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
22 \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
69 \notefontcolor #0000ff
77 \paragraph_separation indent
78 \paragraph_indentation default
80 \math_numbering_side default
85 \paperpagestyle default
86 \tracking_changes false
87 \postpone_fragile_content false
96 \begin_layout Standard
97 \begin_inset Note Note
100 \begin_layout Plain Layout
105 : To be able to view your file as PDF you must have the \SpecialChar LaTeX
110 installed to your \SpecialChar LaTeX
112 If you are using MiK\SpecialChar TeX
113 , you will automatically be asked to install this package
114 when previewing your file, if you are using \SpecialChar TeX
115 Live, use \SpecialChar TeX
116 Live's package manager.
119 \begin_layout Plain Layout
124 : If you wish to compile to PDF with plain \SpecialChar LaTeX
125 (instead of pdf\SpecialChar TeX
126 ), there is currently
127 a bug in the Tufte class that causes errors.
128 You can add the class option 'nols' (put this in the
129 \begin_inset Quotes eld
133 \begin_inset Quotes erd
136 field of Document\SpecialChar menuseparator
137 Settings \SpecialChar menuseparator
138 Document Class) to get rid of the errors, but
139 this also removes letterspacing, an important part of the Tufte design.
153 \begin_inset Note Note
156 \begin_layout Plain Layout
157 author of this example file: Jason Waskiewicz
165 \begin_layout Standard
166 \begin_inset CommandInset toc
167 LatexCommand tableofcontents
174 \begin_layout Chapter
175 The Features of the Tufte-book Class
178 \begin_layout Standard
179 In this document, it was endeavored to show some of the features of the
185 In the first chapter, their use is outlined.
186 In the second chapter, their use through a handout that was created in
187 a calculus class is demonstrated.
190 \begin_layout Section
194 \begin_layout Standard
199 class is based on the work of
204 It provides the same functionality as the
208 class with book-specific additions.
209 Tufte's documents consist of a rather narrow column of text and a wide
210 column of margin notes and margin figures.
211 This is to improve readability.
214 \begin_layout Standard
215 The features provided by this format include:
218 \begin_layout Itemize
222 \begin_layout Itemize
223 Ordinary figures in text with captions in margins
226 \begin_layout Itemize
227 Full width figures and text when needed
230 \begin_layout Itemize
231 \begin_inset Quotes eld
235 \begin_inset Quotes erd
241 \begin_layout Itemize
242 Limited layers of sections and subsections
245 \begin_layout Standard
246 In this sample document, some of these features are demonstrated.
247 For a full demonstration, visit the tufte-latex website:
248 \begin_inset Flex URL
251 \begin_layout Plain Layout
253 https://tufte-latex.github.io/tufte-latex/
261 \begin_layout Section
265 \begin_layout Standard
267 \begin_inset Quotes eld
271 \begin_inset Quotes erd
274 rather than justified.
275 \begin_inset Flex Sidenote
278 \begin_layout Plain Layout
279 To get justified text, add the option
289 Document\SpecialChar menuseparator
290 Settings\SpecialChar menuseparator
298 Ragged right text is used in most of his works, but the class option
302 is provided to change this.
305 \begin_layout Standard
306 Tufte also formats his pages asymmetrically.
307 This means that the marginalia appear on the right side on each page, whether
309 If you prefer, you can change that and have symmetric layout, as common
310 in traditional book typography, by using the
315 \begin_inset Flex Sidenote
318 \begin_layout Plain Layout
319 To create a symmetric layout, add the option
329 Document\SpecialChar menuseparator
330 Settings\SpecialChar menuseparator
341 \begin_layout Standard
342 Finally, Tufte does not number his chapters or his sections.
343 If you like to refer to sections by number, move the
349 Document\SpecialChar menuseparator
350 Settings\SpecialChar menuseparator
353 to the very right (as done in this document).
354 \begin_inset Flex Marginnote
357 \begin_layout Plain Layout
366 \begin_layout Section
370 \begin_layout Standard
371 Tufte uses ordinary figure floats such as the following:
374 \begin_layout Standard
375 \begin_inset Float figure
382 \begin_layout Plain Layout
383 \begin_inset Box Boxed
393 height_special "totalheight"
398 backgroundcolor "none"
401 \begin_layout Plain Layout
402 Imagine your favorite figure inside this box instead of this boring text.
408 \begin_inset Caption Standard
410 \begin_layout Plain Layout
411 An ordinary figure float.
424 \begin_layout Standard
425 Furthermore, he uses margin figures, as shown in Fig.
430 \begin_inset CommandInset ref
432 reference "fig:margin-figure"
439 \begin_layout Standard
440 \begin_inset VSpace 5theight%
446 \begin_layout Standard
447 \begin_inset Float marginfigure
454 \begin_layout Plain Layout
455 \begin_inset Box Boxed
465 height_special "totalheight"
470 backgroundcolor "none"
473 \begin_layout Plain Layout
474 Imagine your favorite photograph of a squirrel inside this box instead of
481 \begin_inset Caption Standard
483 \begin_layout Plain Layout
485 \begin_inset CommandInset label
487 name "fig:margin-figure"
504 \begin_layout Standard
505 \begin_inset Note Greyedout
508 \begin_layout Plain Layout
513 If you are using margin figures or tables you must use the default float
514 placement option in the document settings under
530 \begin_layout Standard
531 In the same vein, the
535 class allows the use of tables, both in the margins and in the text.
536 The margin tables are recommended for a small set of data to illustrate
538 \begin_inset Quotes eld
541 Look, distance-time data is quadratic when the object is falling.
542 \begin_inset Quotes erd
545 More detailed data such as flame test results and comments should be put
546 in a full-width table instead.
549 \begin_layout Standard
554 provides a full-width figure.
555 This one takes up the entire width of the page, i.
556 \begin_inset space \thinspace{}
565 \begin_inset CommandInset ref
567 reference "fig:full-width-figure"
574 \begin_layout Standard
575 \begin_inset Float figure
582 \begin_layout Plain Layout
583 \begin_inset Box Boxed
593 height_special "totalheight"
598 backgroundcolor "none"
601 \begin_layout Plain Layout
602 Imagine your favorite photograph of a squirrel inside this box instead of
609 \begin_inset VSpace defskip
615 \begin_layout Plain Layout
616 \begin_inset Caption Standard
618 \begin_layout Plain Layout
620 \begin_inset CommandInset label
622 name "fig:full-width-figure"
639 \begin_layout Section
643 \begin_layout Standard
644 One of the most prominent and distinctive features of this style is the
645 extensive use of sidenotes.
646 There is a wide margin to provide ample room for sidenotes and small figures.
647 Any footnotes will automatically be converted to sidenotes.
651 \begin_layout Plain Layout
652 This is a sidenote that was entered using a
661 Alternatively, you can also use the
665 inset directly; you'll find it in the
667 Insert\SpecialChar menuseparator
671 \begin_inset Flex Sidenote
674 \begin_layout Plain Layout
675 This is a sidenote that was entered using a
687 \begin_layout Standard
688 If you like to place ancillary information in the margin without the sidenote
689 mark (the superscript number), you can use the
695 \begin_inset Flex Marginnote
698 \begin_layout Plain Layout
699 This is Tufte's margin note.
700 Notice that there isn't a number preceding the note, and there is no number
701 in the main text where this note was written.
706 The normal margin note will work as well, but it will look rather odd.
707 \begin_inset Marginal
710 \begin_layout Plain Layout
711 This is a normal margin note.
720 \begin_layout Standard
721 \begin_inset Flex NewThought
724 \begin_layout Plain Layout
730 innovation is Tufte's
736 Edit\SpecialChar menuseparator
737 TextStyle\SpecialChar menuseparator
741 It introduces new thoughts by means of small caps, as demonstrated in this
746 \begin_layout Standard
747 The Tufte document classes include two new character styles and some improvement
748 s on existing commands for letterspacing.
751 \begin_layout Standard
752 When setting strings of
753 \begin_inset Flex AllCaps
756 \begin_layout Plain Layout
763 \begin_inset Flex SmallCaps
766 \begin_layout Plain Layout
772 , the letterspacing—that is, the spacing between the letters—should be increased
774 \begin_inset CommandInset citation
787 Edit\SpecialChar menuseparator
788 TextStyle\SpecialChar menuseparator
791 ) has proper letterspacing for strings of
792 \begin_inset Flex AllCaps
795 \begin_layout Plain Layout
807 Edit\SpecialChar menuseparator
808 TextStyle\SpecialChar menuseparator
811 ) has letterspacing for
812 \begin_inset Flex SmallCaps
815 \begin_layout Plain Layout
816 small capital letters
822 These commands will also automatically convert the case of the text to
823 upper- or lowercase, respectively.
826 \begin_layout Standard
831 shape has also been redefined to include letterspacing.
832 Its case is left as is, however.
833 This allows one to use both uppercase and lowercase letters:
835 The Initial Letters Of The Words In This Sentence Are Capitalized.
838 \begin_layout Standard
843 paragraph environment provides a paragraph layout that stretches across
844 the main text block and the sidenotes area:
847 \begin_layout Full Width
848 Lorem ipsum dolor sit amet, consectetuer adipiscing elit.
849 Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae, felis.
850 Curabitur dictum gravida mauris.
851 Nam arcu libero, nonummy eget, consectetuer id, vulputate a, magna.
852 Donec vehicula augue eu neque.
853 Pellentesque habitant morbi tristique senectus et netus et malesuada fames
856 Cras viverra metus rhoncus sem.
857 Nulla et lectus vestibulum urna fringilla ultrices.
858 Phasellus eu tellus sit amet tortor gravida placerat.
859 Integer sapien est, iaculis in, pretium quis, viverra ac, nunc.
860 Praesent eget sem vel leo ultrices bibendum.
862 Morbi dolor nulla, malesuada eu, pulvinar at, mollis ac, nulla.
863 Curabitur auctor semper nulla.
864 Donec varius orci eget risus.
865 Duis nibh mi, congue eu, accumsan eleifend, sagittis quis, diam.
866 Duis eget orci sit amet orci dignissim rutrum.
869 \begin_layout Section
873 \begin_layout Standard
874 References are placed alongside their citations as sidenotes, as well.
875 This can be accomplished using the normal citation command.
879 \begin_layout Plain Layout
880 The previous section includes a citation.
888 \begin_layout Standard
889 The complete list of references may also be printed automatically by using
892 Insert\SpecialChar menuseparator
893 Lists/TOC\SpecialChar menuseparator
901 (see the end of this document for an example.) If you do not want to print
902 a bibliography at the end of your document, place the
911 inset inside a \SpecialChar LyX
912 note and use the \SpecialChar LaTeX
922 \begin_layout Chapter
923 Calculation of Volume: Sections 2.12–2.13
926 \begin_layout Standard
927 Imagine taking a function like
928 \begin_inset Formula $y=\sqrt{x}$
931 and rotating it in 3 dimensions around the x-axis.
932 The resulting shape would look somewhat like a cup (on its side).
933 Interestingly, integration empowers us to do exactly this and to find out
934 how much water that cup could hold.
937 \begin_layout Section
941 \begin_layout Standard
942 \begin_inset Float marginfigure
949 \begin_layout Plain Layout
950 \begin_inset Box Boxed
960 height_special "totalheight"
965 backgroundcolor "none"
968 \begin_layout Plain Layout
969 I had a graph of the square root function here.
975 \begin_inset Caption Standard
977 \begin_layout Plain Layout
978 \begin_inset CommandInset label
980 name "mar:A-graph-of"
985 \begin_inset Formula $f(x)=\sqrt{x}$
1001 \begin_layout Standard
1002 \begin_inset Float marginfigure
1009 \begin_layout Plain Layout
1010 \begin_inset Box Boxed
1020 height_special "totalheight"
1025 backgroundcolor "none"
1028 \begin_layout Plain Layout
1029 Here I rotated the square root function and then drew a disk on the figure
1030 to illustrate how I would calculate the volume of the figure.
1036 \begin_inset Caption Standard
1038 \begin_layout Plain Layout
1039 \begin_inset CommandInset label
1046 \begin_inset Formula $f(x)=\sqrt{x}$
1049 rotated about the x-axis and with additional remarks for integration.
1062 \begin_layout Standard
1064 \begin_inset CommandInset ref
1066 reference "mar:A-graph-of"
1070 shows the plot of the function
1071 \begin_inset Formula $f(x)=\sqrt{x}.$
1074 Now, imagine that we rotate that function about the x-axis.
1075 The resulting figure would be somewhat like figure
1076 \begin_inset CommandInset ref
1078 reference "mar:rotated"
1083 This is akin to a cup lying on its side.
1084 For the sake of clarity, the artist (me) drew a circle on the end of the
1085 figure to show that it is indeed rotated.
1088 \begin_layout Standard
1089 Now, suppose we wished to find the volume of the figure.
1090 When we integrated the original square root function to find its area,
1091 we imagined a series of rectangles inside the figure.
1093 \begin_inset Formula $h=f(x)$
1097 \begin_inset Formula $dx$
1101 Since height multiplied by width was the area of each rectangle, we summed
1102 these areas and rewrote this as
1103 \begin_inset Formula $\int\,f(x)\,dx$
1106 , or, in this specific case,
1107 \begin_inset Formula $\int\,\sqrt{x}\,dx$
1113 \begin_layout Standard
1114 To find the volume of our rotated figure the prodecure is quite similar.
1115 Begin by rotating each rectangle about the x-axis.
1116 This creates a series of cylinders.
1117 \begin_inset Flex Sidenote
1120 \begin_layout Plain Layout
1121 The text refers to these cylinders as "disks".
1122 This is standard practice in all the Calculus books I checked.
1127 Then, we can find the volume of each cylinder/disk.
1128 The basic formula is:
1131 \begin_layout Standard
1132 \begin_inset Formula
1142 \begin_layout Standard
1145 \begin_inset Formula $h$
1148 is the height of the cylinder (width of the rectangle)
1149 \begin_inset Formula $dx$
1153 The area of each figure is a circle where
1154 \begin_inset Formula $A=\pi r^{2}$
1158 The radius in this case is the function
1159 \begin_inset Formula $f(x)$
1166 \begin_layout Standard
1167 \begin_inset Formula
1177 \begin_layout Standard
1179 In our specific case,
1182 \begin_layout Standard
1183 \begin_inset Formula
1185 A & = & \pi\left(\sqrt{x}\right)^{2}\\
1194 \begin_layout Standard
1195 To calculate the volume of one disk, we have
1198 \begin_layout Standard
1199 \begin_inset Formula
1209 \begin_layout Standard
1211 or, in the general case
1214 \begin_layout Standard
1215 \begin_inset Formula
1225 \begin_layout Standard
1226 To find the volume of the figure between points
1227 \begin_inset Formula $a$
1231 \begin_inset Formula $b$
1234 we sum the volumes by means of integration:
1237 \begin_layout Standard
1238 \begin_inset Formula
1240 \int_{a}^{b}\,\pi f^{2}(x)\,dx
1248 \begin_layout Standard
1250 In the specific example, over the interval
1251 \begin_inset Formula $[0,4]$
1257 \begin_layout Standard
1258 \begin_inset Formula
1260 \int_{0}^{4}\,\pi x\,dx & = & \pi\int_{0}^{4}\,x\,dx\\
1261 & = & \pi\left.\left(\frac{x^{2}}{2}\right)\right|_{0}^{4}\\
1262 & = & \pi\left(\frac{4^{2}}{2}-0\right)\\
1271 \begin_layout Standard
1272 \begin_inset Flex NewThought
1275 \begin_layout Plain Layout
1281 a special hole down the length of the cup we just worked with.
1282 It is made with a quadratic shaped bit.
1283 \begin_inset Flex Sidenote
1286 \begin_layout Plain Layout
1287 I have no idea how I'd do this in real life, but I'm making a point.
1292 I find that the hole the bit makes can be modeled with the function
1293 \begin_inset Formula $g(x)=\frac{x^{2}}{16}$
1297 I would need to subtract the volume of the material removed from the volume
1299 \begin_inset Quotes eld
1303 \begin_inset Quotes erd
1307 Each individual cylinder would become like a
1308 \begin_inset Quotes eld
1312 \begin_inset Quotes erd
1316 To get the area of one washer, I would use the formula
1319 \begin_layout Standard
1320 \begin_inset Float marginfigure
1327 \begin_layout Plain Layout
1328 \begin_inset Box Boxed
1338 height_special "totalheight"
1343 backgroundcolor "none"
1346 \begin_layout Plain Layout
1347 Here I used RLPlot to draw the square root function and the quadratic function.
1348 Then I used Inkscape to shade the area between them.
1354 \begin_inset Caption Standard
1356 \begin_layout Plain Layout
1358 \begin_inset Formula $f(x)$
1362 \begin_inset Formula $g(x)$
1365 and the area left by
1366 \begin_inset Formula $f(x)-g(x)$
1382 \begin_layout Standard
1383 \begin_inset Formula
1385 A_{washer} & = & A_{cup}-A_{drill}\\
1386 & = & \pi f^{2}(x)-\pi g^{2}(x)\\
1387 & = & \pi\left(f^{2}(x)-g^{2}(x)\right)
1395 \begin_layout Standard
1396 The volume of each washer would be
1399 \begin_layout Standard
1400 \begin_inset Formula
1402 V_{washer} & = & A_{washer}\,dx\\
1403 & = & \pi\left(f^{2}(x)-g^{2}(x)\right)\,dx
1411 \begin_layout Standard
1413 Then, by summing the volumes of all the washers between points
1414 \begin_inset Formula $a$
1418 \begin_inset Formula $b$
1421 , the integral is derived:
1424 \begin_layout Standard
1425 \begin_inset Formula
1427 \int_{a}^{b}\,\pi\left(f^{2}(x)-g^{2}(x)\right)\,dx
1435 \begin_layout Standard
1436 In the case of our quadratic drill bit::
1437 \begin_inset Float marginfigure
1444 \begin_layout Plain Layout
1445 \begin_inset Box Boxed
1455 height_special "totalheight"
1460 backgroundcolor "none"
1463 \begin_layout Plain Layout
1464 This was the rotated set of 2 functions.
1470 \begin_inset Caption Standard
1472 \begin_layout Plain Layout
1473 The cup with a quadratic hole drilled down its length
1486 \begin_layout Standard
1487 \begin_inset Formula
1489 \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\\
1490 & = & \pi\left(\int_{0}^{4}\,x\,dx-\int_{0}^{4}\,\frac{x^{4}}{256}\,dx\right)\\
1491 & = & \pi\left(\left.\left(\frac{x^{2}}{2}\right)\right|_{0}^{4}-\left.\left(\frac{x^{5}}{1280}\right)\right|_{0}^{4}\right)\\
1492 & = & \pi\left(\left(\frac{4^{2}}{2}-0\right)-\left(\frac{4^{5}}{1280}-0\right)\right)\\
1493 & = & \pi\left(8-0.8\right)\\
1502 \begin_layout Standard
1506 \begin_layout Section
1510 \begin_layout Itemize
1511 p114: 1, 4, 5, 6, 8, 10, 12, 15
1514 \begin_layout Standard
1515 \begin_inset CommandInset bibtex
1517 bibfiles "../biblioExample"