibendum.
843 Morbi dolor nulla, malesuada eu, pulvinar at, mollis ac, nulla.
844 Curabitur auctor semper nulla.
845 Donec varius orci eget risus.
846 Duis nibh mi, congue eu, accumsan eleifend, sagittis quis, diam.
847 Duis eget orci sit amet orci dignissim rutrum.
850 \begin_layout Section
854 \begin_layout Standard
855 References are placed alongside their citations as sidenotes, as well.
856 This can be accomplished using the normal citation command.
860 \begin_layout Plain Layout
861 The previous section includes a citation.
869 \begin_layout Standard
870 The complete list of references may also be printed automatically by using
873 Insert\SpecialChar menuseparator
874 Lists/TOC\SpecialChar menuseparator
882 (see the end of this document for an example.) If you do not want to print
883 a bibliography at the end of your document, place the
892 inset inside a \SpecialChar LyX
893 note and use the \SpecialChar LaTeX
903 \begin_layout Chapter
904 Calculation of Volume: Sections 2.12–2.13
907 \begin_layout Standard
908 Imagine taking a function like
909 \begin_inset Formula $y=\sqrt{x}$
912 and rotating it in 3 dimensions around the x-axis.
913 The resulting shape would look somewhat like a cup (on its side).
914 Interestingly, integration empowers us to do exactly this and to find out
915 how much water that cup could hold.
918 \begin_layout Section
922 \begin_layout Standard
923 \begin_inset Float marginfigure
928 \begin_layout Plain Layout
929 \begin_inset Box Boxed
939 height_special "totalheight"
944 backgroundcolor "none"
947 \begin_layout Plain Layout
948 I had a graph of the square root function here.
954 \begin_inset Caption Standard
956 \begin_layout Plain Layout
957 \begin_inset CommandInset label
959 name "mar:A-graph-of"
964 \begin_inset Formula $f(x)=\sqrt{x}$
980 \begin_layout Standard
981 \begin_inset Float marginfigure
986 \begin_layout Plain Layout
987 \begin_inset Box Boxed
997 height_special "totalheight"
1002 backgroundcolor "none"
1005 \begin_layout Plain Layout
1006 Here I rotated the square root function and then drew a disk on the figure
1007 to illustrate how I would calculate the volume of the figure.
1013 \begin_inset Caption Standard
1015 \begin_layout Plain Layout
1016 \begin_inset CommandInset label
1023 \begin_inset Formula $f(x)=\sqrt{x}$
1026 rotated about the x-axis and with additional remarks for integration.
1039 \begin_layout Standard
1041 \begin_inset CommandInset ref
1043 reference "mar:A-graph-of"
1047 shows the plot of the function
1048 \begin_inset Formula $f(x)=\sqrt{x}.$
1051 Now, imagine that we rotate that function about the x-axis.
1052 The resulting figure would be somewhat like figure
1053 \begin_inset CommandInset ref
1055 reference "mar:rotated"
1060 This is akin to a cup lying on its side.
1061 For the sake of clarity, the artist (me) drew a circle on the end of the
1062 figure to show that it is indeed rotated.
1065 \begin_layout Standard
1066 Now, suppose we wished to find the volume of the figure.
1067 When we integrated the original square root function to find its area,
1068 we imagined a series of rectangles inside the figure.
1070 \begin_inset Formula $h=f(x)$
1074 \begin_inset Formula $dx$
1078 Since height multiplied by width was the area of each rectangle, we summed
1079 these areas and rewrote this as
1080 \begin_inset Formula $\int\,f(x)\,dx$
1083 , or, in this specific case,
1084 \begin_inset Formula $\int\,\sqrt{x}\,dx$
1090 \begin_layout Standard
1091 To find the volume of our rotated figure the prodecure is quite similar.
1092 Begin by rotating each rectangle about the x-axis.
1093 This creates a series of cylinders.
1094 \begin_inset Flex Sidenote
1097 \begin_layout Plain Layout
1098 The text refers to these cylinders as "disks".
1099 This is standard practice in all the Calculus books I checked.
1104 Then, we can find the volume of each cylinder/disk.
1105 The basic formula is:
1108 \begin_layout Standard
1109 \begin_inset Formula
1119 \begin_layout Standard
1122 \begin_inset Formula $h$
1125 is the height of the cylinder (width of the rectangle)
1126 \begin_inset Formula $dx$
1130 The area of each figure is a circle where
1131 \begin_inset Formula $A=\pi r^{2}$
1135 The radius in this case is the function
1136 \begin_inset Formula $f(x)$
1143 \begin_layout Standard
1144 \begin_inset Formula
1154 \begin_layout Standard
1156 In our specific case,
1159 \begin_layout Standard
1160 \begin_inset Formula
1162 A & = & \pi\left(\sqrt{x}\right)^{2}\\
1171 \begin_layout Standard
1172 To calculate the volume of one disk, we have
1175 \begin_layout Standard
1176 \begin_inset Formula
1186 \begin_layout Standard
1188 or, in the general case
1191 \begin_layout Standard
1192 \begin_inset Formula
1202 \begin_layout Standard
1203 To find the volume of the figure between points
1204 \begin_inset Formula $a$
1208 \begin_inset Formula $b$
1211 we sum the volumes by means of integration:
1214 \begin_layout Standard
1215 \begin_inset Formula
1217 \int_{a}^{b}\,\pi f^{2}(x)\,dx
1225 \begin_layout Standard
1227 In the specific example, over the interval
1228 \begin_inset Formula $[0,4]$
1234 \begin_layout Standard
1235 \begin_inset Formula
1237 \int_{0}^{4}\,\pi x\,dx & = & \pi\int_{0}^{4}\,x\,dx\\
1238 & = & \pi\left.\left(\frac{x^{2}}{2}\right)\right|_{0}^{4}\\
1239 & = & \pi\left(\frac{4^{2}}{2}-0\right)\\
1248 \begin_layout Standard
1249 \begin_inset Flex NewThought
1252 \begin_layout Plain Layout
1258 a special hole down the length of the cup we just worked with.
1259 It is made with a quadratic shaped bit.
1260 \begin_inset Flex Sidenote
1263 \begin_layout Plain Layout
1264 I have no idea how I'd do this in real life, but I'm making a point.
1269 I find that the hole the bit makes can be modeled with the function
1270 \begin_inset Formula $g(x)=\frac{x^{2}}{16}$
1274 I would need to subtract the volume of the material removed from the volume
1276 \begin_inset Quotes eld
1280 \begin_inset Quotes erd
1284 Each individual cylinder would become like a
1285 \begin_inset Quotes eld
1289 \begin_inset Quotes erd
1293 To get the area of one washer, I would use the formula
1296 \begin_layout Standard
1297 \begin_inset Float marginfigure
1302 \begin_layout Plain Layout
1303 \begin_inset Box Boxed
1313 height_special "totalheight"
1318 backgroundcolor "none"
1321 \begin_layout Plain Layout
1322 Here I used RLPlot to draw the square root function and the quadratic function.
1323 Then I used Inkscape to shade the area between them.
1329 \begin_inset Caption Standard
1331 \begin_layout Plain Layout
1333 \begin_inset Formula $f(x)$
1337 \begin_inset Formula $g(x)$
1340 and the area left by
1341 \begin_inset Formula $f(x)-g(x)$
1357 \begin_layout Standard
1358 \begin_inset Formula
1360 A_{washer} & = & A_{cup}-A_{drill}\\
1361 & = & \pi f^{2}(x)-\pi g^{2}(x)\\
1362 & = & \pi\left(f^{2}(x)-g^{2}(x)\right)
1370 \begin_layout Standard
1371 The volume of each washer would be
1374 \begin_layout Standard
1375 \begin_inset Formula
1377 V_{washer} & = & A_{washer}\,dx\\
1378 & = & \pi\left(f^{2}(x)-g^{2}(x)\right)\,dx
1386 \begin_layout Standard
1388 Then, by summing the volumes of all the washers between points
1389 \begin_inset Formula $a$
1393 \begin_inset Formula $b$
1396 , the integral is derived:
1399 \begin_layout Standard
1400 \begin_inset Formula
1402 \int_{a}^{b}\,\pi\left(f^{2}(x)-g^{2}(x)\right)\,dx
1410 \begin_layout Standard
1411 In the case of our quadratic drill bit::
1412 \begin_inset Float marginfigure
1417 \begin_layout Plain Layout
1418 \begin_inset Box Boxed
1428 height_special "totalheight"
1433 backgroundcolor "none"
1436 \begin_layout Plain Layout
1437 This was the rotated set of 2 functions.
1443 \begin_inset Caption Standard
1445 \begin_layout Plain Layout
1446 The cup with a quadratic hole drilled down its length
1459 \begin_layout Standard
1460 \begin_inset Formula
1462 \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\\
1463 & = & \pi\left(\int_{0}^{4}\,x\,dx-\int_{0}^{4}\,\frac{x^{4}}{256}\,dx\right)\\
1464 & = & \pi\left(\left.\left(\frac{x^{2}}{2}\right)\right|_{0}^{4}-\left.\left(\frac{x^{5}}{1280}\right)\right|_{0}^{4}\right)\\
1465 & = & \pi\left(\left(\frac{4^{2}}{2}-0\right)-\left(\frac{4^{5}}{1280}-0\right)\right)\\
1466 & = & \pi\left(8-0.8\right)\\
1475 \begin_layout Standard
1479 \begin_layout Section
1483 \begin_layout Itemize
1484 p114: 1, 4, 5, 6, 8, 10, 12, 15
1487 \begin_layout Standard
1488 \begin_inset CommandInset bibtex
1490 bibfiles "biblioExample"