1 #LyX 2.4 created this file. For more info see https://www.lyx.org/
5 \save_transient_properties true
6 \origin /systemlyxdir/examples/Books/
8 \use_default_options true
9 \maintain_unincluded_children no
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
23 \font_typewriter_osf false
24 \font_sf_scale 100 100
25 \font_tt_scale 100 100
27 \use_dash_ligatures false
29 \default_output_format pdf2
31 \bibtex_command bibtex
32 \index_command default
33 \float_placement class
34 \float_alignment class
35 \paperfontsize default
39 \pdf_bookmarksnumbered false
40 \pdf_bookmarksopen true
41 \pdf_bookmarksopenlevel 1
49 \use_package amsmath 1
50 \use_package amssymb 1
53 \use_package mathdots 1
54 \use_package mathtools 1
56 \use_package stackrel 1
57 \use_package stmaryrd 1
58 \use_package undertilde 1
60 \cite_engine_type authoryear
64 \paperorientation portrait
70 \notefontcolor #0000ff
77 \paragraph_separation indent
78 \paragraph_indentation default
80 \math_numbering_side default
85 \paperpagestyle default
87 \tracking_changes false
90 \postpone_fragile_content false
94 \docbook_table_output 0
95 \docbook_mathml_prefix 1
100 \begin_layout Standard
101 \begin_inset Note Note
104 \begin_layout Plain Layout
110 To be able to view your file as PDF you must have the \SpecialChar LaTeX
115 installed to your \SpecialChar LaTeX
117 If you are using MiK\SpecialChar TeX
119 you will automatically be asked to install this package when previewing your file,
120 if you are using \SpecialChar TeX
123 Live's package manager.
126 \begin_layout Plain Layout
132 If you wish to compile to PDF with plain \SpecialChar LaTeX
133 (instead of pdf\SpecialChar TeX
135 there is currently a bug in the Tufte class that causes errors.
136 You can add the class option 'nols' (put this in the
137 \begin_inset Quotes eld
141 \begin_inset Quotes erd
144 field of Document\SpecialChar menuseparator
145 Settings \SpecialChar menuseparator
146 Document Class) to get rid of the errors,
147 but this also removes letterspacing,
148 an important part of the Tufte design.
162 \begin_inset Note Note
165 \begin_layout Plain Layout
166 author of this example file:
175 \begin_layout Standard
176 \begin_inset CommandInset toc
177 LatexCommand tableofcontents
184 \begin_layout Chapter
185 The Features of the Tufte-book Class
188 \begin_layout Standard
190 it was endeavored to show some of the features of the
195 In the first chapter,
196 their use is outlined.
197 In the second chapter,
198 their use through a handout that was created in a calculus class is demonstrated.
201 \begin_layout Section
205 \begin_layout Standard
210 class is based on the work of
215 It provides the same functionality as the
219 class with book-specific additions.
220 Tufte's documents consist of a rather narrow column of text and a wide column of margin notes and margin figures.
221 This is to improve readability.
224 \begin_layout Standard
225 The features provided by this format include:
228 \begin_layout Itemize
232 \begin_layout Itemize
233 Ordinary figures in text with captions in margins
236 \begin_layout Itemize
237 Full width figures and text when needed
240 \begin_layout Itemize
241 \begin_inset Quotes eld
245 \begin_inset Quotes erd
251 \begin_layout Itemize
252 Limited layers of sections and subsections
255 \begin_layout Standard
256 In this sample document,
257 some of these features are demonstrated.
258 For a full demonstration,
259 visit the tufte-latex website:
261 \begin_inset Flex URL
264 \begin_layout Plain Layout
266 https://tufte-latex.github.io/tufte-latex/
274 \begin_layout Section
278 \begin_layout Standard
280 \begin_inset Quotes eld
284 \begin_inset Quotes erd
287 rather than justified.
288 \begin_inset Flex Sidenote
291 \begin_layout Plain Layout
292 To get justified text,
303 Document\SpecialChar menuseparator
304 Settings\SpecialChar menuseparator
312 Ragged right text is used in most of his works,
317 is provided to change this.
320 \begin_layout Standard
321 Tufte also formats his pages asymmetrically.
322 This means that the marginalia appear on the right side on each page,
325 you can change that and have symmetric layout,
326 as common in traditional book typography,
332 \begin_inset Flex Sidenote
335 \begin_layout Plain Layout
336 To create a symmetric layout,
347 Document\SpecialChar menuseparator
348 Settings\SpecialChar menuseparator
359 \begin_layout Standard
361 Tufte does not number his chapters or his sections.
362 If you like to refer to sections by number,
369 Document\SpecialChar menuseparator
370 Settings\SpecialChar menuseparator
373 to the very right (as done in this document).
374 \begin_inset Flex Marginnote
377 \begin_layout Plain Layout
386 \begin_layout Section
390 \begin_layout Standard
391 Tufte uses ordinary figure floats such as the following:
394 \begin_layout Standard
395 \begin_inset Float figure
402 \begin_layout Plain Layout
403 \begin_inset Box Boxed
413 height_special "totalheight"
418 backgroundcolor "none"
421 \begin_layout Plain Layout
422 Imagine your favorite figure inside this box instead of this boring text.
428 \begin_inset Caption Standard
430 \begin_layout Plain Layout
431 An ordinary figure float.
444 \begin_layout Standard
446 he uses margin figures,
452 \begin_inset CommandInset ref
454 reference "fig:margin-figure"
462 \begin_layout Standard
463 \begin_inset VSpace 5theight%
469 \begin_layout Standard
470 \begin_inset Float marginfigure
477 \begin_layout Plain Layout
478 \begin_inset Box Boxed
488 height_special "totalheight"
493 backgroundcolor "none"
496 \begin_layout Plain Layout
497 Imagine your favorite photograph of a squirrel inside this box instead of this boring text.
503 \begin_inset Caption Standard
505 \begin_layout Plain Layout
507 \begin_inset CommandInset label
509 name "fig:margin-figure"
526 \begin_layout Standard
527 \begin_inset Note Greyedout
530 \begin_layout Plain Layout
536 If you are using margin figures or tables you must use the default float placement option in the document settings under
552 \begin_layout Standard
558 class allows the use of tables,
559 both in the margins and in the text.
560 The margin tables are recommended for a small set of data to illustrate a concept such as
561 \begin_inset Quotes eld
565 distance-time data is quadratic when the object is falling.
566 \begin_inset Quotes erd
569 More detailed data such as flame test results and comments should be put in a full-width table instead.
572 \begin_layout Standard
578 provides a full-width figure.
579 This one takes up the entire width of the page,
581 \begin_inset space \thinspace{}
591 \begin_inset CommandInset ref
593 reference "fig:full-width-figure"
601 \begin_layout Standard
602 \begin_inset Float figure
609 \begin_layout Plain Layout
610 \begin_inset Box Boxed
620 height_special "totalheight"
625 backgroundcolor "none"
628 \begin_layout Plain Layout
629 Imagine your favorite photograph of a squirrel inside this box instead of this boring text.
635 \begin_inset VSpace defskip
641 \begin_layout Plain Layout
642 \begin_inset Caption Standard
644 \begin_layout Plain Layout
646 \begin_inset CommandInset label
648 name "fig:full-width-figure"
665 \begin_layout Section
669 \begin_layout Standard
670 One of the most prominent and distinctive features of this style is the extensive use of sidenotes.
671 There is a wide margin to provide ample room for sidenotes and small figures.
672 Any footnotes will automatically be converted to sidenotes.
676 \begin_layout Plain Layout
677 This is a sidenote that was entered using a
692 you'll find it in the
694 Insert\SpecialChar menuseparator
698 \begin_inset Flex Sidenote
701 \begin_layout Plain Layout
702 This is a sidenote that was entered using a
714 \begin_layout Standard
715 If you like to place ancillary information in the margin without the sidenote mark (the superscript number),
722 \begin_inset Flex Marginnote
725 \begin_layout Plain Layout
726 This is Tufte's margin note.
727 Notice that there isn't a number preceding the note,
728 and there is no number in the main text where this note was written.
733 The normal margin note will work as well,
734 but it will look rather odd.
735 \begin_inset Marginal
738 \begin_layout Plain Layout
739 This is a normal margin note.
748 \begin_layout Standard
749 \begin_inset Flex NewThought
752 \begin_layout Plain Layout
758 innovation is Tufte's
764 Edit\SpecialChar menuseparator
765 TextStyle\SpecialChar menuseparator
769 It introduces new thoughts by means of small caps,
770 as demonstrated in this paragraph.
774 \begin_layout Standard
775 The Tufte document classes include two new character styles and some improvements on existing commands for letterspacing.
778 \begin_layout Standard
779 When setting strings of
780 \begin_inset Flex AllCaps
783 \begin_layout Plain Layout
790 \begin_inset Flex SmallCaps
793 \begin_layout Plain Layout
802 the spacing between the letters—
803 should be increased slightly.
804 \begin_inset CommandInset citation
817 Edit\SpecialChar menuseparator
818 TextStyle\SpecialChar menuseparator
821 ) has proper letterspacing for strings of
822 \begin_inset Flex AllCaps
825 \begin_layout Plain Layout
838 Edit\SpecialChar menuseparator
839 TextStyle\SpecialChar menuseparator
842 ) has letterspacing for
843 \begin_inset Flex SmallCaps
846 \begin_layout Plain Layout
847 small capital letters
853 These commands will also automatically convert the case of the text to upper- or lowercase,
857 \begin_layout Standard
862 shape has also been redefined to include letterspacing.
863 Its case is left as is,
865 This allows one to use both uppercase and lowercase letters:
868 The Initial Letters Of The Words In This Sentence Are Capitalized.
871 \begin_layout Standard
877 paragraph environment provides a paragraph layout that stretches across the main text block and the sidenotes area:
880 \begin_layout Full Width
881 Lorem ipsum dolor sit amet,
882 consectetuer adipiscing elit.
888 Curabitur dictum gravida mauris.
894 Donec vehicula augue eu neque.
895 Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas.
897 Cras viverra metus rhoncus sem.
898 Nulla et lectus vestibulum urna fringilla ultrices.
899 Phasellus eu tellus sit amet tortor gravida placerat.
905 Praesent eget sem vel leo ultrices bibendum.
912 Curabitur auctor semper nulla.
913 Donec varius orci eget risus.
919 Duis eget orci sit amet orci dignissim rutrum.
922 \begin_layout Section
926 \begin_layout Standard
927 References are placed alongside their citations as sidenotes,
929 This can be accomplished using the normal citation command.
933 \begin_layout Plain Layout
934 The previous section includes a citation.
942 \begin_layout Standard
943 The complete list of references may also be printed automatically by using
945 Insert\SpecialChar menuseparator
946 Lists/TOC\SpecialChar menuseparator
954 (see the end of this document for an example.) If you do not want to print a bibliography at the end of your document,
964 inset inside a \SpecialChar LyX
965 note and use the \SpecialChar LaTeX
975 \begin_layout Chapter
976 Calculation of Volume:
980 \begin_layout Standard
981 Imagine taking a function like
982 \begin_inset Formula $y=\sqrt{x}$
985 and rotating it in 3 dimensions around the x-axis.
986 The resulting shape would look somewhat like a cup (on its side).
988 integration empowers us to do exactly this and to find out how much water that cup could hold.
991 \begin_layout Section
995 \begin_layout Standard
996 \begin_inset Float marginfigure
1003 \begin_layout Plain Layout
1004 \begin_inset Box Boxed
1014 height_special "totalheight"
1019 backgroundcolor "none"
1022 \begin_layout Plain Layout
1023 I had a graph of the square root function here.
1029 \begin_inset Caption Standard
1031 \begin_layout Plain Layout
1032 \begin_inset CommandInset label
1034 name "mar:A-graph-of"
1039 \begin_inset Formula $f(x)=\sqrt{x}$
1055 \begin_layout Standard
1056 \begin_inset Float marginfigure
1063 \begin_layout Plain Layout
1064 \begin_inset Box Boxed
1074 height_special "totalheight"
1079 backgroundcolor "none"
1082 \begin_layout Plain Layout
1083 Here I rotated the square root function and then drew a disk on the figure to illustrate how I would calculate the volume of the figure.
1089 \begin_inset Caption Standard
1091 \begin_layout Plain Layout
1092 \begin_inset CommandInset label
1099 \begin_inset Formula $f(x)=\sqrt{x}$
1102 rotated about the x-axis and with additional remarks for integration.
1115 \begin_layout Standard
1117 \begin_inset CommandInset ref
1119 reference "mar:A-graph-of"
1124 shows the plot of the function
1125 \begin_inset Formula $f(x)=\sqrt{x}.$
1129 imagine that we rotate that function about the x-axis.
1130 The resulting figure would be somewhat like figure
1131 \begin_inset CommandInset ref
1133 reference "mar:rotated"
1139 This is akin to a cup lying on its side.
1140 For the sake of clarity,
1141 the artist (me) drew a circle on the end of the figure to show that it is indeed rotated.
1144 \begin_layout Standard
1146 suppose we wished to find the volume of the figure.
1147 When we integrated the original square root function to find its area,
1148 we imagined a series of rectangles inside the figure.
1150 \begin_inset Formula $h=f(x)$
1154 \begin_inset Formula $dx$
1158 Since height multiplied by width was the area of each rectangle,
1159 we summed these areas and rewrote this as
1160 \begin_inset Formula $\int\,f(x)\,dx$
1165 in this specific case,
1167 \begin_inset Formula $\int\,\sqrt{x}\,dx$
1173 \begin_layout Standard
1174 To find the volume of our rotated figure the prodecure is quite similar.
1175 Begin by rotating each rectangle about the x-axis.
1176 This creates a series of cylinders.
1177 \begin_inset Flex Sidenote
1180 \begin_layout Plain Layout
1181 The text refers to these cylinders as "disks".
1182 This is standard practice in all the Calculus books I checked.
1188 we can find the volume of each cylinder/disk.
1189 The basic formula is:
1192 \begin_layout Standard
1193 \begin_inset Formula
1203 \begin_layout Standard
1206 \begin_inset Formula $h$
1209 is the height of the cylinder (width of the rectangle)
1210 \begin_inset Formula $dx$
1214 The area of each figure is a circle where
1215 \begin_inset Formula $A=\pi r^{2}$
1219 The radius in this case is the function
1220 \begin_inset Formula $f(x)$
1227 \begin_layout Standard
1228 \begin_inset Formula
1238 \begin_layout Standard
1240 In our specific case,
1244 \begin_layout Standard
1245 \begin_inset Formula
1247 A & = & \pi\left(\sqrt{x}\right)^{2}\\
1256 \begin_layout Standard
1257 To calculate the volume of one disk,
1261 \begin_layout Standard
1262 \begin_inset Formula
1272 \begin_layout Standard
1278 \begin_layout Standard
1279 \begin_inset Formula
1289 \begin_layout Standard
1290 To find the volume of the figure between points
1291 \begin_inset Formula $a$
1295 \begin_inset Formula $b$
1298 we sum the volumes by means of integration:
1301 \begin_layout Standard
1302 \begin_inset Formula
1304 \int_{a}^{b}\,\pi f^{2}(x)\,dx
1312 \begin_layout Standard
1314 In the specific example,
1316 \begin_inset Formula $[0,4]$
1322 \begin_layout Standard
1323 \begin_inset Formula
1325 \int_{0}^{4}\,\pi x\,dx & = & \pi\int_{0}^{4}\,x\,dx\\
1326 & = & \pi\left.\left(\frac{x^{2}}{2}\right)\right|_{0}^{4}\\
1327 & = & \pi\left(\frac{4^{2}}{2}-0\right)\\
1336 \begin_layout Standard
1337 \begin_inset Flex NewThought
1340 \begin_layout Plain Layout
1346 a special hole down the length of the cup we just worked with.
1347 It is made with a quadratic shaped bit.
1348 \begin_inset Flex Sidenote
1351 \begin_layout Plain Layout
1352 I have no idea how I'd do this in real life,
1353 but I'm making a point.
1358 I find that the hole the bit makes can be modeled with the function
1359 \begin_inset Formula $g(x)=\frac{x^{2}}{16}$
1363 I would need to subtract the volume of the material removed from the volume of the entire
1364 \begin_inset Quotes eld
1368 \begin_inset Quotes erd
1372 Each individual cylinder would become like a
1373 \begin_inset Quotes eld
1377 \begin_inset Quotes erd
1381 To get the area of one washer,
1382 I would use the formula
1385 \begin_layout Standard
1386 \begin_inset Float marginfigure
1393 \begin_layout Plain Layout
1394 \begin_inset Box Boxed
1404 height_special "totalheight"
1409 backgroundcolor "none"
1412 \begin_layout Plain Layout
1413 Here I used RLPlot to draw the square root function and the quadratic function.
1414 Then I used Inkscape to shade the area between them.
1420 \begin_inset Caption Standard
1422 \begin_layout Plain Layout
1424 \begin_inset Formula $f(x)$
1428 \begin_inset Formula $g(x)$
1431 and the area left by
1432 \begin_inset Formula $f(x)-g(x)$
1448 \begin_layout Standard
1449 \begin_inset Formula
1451 A_{washer} & = & A_{cup}-A_{drill}\\
1452 & = & \pi f^{2}(x)-\pi g^{2}(x)\\
1453 & = & \pi\left(f^{2}(x)-g^{2}(x)\right)
1461 \begin_layout Standard
1462 The volume of each washer would be
1465 \begin_layout Standard
1466 \begin_inset Formula
1468 V_{washer} & = & A_{washer}\,dx\\
1469 & = & \pi\left(f^{2}(x)-g^{2}(x)\right)\,dx
1477 \begin_layout Standard
1480 by summing the volumes of all the washers between points
1481 \begin_inset Formula $a$
1485 \begin_inset Formula $b$
1489 the integral is derived:
1492 \begin_layout Standard
1493 \begin_inset Formula
1495 \int_{a}^{b}\,\pi\left(f^{2}(x)-g^{2}(x)\right)\,dx
1503 \begin_layout Standard
1504 In the case of our quadratic drill bit::
1505 \begin_inset Float marginfigure
1512 \begin_layout Plain Layout
1513 \begin_inset Box Boxed
1523 height_special "totalheight"
1528 backgroundcolor "none"
1531 \begin_layout Plain Layout
1532 This was the rotated set of 2 functions.
1538 \begin_inset Caption Standard
1540 \begin_layout Plain Layout
1541 The cup with a quadratic hole drilled down its length
1554 \begin_layout Standard
1555 \begin_inset Formula
1557 \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\\
1558 & = & \pi\left(\int_{0}^{4}\,x\,dx-\int_{0}^{4}\,\frac{x^{4}}{256}\,dx\right)\\
1559 & = & \pi\left(\left.\left(\frac{x^{2}}{2}\right)\right|_{0}^{4}-\left.\left(\frac{x^{5}}{1280}\right)\right|_{0}^{4}\right)\\
1560 & = & \pi\left(\left(\frac{4^{2}}{2}-0\right)-\left(\frac{4^{5}}{1280}-0\right)\right)\\
1561 & = & \pi\left(8-0.8\right)\\
1570 \begin_layout Standard
1574 \begin_layout Section
1578 \begin_layout Itemize
1590 \begin_layout Standard
1591 \begin_inset CommandInset bibtex
1593 bibfiles "../biblioExample"