1 #LyX 2.1 created this file. For more info see http://www.lyx.org/
6 \use_default_options true
7 \maintain_unincluded_children false
9 \language_package default
14 \font_typewriter default
16 \font_default_family default
17 \use_non_tex_fonts false
23 \default_output_format pdf2
25 \bibtex_command default
26 \index_command default
27 \paperfontsize default
31 \pdf_bookmarksnumbered false
32 \pdf_bookmarksopen true
33 \pdf_bookmarksopenlevel 1
41 \use_package amsmath 1
42 \use_package amssymb 1
45 \use_package mathdots 1
46 \use_package mathtools 0
48 \use_package stackrel 0
49 \use_package stmaryrd 0
50 \use_package undertilde 0
52 \cite_engine_type numerical
56 \paperorientation portrait
60 \notefontcolor #0000ff
67 \paragraph_separation indent
68 \paragraph_indentation default
69 \quotes_language english
72 \paperpagestyle default
73 \tracking_changes false
82 \begin_layout Standard
83 \begin_inset Note Note
86 \begin_layout Plain Layout
91 : To be able to view your file as PDF you must have the LaTeX-package
95 installed to your LaTeX system.
96 If you are using MiKTeX, you will automatically be asked to install this
97 package when previewing your file, if you are using TeXLive, use TeXLive's
101 \begin_layout Plain Layout
106 : If you wish to compile to PDF with plain LaTeX (instead of pdfTeX), there
107 is currently a bug in the Tufte class that causes errors.
108 You can add the class option 'nols' to get rid of the errors, but this
109 also removes letterspacing, an important part of the Tufte design.
123 \begin_inset Note Note
126 \begin_layout Plain Layout
127 author of this example file: Jason Waskiewicz
135 \begin_layout Standard
136 \begin_inset CommandInset toc
137 LatexCommand tableofcontents
144 \begin_layout Chapter
145 The Features of the Tufte-book Class
148 \begin_layout Standard
149 In this document, it was endeavored to show some of the features of the
155 In the first chapter, their use is outlined.
156 In the second chapter, their use through a handout that was created in
157 a calculus class is demonstrated.
160 \begin_layout Section
164 \begin_layout Standard
169 class is based on the work of
174 It provides the same functionality as the
178 class with book-specific additions.
179 Tufte's documents consist of a rather narrow column of text and a wide
180 column of margin notes and margin figures.
181 This is to improve readability.
184 \begin_layout Standard
185 The features provided by this format include:
188 \begin_layout Itemize
192 \begin_layout Itemize
193 Ordinary figures in text with captions in margins
196 \begin_layout Itemize
197 Full width figures and text when needed
200 \begin_layout Itemize
201 \begin_inset Quotes eld
205 \begin_inset Quotes erd
211 \begin_layout Itemize
212 Limited layers of sections and subsections
215 \begin_layout Standard
216 In this sample document, some of these features are demonstrated.
217 For a full demonstration, visit the tufte-latex website:
218 \begin_inset Flex URL
221 \begin_layout Plain Layout
223 http://code.google.com/p/tufte-latex
231 \begin_layout Section
235 \begin_layout Standard
237 \begin_inset Quotes eld
241 \begin_inset Quotes erd
244 rather than justified.
245 \begin_inset Flex Sidenote
248 \begin_layout Plain Layout
249 To get justified text, add the option
259 Document\SpecialChar \menuseparator
260 Settings\SpecialChar \menuseparator
268 Ragged right text is used in most of his works, but the class option
272 is provided to change this.
275 \begin_layout Standard
276 Tufte also formats his pages asymmetrically.
277 This means that the marginalia appear on the right side on each page, whether
279 If you prefer, you can change that and have symmetric layout, as common
280 in traditional book typography, by using the
285 \begin_inset Flex Sidenote
288 \begin_layout Plain Layout
289 To create a symmetric layout, add the option
299 Document\SpecialChar \menuseparator
300 Settings\SpecialChar \menuseparator
311 \begin_layout Standard
312 Finally, Tufte does not number his chapters or his sections.
313 If you like to refer to sections by number, move the
319 Document\SpecialChar \menuseparator
320 Settings\SpecialChar \menuseparator
323 to the very right (as done in this document).
324 \begin_inset Flex Marginnote
327 \begin_layout Plain Layout
336 \begin_layout Section
340 \begin_layout Standard
341 Tufte uses ordinary figure floats such as the following:
344 \begin_layout Standard
345 \begin_inset Float figure
350 \begin_layout Plain Layout
351 \begin_inset Box Boxed
361 height_special "totalheight"
364 \begin_layout Plain Layout
365 Imagine your favorite figure inside this box instead of this boring text.
371 \begin_inset Caption Standard
373 \begin_layout Plain Layout
374 An ordinary figure float.
387 \begin_layout Standard
388 Furthermore, he uses margin figures, as shown in Fig.
393 \begin_inset CommandInset ref
395 reference "fig:margin-figure"
402 \begin_layout Standard
403 \begin_inset VSpace 5theight%
409 \begin_layout Standard
410 \begin_inset Float marginfigure
415 \begin_layout Plain Layout
416 \begin_inset Box Boxed
426 height_special "totalheight"
429 \begin_layout Plain Layout
430 Imagine your favorite photograph of a squirrel inside this box instead of
437 \begin_inset Caption Standard
439 \begin_layout Plain Layout
441 \begin_inset CommandInset label
443 name "fig:margin-figure"
460 \begin_layout Standard
461 \begin_inset Note Greyedout
464 \begin_layout Plain Layout
469 If you are using margin figures or tables you must use the default float
470 placement option in the document settings under
486 \begin_layout Standard
487 In the same vein, the
491 class allows the use of tables, both in the margins and in the text.
492 The margin tables are recommended for a small set of data to illustrate
494 \begin_inset Quotes eld
497 Look, distance-time data is quadratic when the object is falling.
498 \begin_inset Quotes erd
501 More detailed data such as flame test results and comments should be put
502 in a full-width table instead.
505 \begin_layout Standard
510 provides a full-width figure.
511 This one takes up the entire width of the page, i.
512 \begin_inset space \thinspace{}
521 \begin_inset CommandInset ref
523 reference "fig:full-width-figure"
530 \begin_layout Standard
531 \begin_inset Float figure
536 \begin_layout Plain Layout
537 \begin_inset Box Boxed
547 height_special "totalheight"
550 \begin_layout Plain Layout
551 Imagine your favorite photograph of a squirrel inside this box instead of
558 \begin_inset VSpace defskip
564 \begin_layout Plain Layout
565 \begin_inset Caption Standard
567 \begin_layout Plain Layout
569 \begin_inset CommandInset label
571 name "fig:full-width-figure"
588 \begin_layout Section
592 \begin_layout Standard
593 One of the most prominent and distinctive features of this style is the
594 extensive use of sidenotes.
595 There is a wide margin to provide ample room for sidenotes and small figures.
596 Any footnotes will automatically be converted to sidenotes.
600 \begin_layout Plain Layout
601 This is a sidenote that was entered using a
610 Alternatively, you can also use the
614 inset directly; you'll find it in the
616 Insert\SpecialChar \menuseparator
620 \begin_inset Flex Sidenote
623 \begin_layout Plain Layout
624 This is a sidenote that was entered using a
636 \begin_layout Standard
637 If you like to place ancillary information in the margin without the sidenote
638 mark (the superscript number), you can use the
644 \begin_inset Flex Marginnote
647 \begin_layout Plain Layout
648 This is Tufte's margin note.
649 Notice that there isn't a number preceding the note, and there is no number
650 in the main text where this note was written.
655 The normal margin note will work as well, but it will look rather odd.
656 \begin_inset Marginal
659 \begin_layout Plain Layout
660 This is a normal margin note.
669 \begin_layout Standard
670 \begin_inset Flex NewThought
673 \begin_layout Plain Layout
679 innovation is Tufte's
685 Edit\SpecialChar \menuseparator
686 TextStyle\SpecialChar \menuseparator
690 It introduces new thoughts by means of small caps, as demonstrated in this
695 \begin_layout Standard
696 The Tufte document classes include two new character styles and some improvement
697 s on existing commands for letterspacing.
700 \begin_layout Standard
701 When setting strings of
702 \begin_inset Flex AllCaps
705 \begin_layout Plain Layout
712 \begin_inset Flex SmallCaps
715 \begin_layout Plain Layout
721 , the letterspacing---that is, the spacing between the letters---should
722 be increased slightly.
723 \begin_inset CommandInset citation
735 Edit\SpecialChar \menuseparator
736 TextStyle\SpecialChar \menuseparator
739 ) has proper letterspacing for strings of
740 \begin_inset Flex AllCaps
743 \begin_layout Plain Layout
755 Edit\SpecialChar \menuseparator
756 TextStyle\SpecialChar \menuseparator
759 ) has letterspacing for
760 \begin_inset Flex SmallCaps
763 \begin_layout Plain Layout
764 small capital letters
770 These commands will also automatically convert the case of the text to
771 upper- or lowercase, respectively.
774 \begin_layout Standard
779 shape has also been redefined to include letterspacing.
780 Its case is left as is, however.
781 This allows one to use both uppercase and lowercase letters:
783 The Initial Letters Of The Words In This Sentence Are Capitalized.
786 \begin_layout Standard
791 paragraph environment provides a paragraph layout that stretches across
792 the main text block and the sidenotes area:
795 \begin_layout Full Width
796 Lorem ipsum dolor sit amet, consectetuer adipiscing elit.
797 Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae, felis.
798 Curabitur dictum gravida mauris.
799 Nam arcu libero, nonummy eget, consectetuer id, vulputate a, magna.
800 Donec vehicula augue eu neque.
801 Pellentesque habitant morbi tristique senectus et netus et malesuada fames
804 Cras viverra metus rhoncus sem.
805 Nulla et lectus vestibulum urna fringilla ultrices.
806 Phasellus eu tellus sit amet tortor gravida placerat.
807 Integer sapien est, iaculis in, pretium quis, viverra ac, nunc.
808 Praesent eget sem vel leo ultrices bibendum.
810 Morbi dolor nulla, malesuada eu, pulvinar at, mollis ac, nulla.
811 Curabitur auctor semper nulla.
812 Donec varius orci eget risus.
813 Duis nibh mi, congue eu, accumsan eleifend, sagittis quis, diam.
814 Duis eget orci sit amet orci dignissim rutrum.
817 \begin_layout Section
821 \begin_layout Standard
822 References are placed alongside their citations as sidenotes, as well.
823 This can be accomplished using the normal citation command.
827 \begin_layout Plain Layout
828 The previous section includes a citation.
836 \begin_layout Standard
837 The complete list of references may also be printed automatically by using
840 Insert\SpecialChar \menuseparator
841 Lists/TOC\SpecialChar \menuseparator
848 (see the end of this document for an example.) If you do not want to print
849 a bibliography at the end of your document, place the
857 inset inside a LyX note and use the LaTeX command
866 \begin_layout Chapter
867 Calculation of Volume: Sections 2.12–2.13
870 \begin_layout Standard
871 Imagine taking a function like
872 \begin_inset Formula $y=\sqrt{x}$
875 and rotating it in 3 dimensions around the x-axis.
876 The resulting shape would look somewhat like a cup (on its side).
877 Interestingly, integration empowers us to do exactly this and to find out
878 how much water that cup could hold.
881 \begin_layout Section
885 \begin_layout Standard
886 \begin_inset Float marginfigure
891 \begin_layout Plain Layout
892 \begin_inset Box Boxed
902 height_special "totalheight"
905 \begin_layout Plain Layout
906 I had a graph of the square root function here.
912 \begin_inset Caption Standard
914 \begin_layout Plain Layout
915 \begin_inset CommandInset label
917 name "mar:A-graph-of"
922 \begin_inset Formula $f(x)=\sqrt{x}$
938 \begin_layout Standard
939 \begin_inset Float marginfigure
944 \begin_layout Plain Layout
945 \begin_inset Box Boxed
955 height_special "totalheight"
958 \begin_layout Plain Layout
959 Here I rotated the square root function and then drew a disk on the figure
960 to illustrate how I would calculate the volume of the figure.
966 \begin_inset Caption Standard
968 \begin_layout Plain Layout
969 \begin_inset CommandInset label
976 \begin_inset Formula $f(x)=\sqrt{x}$
979 rotated about the x-axis and with additional remarks for integration.
992 \begin_layout Standard
994 \begin_inset CommandInset ref
996 reference "mar:A-graph-of"
1000 shows the plot of the function
1001 \begin_inset Formula $f(x)=\sqrt{x}.$
1004 Now, imagine that we rotate that function about the x-axis.
1005 The resulting figure would be somewhat like figure
1006 \begin_inset CommandInset ref
1008 reference "mar:rotated"
1013 This is akin to a cup lying on its side.
1014 For the sake of clarity, the artist (me) drew a circle on the end of the
1015 figure to show that it is indeed rotated.
1018 \begin_layout Standard
1019 Now, suppose we wished to find the volume of the figure.
1020 When we integrated the original square root function to find its area,
1021 we imagined a series of rectangles inside the figure.
1023 \begin_inset Formula $h=f(x)$
1027 \begin_inset Formula $dx$
1031 Since height multiplied by width was the area of each rectangle, we summed
1032 these areas and rewrote this as
1033 \begin_inset Formula $\int\, f(x)\, dx$
1036 , or, in this specific case,
1037 \begin_inset Formula $\int\,\sqrt{x}\, dx$
1043 \begin_layout Standard
1044 To find the volume of our rotated figure the prodecure is quite similar.
1045 Begin by rotating each rectangle about the x-axis.
1046 This creates a series of cylinders.
1047 \begin_inset Flex Sidenote
1050 \begin_layout Plain Layout
1051 The text refers to these cylinders as "disks".
1052 This is standard practice in all the Calculus books I checked.
1057 Then, we can find the volume of each cylinder/disk.
1058 The basic formula is:
1061 \begin_layout Standard
1062 \begin_inset Formula
1072 \begin_layout Standard
1075 \begin_inset Formula $h$
1078 is the height of the cylinder (width of the rectangle)
1079 \begin_inset Formula $dx$
1083 The area of each figure is a circle where
1084 \begin_inset Formula $A=\pi r^{2}$
1088 The radius in this case is the function
1089 \begin_inset Formula $f(x)$
1096 \begin_layout Standard
1097 \begin_inset Formula
1107 \begin_layout Standard
1109 In our specific case,
1112 \begin_layout Standard
1113 \begin_inset Formula
1115 A & = & \pi\left(\sqrt{x}\right)^{2}\\
1124 \begin_layout Standard
1125 To calculate the volume of one disk, we have
1128 \begin_layout Standard
1129 \begin_inset Formula
1139 \begin_layout Standard
1141 or, in the general case
1144 \begin_layout Standard
1145 \begin_inset Formula
1155 \begin_layout Standard
1156 To find the volume of the figure between points
1157 \begin_inset Formula $a$
1161 \begin_inset Formula $b$
1164 we sum the volumes by means of integration:
1167 \begin_layout Standard
1168 \begin_inset Formula
1170 \int_{a}^{b}\,\pi f^{2}(x)\, dx
1178 \begin_layout Standard
1180 In the specific example, over the interval
1181 \begin_inset Formula $[0,4]$
1187 \begin_layout Standard
1188 \begin_inset Formula
1190 \int_{0}^{4}\,\pi x\, dx & = & \pi\int_{0}^{4}\, x\, dx\\
1191 & = & \pi\left.\left(\frac{x^{2}}{2}\right)\right|_{0}^{4}\\
1192 & = & \pi\left(\frac{4^{2}}{2}-0\right)\\
1201 \begin_layout Standard
1202 \begin_inset Flex NewThought
1205 \begin_layout Plain Layout
1211 a special hole down the length of the cup we just worked with.
1212 It is made with a quadratic shaped bit.
1213 \begin_inset Flex Sidenote
1216 \begin_layout Plain Layout
1217 I have no idea how I'd do this in real life, but I'm making a point.
1222 I find that the hole the bit makes can be modeled with the function
1223 \begin_inset Formula $g(x)=\frac{x^{2}}{16}$
1227 I would need to subtract the volume of the material removed from the volume
1229 \begin_inset Quotes eld
1233 \begin_inset Quotes erd
1237 Each individual cylinder would become like a
1238 \begin_inset Quotes eld
1242 \begin_inset Quotes erd
1246 To get the area of one washer, I would use the formula
1249 \begin_layout Standard
1250 \begin_inset Float marginfigure
1255 \begin_layout Plain Layout
1256 \begin_inset Box Boxed
1266 height_special "totalheight"
1269 \begin_layout Plain Layout
1270 Here I used RLPlot to draw the square root function and the quadratic function.
1271 Then I used Inkscape to shade the area between them.
1277 \begin_inset Caption Standard
1279 \begin_layout Plain Layout
1281 \begin_inset Formula $f(x)$
1285 \begin_inset Formula $g(x)$
1288 and the area left by
1289 \begin_inset Formula $f(x)-g(x)$
1305 \begin_layout Standard
1306 \begin_inset Formula
1308 A_{washer} & = & A_{cup}-A_{drill}\\
1309 & = & \pi f^{2}(x)-\pi g^{2}(x)\\
1310 & = & \pi\left(f^{2}(x)-g^{2}(x)\right)
1318 \begin_layout Standard
1319 The volume of each washer would be
1322 \begin_layout Standard
1323 \begin_inset Formula
1325 V_{washer} & = & A_{washer}\, dx\\
1326 & = & \pi\left(f^{2}(x)-g^{2}(x)\right)\, dx
1334 \begin_layout Standard
1336 Then, by summing the volumes of all the washers between points
1337 \begin_inset Formula $a$
1341 \begin_inset Formula $b$
1344 , the integral is derived:
1347 \begin_layout Standard
1348 \begin_inset Formula
1350 \int_{a}^{b}\,\pi\left(f^{2}(x)-g^{2}(x)\right)\, dx
1358 \begin_layout Standard
1359 In the case of our quadratic drill bit::
1360 \begin_inset Float marginfigure
1365 \begin_layout Plain Layout
1366 \begin_inset Box Boxed
1376 height_special "totalheight"
1379 \begin_layout Plain Layout
1380 This was the rotated set of 2 functions.
1386 \begin_inset Caption Standard
1388 \begin_layout Plain Layout
1389 The cup with a quadratic hole drilled down its length
1402 \begin_layout Standard
1403 \begin_inset Formula
1405 \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\\
1406 & = & \pi\left(\int_{0}^{4}\, x\, dx-\int_{0}^{4}\,\frac{x^{4}}{256}\, dx\right)\\
1407 & = & \pi\left(\left.\left(\frac{x^{2}}{2}\right)\right|_{0}^{4}-\left.\left(\frac{x^{5}}{1280}\right)\right|_{0}^{4}\right)\\
1408 & = & \pi\left(\left(\frac{4^{2}}{2}-0\right)-\left(\frac{4^{5}}{1280}-0\right)\right)\\
1409 & = & \pi\left(8-0.8\right)\\
1418 \begin_layout Standard
1422 \begin_layout Section
1426 \begin_layout Itemize
1427 p114: 1, 4, 5, 6, 8, 10, 12, 15
1430 \begin_layout Standard
1431 \begin_inset CommandInset bibtex
1433 bibfiles "biblioExample"