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
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 \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
65 \notefontcolor #0000ff
72 \paragraph_separation indent
73 \paragraph_indentation default
75 \math_numbering_side default
80 \paperpagestyle default
81 \tracking_changes false
90 \begin_layout Standard
91 \begin_inset Note Note
94 \begin_layout Plain Layout
99 : To be able to view your file as PDF you must have the \SpecialChar LaTeX
104 installed to your \SpecialChar LaTeX
106 If you are using MiK\SpecialChar TeX
107 , you will automatically be asked to install this package
108 when previewing your file, if you are using \SpecialChar TeX
109 Live, use \SpecialChar TeX
110 Live's package manager.
113 \begin_layout Plain Layout
118 : If you wish to compile to PDF with plain \SpecialChar LaTeX
119 (instead of pdf\SpecialChar TeX
120 ), there is currently
121 a bug in the Tufte class that causes errors.
122 You can add the class option 'nols' (put this in the
123 \begin_inset Quotes eld
127 \begin_inset Quotes erd
130 field of Document\SpecialChar menuseparator
131 Settings \SpecialChar menuseparator
132 Document Class) to get rid of the errors, but
133 this also removes letterspacing, an important part of the Tufte design.
147 \begin_inset Note Note
150 \begin_layout Plain Layout
151 author of this example file: Jason Waskiewicz
159 \begin_layout Standard
160 \begin_inset CommandInset toc
161 LatexCommand tableofcontents
168 \begin_layout Chapter
169 The Features of the Tufte-book Class
172 \begin_layout Standard
173 In this document, it was endeavored to show some of the features of the
179 In the first chapter, their use is outlined.
180 In the second chapter, their use through a handout that was created in
181 a calculus class is demonstrated.
184 \begin_layout Section
188 \begin_layout Standard
193 class is based on the work of
198 It provides the same functionality as the
202 class with book-specific additions.
203 Tufte's documents consist of a rather narrow column of text and a wide
204 column of margin notes and margin figures.
205 This is to improve readability.
208 \begin_layout Standard
209 The features provided by this format include:
212 \begin_layout Itemize
216 \begin_layout Itemize
217 Ordinary figures in text with captions in margins
220 \begin_layout Itemize
221 Full width figures and text when needed
224 \begin_layout Itemize
225 \begin_inset Quotes eld
229 \begin_inset Quotes erd
235 \begin_layout Itemize
236 Limited layers of sections and subsections
239 \begin_layout Standard
240 In this sample document, some of these features are demonstrated.
241 For a full demonstration, visit the tufte-latex website:
242 \begin_inset Flex URL
245 \begin_layout Plain Layout
247 https://tufte-latex.github.io/tufte-latex/
255 \begin_layout Section
259 \begin_layout Standard
261 \begin_inset Quotes eld
265 \begin_inset Quotes erd
268 rather than justified.
269 \begin_inset Flex Sidenote
272 \begin_layout Plain Layout
273 To get justified text, add the option
283 Document\SpecialChar menuseparator
284 Settings\SpecialChar menuseparator
292 Ragged right text is used in most of his works, but the class option
296 is provided to change this.
299 \begin_layout Standard
300 Tufte also formats his pages asymmetrically.
301 This means that the marginalia appear on the right side on each page, whether
303 If you prefer, you can change that and have symmetric layout, as common
304 in traditional book typography, by using the
309 \begin_inset Flex Sidenote
312 \begin_layout Plain Layout
313 To create a symmetric layout, add the option
323 Document\SpecialChar menuseparator
324 Settings\SpecialChar menuseparator
335 \begin_layout Standard
336 Finally, Tufte does not number his chapters or his sections.
337 If you like to refer to sections by number, move the
343 Document\SpecialChar menuseparator
344 Settings\SpecialChar menuseparator
347 to the very right (as done in this document).
348 \begin_inset Flex Marginnote
351 \begin_layout Plain Layout
360 \begin_layout Section
364 \begin_layout Standard
365 Tufte uses ordinary figure floats such as the following:
368 \begin_layout Standard
369 \begin_inset Float figure
374 \begin_layout Plain Layout
375 \begin_inset Box Boxed
385 height_special "totalheight"
390 backgroundcolor "none"
393 \begin_layout Plain Layout
394 Imagine your favorite figure inside this box instead of this boring text.
400 \begin_inset Caption Standard
402 \begin_layout Plain Layout
403 An ordinary figure float.
416 \begin_layout Standard
417 Furthermore, he uses margin figures, as shown in Fig.
422 \begin_inset CommandInset ref
424 reference "fig:margin-figure"
431 \begin_layout Standard
432 \begin_inset VSpace 5theight%
438 \begin_layout Standard
439 \begin_inset Float marginfigure
444 \begin_layout Plain Layout
445 \begin_inset Box Boxed
455 height_special "totalheight"
460 backgroundcolor "none"
463 \begin_layout Plain Layout
464 Imagine your favorite photograph of a squirrel inside this box instead of
471 \begin_inset Caption Standard
473 \begin_layout Plain Layout
475 \begin_inset CommandInset label
477 name "fig:margin-figure"
494 \begin_layout Standard
495 \begin_inset Note Greyedout
498 \begin_layout Plain Layout
503 If you are using margin figures or tables you must use the default float
504 placement option in the document settings under
520 \begin_layout Standard
521 In the same vein, the
525 class allows the use of tables, both in the margins and in the text.
526 The margin tables are recommended for a small set of data to illustrate
528 \begin_inset Quotes eld
531 Look, distance-time data is quadratic when the object is falling.
532 \begin_inset Quotes erd
535 More detailed data such as flame test results and comments should be put
536 in a full-width table instead.
539 \begin_layout Standard
544 provides a full-width figure.
545 This one takes up the entire width of the page, i.
546 \begin_inset space \thinspace{}
555 \begin_inset CommandInset ref
557 reference "fig:full-width-figure"
564 \begin_layout Standard
565 \begin_inset Float figure
570 \begin_layout Plain Layout
571 \begin_inset Box Boxed
581 height_special "totalheight"
586 backgroundcolor "none"
589 \begin_layout Plain Layout
590 Imagine your favorite photograph of a squirrel inside this box instead of
597 \begin_inset VSpace defskip
603 \begin_layout Plain Layout
604 \begin_inset Caption Standard
606 \begin_layout Plain Layout
608 \begin_inset CommandInset label
610 name "fig:full-width-figure"
627 \begin_layout Section
631 \begin_layout Standard
632 One of the most prominent and distinctive features of this style is the
633 extensive use of sidenotes.
634 There is a wide margin to provide ample room for sidenotes and small figures.
635 Any footnotes will automatically be converted to sidenotes.
639 \begin_layout Plain Layout
640 This is a sidenote that was entered using a
649 Alternatively, you can also use the
653 inset directly; you'll find it in the
655 Insert\SpecialChar menuseparator
659 \begin_inset Flex Sidenote
662 \begin_layout Plain Layout
663 This is a sidenote that was entered using a
675 \begin_layout Standard
676 If you like to place ancillary information in the margin without the sidenote
677 mark (the superscript number), you can use the
683 \begin_inset Flex Marginnote
686 \begin_layout Plain Layout
687 This is Tufte's margin note.
688 Notice that there isn't a number preceding the note, and there is no number
689 in the main text where this note was written.
694 The normal margin note will work as well, but it will look rather odd.
695 \begin_inset Marginal
698 \begin_layout Plain Layout
699 This is a normal margin note.
708 \begin_layout Standard
709 \begin_inset Flex NewThought
712 \begin_layout Plain Layout
718 innovation is Tufte's
724 Edit\SpecialChar menuseparator
725 TextStyle\SpecialChar menuseparator
729 It introduces new thoughts by means of small caps, as demonstrated in this
734 \begin_layout Standard
735 The Tufte document classes include two new character styles and some improvement
736 s on existing commands for letterspacing.
739 \begin_layout Standard
740 When setting strings of
741 \begin_inset Flex AllCaps
744 \begin_layout Plain Layout
751 \begin_inset Flex SmallCaps
754 \begin_layout Plain Layout
760 , the letterspacing—that is, the spacing between the letters—should be increased
762 \begin_inset CommandInset citation
775 Edit\SpecialChar menuseparator
776 TextStyle\SpecialChar menuseparator
779 ) has proper letterspacing for strings of
780 \begin_inset Flex AllCaps
783 \begin_layout Plain Layout
795 Edit\SpecialChar menuseparator
796 TextStyle\SpecialChar menuseparator
799 ) has letterspacing for
800 \begin_inset Flex SmallCaps
803 \begin_layout Plain Layout
804 small capital letters
810 These commands will also automatically convert the case of the text to
811 upper- or lowercase, respectively.
814 \begin_layout Standard
819 shape has also been redefined to include letterspacing.
820 Its case is left as is, however.
821 This allows one to use both uppercase and lowercase letters:
823 The Initial Letters Of The Words In This Sentence Are Capitalized.
826 \begin_layout Standard
831 paragraph environment provides a paragraph layout that stretches across
832 the main text block and the sidenotes area:
835 \begin_layout Full Width
836 Lorem ipsum dolor sit amet, consectetuer adipiscing elit.
837 Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae, felis.
838 Curabitur dictum gravida mauris.
839 Nam arcu libero, nonummy eget, consectetuer id, vulputate a, magna.
840 Donec vehicula augue eu neque.
841 Pellentesque habitant morbi tristique senectus et netus et malesuada fames
844 Cras viverra metus rhoncus sem.
845 Nulla et lectus vestibulum urna fringilla ultrices.
846 Phasellus eu tellus sit amet tortor gravida placerat.
847 Integer sapien est, iaculis in, pretium quis, viverra ac, nunc.
848 Praesent eget sem vel leo ultrices bibendum.
850 Morbi dolor nulla, malesuada eu, pulvinar at, mollis ac, nulla.
851 Curabitur auctor semper nulla.
852 Donec varius orci eget risus.
853 Duis nibh mi, congue eu, accumsan eleifend, sagittis quis, diam.
854 Duis eget orci sit amet orci dignissim rutrum.
857 \begin_layout Section
861 \begin_layout Standard
862 References are placed alongside their citations as sidenotes, as well.
863 This can be accomplished using the normal citation command.
867 \begin_layout Plain Layout
868 The previous section includes a citation.
876 \begin_layout Standard
877 The complete list of references may also be printed automatically by using
880 Insert\SpecialChar menuseparator
881 Lists/TOC\SpecialChar menuseparator
889 (see the end of this document for an example.) If you do not want to print
890 a bibliography at the end of your document, place the
899 inset inside a \SpecialChar LyX
900 note and use the \SpecialChar LaTeX
910 \begin_layout Chapter
911 Calculation of Volume: Sections 2.12–2.13
914 \begin_layout Standard
915 Imagine taking a function like
916 \begin_inset Formula $y=\sqrt{x}$
919 and rotating it in 3 dimensions around the x-axis.
920 The resulting shape would look somewhat like a cup (on its side).
921 Interestingly, integration empowers us to do exactly this and to find out
922 how much water that cup could hold.
925 \begin_layout Section
929 \begin_layout Standard
930 \begin_inset Float marginfigure
935 \begin_layout Plain Layout
936 \begin_inset Box Boxed
946 height_special "totalheight"
951 backgroundcolor "none"
954 \begin_layout Plain Layout
955 I had a graph of the square root function here.
961 \begin_inset Caption Standard
963 \begin_layout Plain Layout
964 \begin_inset CommandInset label
966 name "mar:A-graph-of"
971 \begin_inset Formula $f(x)=\sqrt{x}$
987 \begin_layout Standard
988 \begin_inset Float marginfigure
993 \begin_layout Plain Layout
994 \begin_inset Box Boxed
1004 height_special "totalheight"
1009 backgroundcolor "none"
1012 \begin_layout Plain Layout
1013 Here I rotated the square root function and then drew a disk on the figure
1014 to illustrate how I would calculate the volume of the figure.
1020 \begin_inset Caption Standard
1022 \begin_layout Plain Layout
1023 \begin_inset CommandInset label
1030 \begin_inset Formula $f(x)=\sqrt{x}$
1033 rotated about the x-axis and with additional remarks for integration.
1046 \begin_layout Standard
1048 \begin_inset CommandInset ref
1050 reference "mar:A-graph-of"
1054 shows the plot of the function
1055 \begin_inset Formula $f(x)=\sqrt{x}.$
1058 Now, imagine that we rotate that function about the x-axis.
1059 The resulting figure would be somewhat like figure
1060 \begin_inset CommandInset ref
1062 reference "mar:rotated"
1067 This is akin to a cup lying on its side.
1068 For the sake of clarity, the artist (me) drew a circle on the end of the
1069 figure to show that it is indeed rotated.
1072 \begin_layout Standard
1073 Now, suppose we wished to find the volume of the figure.
1074 When we integrated the original square root function to find its area,
1075 we imagined a series of rectangles inside the figure.
1077 \begin_inset Formula $h=f(x)$
1081 \begin_inset Formula $dx$
1085 Since height multiplied by width was the area of each rectangle, we summed
1086 these areas and rewrote this as
1087 \begin_inset Formula $\int\,f(x)\,dx$
1090 , or, in this specific case,
1091 \begin_inset Formula $\int\,\sqrt{x}\,dx$
1097 \begin_layout Standard
1098 To find the volume of our rotated figure the prodecure is quite similar.
1099 Begin by rotating each rectangle about the x-axis.
1100 This creates a series of cylinders.
1101 \begin_inset Flex Sidenote
1104 \begin_layout Plain Layout
1105 The text refers to these cylinders as "disks".
1106 This is standard practice in all the Calculus books I checked.
1111 Then, we can find the volume of each cylinder/disk.
1112 The basic formula is:
1115 \begin_layout Standard
1116 \begin_inset Formula
1126 \begin_layout Standard
1129 \begin_inset Formula $h$
1132 is the height of the cylinder (width of the rectangle)
1133 \begin_inset Formula $dx$
1137 The area of each figure is a circle where
1138 \begin_inset Formula $A=\pi r^{2}$
1142 The radius in this case is the function
1143 \begin_inset Formula $f(x)$
1150 \begin_layout Standard
1151 \begin_inset Formula
1161 \begin_layout Standard
1163 In our specific case,
1166 \begin_layout Standard
1167 \begin_inset Formula
1169 A & = & \pi\left(\sqrt{x}\right)^{2}\\
1178 \begin_layout Standard
1179 To calculate the volume of one disk, we have
1182 \begin_layout Standard
1183 \begin_inset Formula
1193 \begin_layout Standard
1195 or, in the general case
1198 \begin_layout Standard
1199 \begin_inset Formula
1209 \begin_layout Standard
1210 To find the volume of the figure between points
1211 \begin_inset Formula $a$
1215 \begin_inset Formula $b$
1218 we sum the volumes by means of integration:
1221 \begin_layout Standard
1222 \begin_inset Formula
1224 \int_{a}^{b}\,\pi f^{2}(x)\,dx
1232 \begin_layout Standard
1234 In the specific example, over the interval
1235 \begin_inset Formula $[0,4]$
1241 \begin_layout Standard
1242 \begin_inset Formula
1244 \int_{0}^{4}\,\pi x\,dx & = & \pi\int_{0}^{4}\,x\,dx\\
1245 & = & \pi\left.\left(\frac{x^{2}}{2}\right)\right|_{0}^{4}\\
1246 & = & \pi\left(\frac{4^{2}}{2}-0\right)\\
1255 \begin_layout Standard
1256 \begin_inset Flex NewThought
1259 \begin_layout Plain Layout
1265 a special hole down the length of the cup we just worked with.
1266 It is made with a quadratic shaped bit.
1267 \begin_inset Flex Sidenote
1270 \begin_layout Plain Layout
1271 I have no idea how I'd do this in real life, but I'm making a point.
1276 I find that the hole the bit makes can be modeled with the function
1277 \begin_inset Formula $g(x)=\frac{x^{2}}{16}$
1281 I would need to subtract the volume of the material removed from the volume
1283 \begin_inset Quotes eld
1287 \begin_inset Quotes erd
1291 Each individual cylinder would become like a
1292 \begin_inset Quotes eld
1296 \begin_inset Quotes erd
1300 To get the area of one washer, I would use the formula
1303 \begin_layout Standard
1304 \begin_inset Float marginfigure
1309 \begin_layout Plain Layout
1310 \begin_inset Box Boxed
1320 height_special "totalheight"
1325 backgroundcolor "none"
1328 \begin_layout Plain Layout
1329 Here I used RLPlot to draw the square root function and the quadratic function.
1330 Then I used Inkscape to shade the area between them.
1336 \begin_inset Caption Standard
1338 \begin_layout Plain Layout
1340 \begin_inset Formula $f(x)$
1344 \begin_inset Formula $g(x)$
1347 and the area left by
1348 \begin_inset Formula $f(x)-g(x)$
1364 \begin_layout Standard
1365 \begin_inset Formula
1367 A_{washer} & = & A_{cup}-A_{drill}\\
1368 & = & \pi f^{2}(x)-\pi g^{2}(x)\\
1369 & = & \pi\left(f^{2}(x)-g^{2}(x)\right)
1377 \begin_layout Standard
1378 The volume of each washer would be
1381 \begin_layout Standard
1382 \begin_inset Formula
1384 V_{washer} & = & A_{washer}\,dx\\
1385 & = & \pi\left(f^{2}(x)-g^{2}(x)\right)\,dx
1393 \begin_layout Standard
1395 Then, by summing the volumes of all the washers between points
1396 \begin_inset Formula $a$
1400 \begin_inset Formula $b$
1403 , the integral is derived:
1406 \begin_layout Standard
1407 \begin_inset Formula
1409 \int_{a}^{b}\,\pi\left(f^{2}(x)-g^{2}(x)\right)\,dx
1417 \begin_layout Standard
1418 In the case of our quadratic drill bit::
1419 \begin_inset Float marginfigure
1424 \begin_layout Plain Layout
1425 \begin_inset Box Boxed
1435 height_special "totalheight"
1440 backgroundcolor "none"
1443 \begin_layout Plain Layout
1444 This was the rotated set of 2 functions.
1450 \begin_inset Caption Standard
1452 \begin_layout Plain Layout
1453 The cup with a quadratic hole drilled down its length
1466 \begin_layout Standard
1467 \begin_inset Formula
1469 \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\\
1470 & = & \pi\left(\int_{0}^{4}\,x\,dx-\int_{0}^{4}\,\frac{x^{4}}{256}\,dx\right)\\
1471 & = & \pi\left(\left.\left(\frac{x^{2}}{2}\right)\right|_{0}^{4}-\left.\left(\frac{x^{5}}{1280}\right)\right|_{0}^{4}\right)\\
1472 & = & \pi\left(\left(\frac{4^{2}}{2}-0\right)-\left(\frac{4^{5}}{1280}-0\right)\right)\\
1473 & = & \pi\left(8-0.8\right)\\
1482 \begin_layout Standard
1486 \begin_layout Section
1490 \begin_layout Itemize
1491 p114: 1, 4, 5, 6, 8, 10, 12, 15
1494 \begin_layout Standard
1495 \begin_inset CommandInset bibtex
1497 bibfiles "biblioExample"