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 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 \float_placement class
32 \float_alignment class
33 \paperfontsize default
37 \pdf_bookmarksnumbered false
38 \pdf_bookmarksopen true
39 \pdf_bookmarksopenlevel 1
47 \use_package amsmath 1
48 \use_package amssymb 1
51 \use_package mathdots 1
52 \use_package mathtools 1
54 \use_package stackrel 1
55 \use_package stmaryrd 1
56 \use_package undertilde 1
58 \cite_engine_type authoryear
62 \paperorientation portrait
67 \notefontcolor #0000ff
74 \paragraph_separation indent
75 \paragraph_indentation default
77 \math_numbering_side default
82 \paperpagestyle default
83 \tracking_changes false
92 \begin_layout Standard
93 \begin_inset Note Note
96 \begin_layout Plain Layout
101 : To be able to view your file as PDF you must have the \SpecialChar LaTeX
106 installed to your \SpecialChar LaTeX
108 If you are using MiK\SpecialChar TeX
109 , you will automatically be asked to install this package
110 when previewing your file, if you are using \SpecialChar TeX
111 Live, use \SpecialChar TeX
112 Live's package manager.
115 \begin_layout Plain Layout
120 : If you wish to compile to PDF with plain \SpecialChar LaTeX
121 (instead of pdf\SpecialChar TeX
122 ), there is currently
123 a bug in the Tufte class that causes errors.
124 You can add the class option 'nols' (put this in the
125 \begin_inset Quotes eld
129 \begin_inset Quotes erd
132 field of Document\SpecialChar menuseparator
133 Settings \SpecialChar menuseparator
134 Document Class) to get rid of the errors, but
135 this also removes letterspacing, an important part of the Tufte design.
149 \begin_inset Note Note
152 \begin_layout Plain Layout
153 author of this example file: Jason Waskiewicz
161 \begin_layout Standard
162 \begin_inset CommandInset toc
163 LatexCommand tableofcontents
170 \begin_layout Chapter
171 The Features of the Tufte-book Class
174 \begin_layout Standard
175 In this document, it was endeavored to show some of the features of the
181 In the first chapter, their use is outlined.
182 In the second chapter, their use through a handout that was created in
183 a calculus class is demonstrated.
186 \begin_layout Section
190 \begin_layout Standard
195 class is based on the work of
200 It provides the same functionality as the
204 class with book-specific additions.
205 Tufte's documents consist of a rather narrow column of text and a wide
206 column of margin notes and margin figures.
207 This is to improve readability.
210 \begin_layout Standard
211 The features provided by this format include:
214 \begin_layout Itemize
218 \begin_layout Itemize
219 Ordinary figures in text with captions in margins
222 \begin_layout Itemize
223 Full width figures and text when needed
226 \begin_layout Itemize
227 \begin_inset Quotes eld
231 \begin_inset Quotes erd
237 \begin_layout Itemize
238 Limited layers of sections and subsections
241 \begin_layout Standard
242 In this sample document, some of these features are demonstrated.
243 For a full demonstration, visit the tufte-latex website:
244 \begin_inset Flex URL
247 \begin_layout Plain Layout
249 https://tufte-latex.github.io/tufte-latex/
257 \begin_layout Section
261 \begin_layout Standard
263 \begin_inset Quotes eld
267 \begin_inset Quotes erd
270 rather than justified.
271 \begin_inset Flex Sidenote
274 \begin_layout Plain Layout
275 To get justified text, add the option
285 Document\SpecialChar menuseparator
286 Settings\SpecialChar menuseparator
294 Ragged right text is used in most of his works, but the class option
298 is provided to change this.
301 \begin_layout Standard
302 Tufte also formats his pages asymmetrically.
303 This means that the marginalia appear on the right side on each page, whether
305 If you prefer, you can change that and have symmetric layout, as common
306 in traditional book typography, by using the
311 \begin_inset Flex Sidenote
314 \begin_layout Plain Layout
315 To create a symmetric layout, add the option
325 Document\SpecialChar menuseparator
326 Settings\SpecialChar menuseparator
337 \begin_layout Standard
338 Finally, Tufte does not number his chapters or his sections.
339 If you like to refer to sections by number, move the
345 Document\SpecialChar menuseparator
346 Settings\SpecialChar menuseparator
349 to the very right (as done in this document).
350 \begin_inset Flex Marginnote
353 \begin_layout Plain Layout
362 \begin_layout Section
366 \begin_layout Standard
367 Tufte uses ordinary figure floats such as the following:
370 \begin_layout Standard
371 \begin_inset Float figure
378 \begin_layout Plain Layout
379 \begin_inset Box Boxed
389 height_special "totalheight"
394 backgroundcolor "none"
397 \begin_layout Plain Layout
398 Imagine your favorite figure inside this box instead of this boring text.
404 \begin_inset Caption Standard
406 \begin_layout Plain Layout
407 An ordinary figure float.
420 \begin_layout Standard
421 Furthermore, he uses margin figures, as shown in Fig.
426 \begin_inset CommandInset ref
428 reference "fig:margin-figure"
435 \begin_layout Standard
436 \begin_inset VSpace 5theight%
442 \begin_layout Standard
443 \begin_inset Float marginfigure
450 \begin_layout Plain Layout
451 \begin_inset Box Boxed
461 height_special "totalheight"
466 backgroundcolor "none"
469 \begin_layout Plain Layout
470 Imagine your favorite photograph of a squirrel inside this box instead of
477 \begin_inset Caption Standard
479 \begin_layout Plain Layout
481 \begin_inset CommandInset label
483 name "fig:margin-figure"
500 \begin_layout Standard
501 \begin_inset Note Greyedout
504 \begin_layout Plain Layout
509 If you are using margin figures or tables you must use the default float
510 placement option in the document settings under
526 \begin_layout Standard
527 In the same vein, the
531 class allows the use of tables, both in the margins and in the text.
532 The margin tables are recommended for a small set of data to illustrate
534 \begin_inset Quotes eld
537 Look, distance-time data is quadratic when the object is falling.
538 \begin_inset Quotes erd
541 More detailed data such as flame test results and comments should be put
542 in a full-width table instead.
545 \begin_layout Standard
550 provides a full-width figure.
551 This one takes up the entire width of the page, i.
552 \begin_inset space \thinspace{}
561 \begin_inset CommandInset ref
563 reference "fig:full-width-figure"
570 \begin_layout Standard
571 \begin_inset Float figure
578 \begin_layout Plain Layout
579 \begin_inset Box Boxed
589 height_special "totalheight"
594 backgroundcolor "none"
597 \begin_layout Plain Layout
598 Imagine your favorite photograph of a squirrel inside this box instead of
605 \begin_inset VSpace defskip
611 \begin_layout Plain Layout
612 \begin_inset Caption Standard
614 \begin_layout Plain Layout
616 \begin_inset CommandInset label
618 name "fig:full-width-figure"
635 \begin_layout Section
639 \begin_layout Standard
640 One of the most prominent and distinctive features of this style is the
641 extensive use of sidenotes.
642 There is a wide margin to provide ample room for sidenotes and small figures.
643 Any footnotes will automatically be converted to sidenotes.
647 \begin_layout Plain Layout
648 This is a sidenote that was entered using a
657 Alternatively, you can also use the
661 inset directly; you'll find it in the
663 Insert\SpecialChar menuseparator
667 \begin_inset Flex Sidenote
670 \begin_layout Plain Layout
671 This is a sidenote that was entered using a
683 \begin_layout Standard
684 If you like to place ancillary information in the margin without the sidenote
685 mark (the superscript number), you can use the
691 \begin_inset Flex Marginnote
694 \begin_layout Plain Layout
695 This is Tufte's margin note.
696 Notice that there isn't a number preceding the note, and there is no number
697 in the main text where this note was written.
702 The normal margin note will work as well, but it will look rather odd.
703 \begin_inset Marginal
706 \begin_layout Plain Layout
707 This is a normal margin note.
716 \begin_layout Standard
717 \begin_inset Flex NewThought
720 \begin_layout Plain Layout
726 innovation is Tufte's
732 Edit\SpecialChar menuseparator
733 TextStyle\SpecialChar menuseparator
737 It introduces new thoughts by means of small caps, as demonstrated in this
742 \begin_layout Standard
743 The Tufte document classes include two new character styles and some improvement
744 s on existing commands for letterspacing.
747 \begin_layout Standard
748 When setting strings of
749 \begin_inset Flex AllCaps
752 \begin_layout Plain Layout
759 \begin_inset Flex SmallCaps
762 \begin_layout Plain Layout
768 , the letterspacing—that is, the spacing between the letters—should be increased
770 \begin_inset CommandInset citation
783 Edit\SpecialChar menuseparator
784 TextStyle\SpecialChar menuseparator
787 ) has proper letterspacing for strings of
788 \begin_inset Flex AllCaps
791 \begin_layout Plain Layout
803 Edit\SpecialChar menuseparator
804 TextStyle\SpecialChar menuseparator
807 ) has letterspacing for
808 \begin_inset Flex SmallCaps
811 \begin_layout Plain Layout
812 small capital letters
818 These commands will also automatically convert the case of the text to
819 upper- or lowercase, respectively.
822 \begin_layout Standard
827 shape has also been redefined to include letterspacing.
828 Its case is left as is, however.
829 This allows one to use both uppercase and lowercase letters:
831 The Initial Letters Of The Words In This Sentence Are Capitalized.
834 \begin_layout Standard
839 paragraph environment provides a paragraph layout that stretches across
840 the main text block and the sidenotes area:
843 \begin_layout Full Width
844 Lorem ipsum dolor sit amet, consectetuer adipiscing elit.
845 Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae, felis.
846 Curabitur dictum gravida mauris.
847 Nam arcu libero, nonummy eget, consectetuer id, vulputate a, magna.
848 Donec vehicula augue eu neque.
849 Pellentesque habitant morbi tristique senectus et netus et malesuada fames
852 Cras viverra metus rhoncus sem.
853 Nulla et lectus vestibulum urna fringilla ultrices.
854 Phasellus eu tellus sit amet tortor gravida placerat.
855 Integer sapien est, iaculis in, pretium quis, viverra ac, nunc.
856 Praesent eget sem vel leo ultrices bibendum.
858 Morbi dolor nulla, malesuada eu, pulvinar at, mollis ac, nulla.
859 Curabitur auctor semper nulla.
860 Donec varius orci eget risus.
861 Duis nibh mi, congue eu, accumsan eleifend, sagittis quis, diam.
862 Duis eget orci sit amet orci dignissim rutrum.
865 \begin_layout Section
869 \begin_layout Standard
870 References are placed alongside their citations as sidenotes, as well.
871 This can be accomplished using the normal citation command.
875 \begin_layout Plain Layout
876 The previous section includes a citation.
884 \begin_layout Standard
885 The complete list of references may also be printed automatically by using
888 Insert\SpecialChar menuseparator
889 Lists/TOC\SpecialChar menuseparator
897 (see the end of this document for an example.) If you do not want to print
898 a bibliography at the end of your document, place the
907 inset inside a \SpecialChar LyX
908 note and use the \SpecialChar LaTeX
918 \begin_layout Chapter
919 Calculation of Volume: Sections 2.12–2.13
922 \begin_layout Standard
923 Imagine taking a function like
924 \begin_inset Formula $y=\sqrt{x}$
927 and rotating it in 3 dimensions around the x-axis.
928 The resulting shape would look somewhat like a cup (on its side).
929 Interestingly, integration empowers us to do exactly this and to find out
930 how much water that cup could hold.
933 \begin_layout Section
937 \begin_layout Standard
938 \begin_inset Float marginfigure
945 \begin_layout Plain Layout
946 \begin_inset Box Boxed
956 height_special "totalheight"
961 backgroundcolor "none"
964 \begin_layout Plain Layout
965 I had a graph of the square root function here.
971 \begin_inset Caption Standard
973 \begin_layout Plain Layout
974 \begin_inset CommandInset label
976 name "mar:A-graph-of"
981 \begin_inset Formula $f(x)=\sqrt{x}$
997 \begin_layout Standard
998 \begin_inset Float marginfigure
1005 \begin_layout Plain Layout
1006 \begin_inset Box Boxed
1016 height_special "totalheight"
1021 backgroundcolor "none"
1024 \begin_layout Plain Layout
1025 Here I rotated the square root function and then drew a disk on the figure
1026 to illustrate how I would calculate the volume of the figure.
1032 \begin_inset Caption Standard
1034 \begin_layout Plain Layout
1035 \begin_inset CommandInset label
1042 \begin_inset Formula $f(x)=\sqrt{x}$
1045 rotated about the x-axis and with additional remarks for integration.
1058 \begin_layout Standard
1060 \begin_inset CommandInset ref
1062 reference "mar:A-graph-of"
1066 shows the plot of the function
1067 \begin_inset Formula $f(x)=\sqrt{x}.$
1070 Now, imagine that we rotate that function about the x-axis.
1071 The resulting figure would be somewhat like figure
1072 \begin_inset CommandInset ref
1074 reference "mar:rotated"
1079 This is akin to a cup lying on its side.
1080 For the sake of clarity, the artist (me) drew a circle on the end of the
1081 figure to show that it is indeed rotated.
1084 \begin_layout Standard
1085 Now, suppose we wished to find the volume of the figure.
1086 When we integrated the original square root function to find its area,
1087 we imagined a series of rectangles inside the figure.
1089 \begin_inset Formula $h=f(x)$
1093 \begin_inset Formula $dx$
1097 Since height multiplied by width was the area of each rectangle, we summed
1098 these areas and rewrote this as
1099 \begin_inset Formula $\int\,f(x)\,dx$
1102 , or, in this specific case,
1103 \begin_inset Formula $\int\,\sqrt{x}\,dx$
1109 \begin_layout Standard
1110 To find the volume of our rotated figure the prodecure is quite similar.
1111 Begin by rotating each rectangle about the x-axis.
1112 This creates a series of cylinders.
1113 \begin_inset Flex Sidenote
1116 \begin_layout Plain Layout
1117 The text refers to these cylinders as "disks".
1118 This is standard practice in all the Calculus books I checked.
1123 Then, we can find the volume of each cylinder/disk.
1124 The basic formula is:
1127 \begin_layout Standard
1128 \begin_inset Formula
1138 \begin_layout Standard
1141 \begin_inset Formula $h$
1144 is the height of the cylinder (width of the rectangle)
1145 \begin_inset Formula $dx$
1149 The area of each figure is a circle where
1150 \begin_inset Formula $A=\pi r^{2}$
1154 The radius in this case is the function
1155 \begin_inset Formula $f(x)$
1162 \begin_layout Standard
1163 \begin_inset Formula
1173 \begin_layout Standard
1175 In our specific case,
1178 \begin_layout Standard
1179 \begin_inset Formula
1181 A & = & \pi\left(\sqrt{x}\right)^{2}\\
1190 \begin_layout Standard
1191 To calculate the volume of one disk, we have
1194 \begin_layout Standard
1195 \begin_inset Formula
1205 \begin_layout Standard
1207 or, in the general case
1210 \begin_layout Standard
1211 \begin_inset Formula
1221 \begin_layout Standard
1222 To find the volume of the figure between points
1223 \begin_inset Formula $a$
1227 \begin_inset Formula $b$
1230 we sum the volumes by means of integration:
1233 \begin_layout Standard
1234 \begin_inset Formula
1236 \int_{a}^{b}\,\pi f^{2}(x)\,dx
1244 \begin_layout Standard
1246 In the specific example, over the interval
1247 \begin_inset Formula $[0,4]$
1253 \begin_layout Standard
1254 \begin_inset Formula
1256 \int_{0}^{4}\,\pi x\,dx & = & \pi\int_{0}^{4}\,x\,dx\\
1257 & = & \pi\left.\left(\frac{x^{2}}{2}\right)\right|_{0}^{4}\\
1258 & = & \pi\left(\frac{4^{2}}{2}-0\right)\\
1267 \begin_layout Standard
1268 \begin_inset Flex NewThought
1271 \begin_layout Plain Layout
1277 a special hole down the length of the cup we just worked with.
1278 It is made with a quadratic shaped bit.
1279 \begin_inset Flex Sidenote
1282 \begin_layout Plain Layout
1283 I have no idea how I'd do this in real life, but I'm making a point.
1288 I find that the hole the bit makes can be modeled with the function
1289 \begin_inset Formula $g(x)=\frac{x^{2}}{16}$
1293 I would need to subtract the volume of the material removed from the volume
1295 \begin_inset Quotes eld
1299 \begin_inset Quotes erd
1303 Each individual cylinder would become like a
1304 \begin_inset Quotes eld
1308 \begin_inset Quotes erd
1312 To get the area of one washer, I would use the formula
1315 \begin_layout Standard
1316 \begin_inset Float marginfigure
1323 \begin_layout Plain Layout
1324 \begin_inset Box Boxed
1334 height_special "totalheight"
1339 backgroundcolor "none"
1342 \begin_layout Plain Layout
1343 Here I used RLPlot to draw the square root function and the quadratic function.
1344 Then I used Inkscape to shade the area between them.
1350 \begin_inset Caption Standard
1352 \begin_layout Plain Layout
1354 \begin_inset Formula $f(x)$
1358 \begin_inset Formula $g(x)$
1361 and the area left by
1362 \begin_inset Formula $f(x)-g(x)$
1378 \begin_layout Standard
1379 \begin_inset Formula
1381 A_{washer} & = & A_{cup}-A_{drill}\\
1382 & = & \pi f^{2}(x)-\pi g^{2}(x)\\
1383 & = & \pi\left(f^{2}(x)-g^{2}(x)\right)
1391 \begin_layout Standard
1392 The volume of each washer would be
1395 \begin_layout Standard
1396 \begin_inset Formula
1398 V_{washer} & = & A_{washer}\,dx\\
1399 & = & \pi\left(f^{2}(x)-g^{2}(x)\right)\,dx
1407 \begin_layout Standard
1409 Then, by summing the volumes of all the washers between points
1410 \begin_inset Formula $a$
1414 \begin_inset Formula $b$
1417 , the integral is derived:
1420 \begin_layout Standard
1421 \begin_inset Formula
1423 \int_{a}^{b}\,\pi\left(f^{2}(x)-g^{2}(x)\right)\,dx
1431 \begin_layout Standard
1432 In the case of our quadratic drill bit::
1433 \begin_inset Float marginfigure
1440 \begin_layout Plain Layout
1441 \begin_inset Box Boxed
1451 height_special "totalheight"
1456 backgroundcolor "none"
1459 \begin_layout Plain Layout
1460 This was the rotated set of 2 functions.
1466 \begin_inset Caption Standard
1468 \begin_layout Plain Layout
1469 The cup with a quadratic hole drilled down its length
1482 \begin_layout Standard
1483 \begin_inset Formula
1485 \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\\
1486 & = & \pi\left(\int_{0}^{4}\,x\,dx-\int_{0}^{4}\,\frac{x^{4}}{256}\,dx\right)\\
1487 & = & \pi\left(\left.\left(\frac{x^{2}}{2}\right)\right|_{0}^{4}-\left.\left(\frac{x^{5}}{1280}\right)\right|_{0}^{4}\right)\\
1488 & = & \pi\left(\left(\frac{4^{2}}{2}-0\right)-\left(\frac{4^{5}}{1280}-0\right)\right)\\
1489 & = & \pi\left(8-0.8\right)\\
1498 \begin_layout Standard
1502 \begin_layout Section
1506 \begin_layout Itemize
1507 p114: 1, 4, 5, 6, 8, 10, 12, 15
1510 \begin_layout Standard
1511 \begin_inset CommandInset bibtex
1513 bibfiles "../biblioExample"