1 #LyX 2.1 created this file. For more info see http://www.lyx.org/
6 \use_default_options true
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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 bibtex
26 \index_command default
27 \paperfontsize default
31 \pdf_bookmarksnumbered false
32 \pdf_bookmarksopen true
33 \pdf_bookmarksopenlevel 1
41 \use_package amsmath 1
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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 default
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' (put this in the
109 \begin_inset Quotes eld
113 \begin_inset Quotes erd
116 field of Document\SpecialChar \menuseparator
117 Settings \SpecialChar \menuseparator
118 Document Class) to get rid of the errors, but
119 this also removes letterspacing, an important part of the Tufte design.
133 \begin_inset Note Note
136 \begin_layout Plain Layout
137 author of this example file: Jason Waskiewicz
145 \begin_layout Standard
146 \begin_inset CommandInset toc
147 LatexCommand tableofcontents
154 \begin_layout Chapter
155 The Features of the Tufte-book Class
158 \begin_layout Standard
159 In this document, it was endeavored to show some of the features of the
165 In the first chapter, their use is outlined.
166 In the second chapter, their use through a handout that was created in
167 a calculus class is demonstrated.
170 \begin_layout Section
174 \begin_layout Standard
179 class is based on the work of
184 It provides the same functionality as the
188 class with book-specific additions.
189 Tufte's documents consist of a rather narrow column of text and a wide
190 column of margin notes and margin figures.
191 This is to improve readability.
194 \begin_layout Standard
195 The features provided by this format include:
198 \begin_layout Itemize
202 \begin_layout Itemize
203 Ordinary figures in text with captions in margins
206 \begin_layout Itemize
207 Full width figures and text when needed
210 \begin_layout Itemize
211 \begin_inset Quotes eld
215 \begin_inset Quotes erd
221 \begin_layout Itemize
222 Limited layers of sections and subsections
225 \begin_layout Standard
226 In this sample document, some of these features are demonstrated.
227 For a full demonstration, visit the tufte-latex website:
228 \begin_inset Flex URL
231 \begin_layout Plain Layout
233 http://code.google.com/p/tufte-latex
241 \begin_layout Section
245 \begin_layout Standard
247 \begin_inset Quotes eld
251 \begin_inset Quotes erd
254 rather than justified.
255 \begin_inset Flex Sidenote
258 \begin_layout Plain Layout
259 To get justified text, add the option
269 Document\SpecialChar \menuseparator
270 Settings\SpecialChar \menuseparator
278 Ragged right text is used in most of his works, but the class option
282 is provided to change this.
285 \begin_layout Standard
286 Tufte also formats his pages asymmetrically.
287 This means that the marginalia appear on the right side on each page, whether
289 If you prefer, you can change that and have symmetric layout, as common
290 in traditional book typography, by using the
295 \begin_inset Flex Sidenote
298 \begin_layout Plain Layout
299 To create a symmetric layout, add the option
309 Document\SpecialChar \menuseparator
310 Settings\SpecialChar \menuseparator
321 \begin_layout Standard
322 Finally, Tufte does not number his chapters or his sections.
323 If you like to refer to sections by number, move the
329 Document\SpecialChar \menuseparator
330 Settings\SpecialChar \menuseparator
333 to the very right (as done in this document).
334 \begin_inset Flex Marginnote
337 \begin_layout Plain Layout
346 \begin_layout Section
350 \begin_layout Standard
351 Tufte uses ordinary figure floats such as the following:
354 \begin_layout Standard
355 \begin_inset Float figure
360 \begin_layout Plain Layout
361 \begin_inset Box Boxed
371 height_special "totalheight"
374 \begin_layout Plain Layout
375 Imagine your favorite figure inside this box instead of this boring text.
381 \begin_inset Caption Standard
383 \begin_layout Plain Layout
384 An ordinary figure float.
397 \begin_layout Standard
398 Furthermore, he uses margin figures, as shown in Fig.
403 \begin_inset CommandInset ref
405 reference "fig:margin-figure"
412 \begin_layout Standard
413 \begin_inset VSpace 5theight%
419 \begin_layout Standard
420 \begin_inset Float marginfigure
425 \begin_layout Plain Layout
426 \begin_inset Box Boxed
436 height_special "totalheight"
439 \begin_layout Plain Layout
440 Imagine your favorite photograph of a squirrel inside this box instead of
447 \begin_inset Caption Standard
449 \begin_layout Plain Layout
451 \begin_inset CommandInset label
453 name "fig:margin-figure"
470 \begin_layout Standard
471 \begin_inset Note Greyedout
474 \begin_layout Plain Layout
479 If you are using margin figures or tables you must use the default float
480 placement option in the document settings under
496 \begin_layout Standard
497 In the same vein, the
501 class allows the use of tables, both in the margins and in the text.
502 The margin tables are recommended for a small set of data to illustrate
504 \begin_inset Quotes eld
507 Look, distance-time data is quadratic when the object is falling.
508 \begin_inset Quotes erd
511 More detailed data such as flame test results and comments should be put
512 in a full-width table instead.
515 \begin_layout Standard
520 provides a full-width figure.
521 This one takes up the entire width of the page, i.
522 \begin_inset space \thinspace{}
531 \begin_inset CommandInset ref
533 reference "fig:full-width-figure"
540 \begin_layout Standard
541 \begin_inset Float figure
546 \begin_layout Plain Layout
547 \begin_inset Box Boxed
557 height_special "totalheight"
560 \begin_layout Plain Layout
561 Imagine your favorite photograph of a squirrel inside this box instead of
568 \begin_inset VSpace defskip
574 \begin_layout Plain Layout
575 \begin_inset Caption Standard
577 \begin_layout Plain Layout
579 \begin_inset CommandInset label
581 name "fig:full-width-figure"
598 \begin_layout Section
602 \begin_layout Standard
603 One of the most prominent and distinctive features of this style is the
604 extensive use of sidenotes.
605 There is a wide margin to provide ample room for sidenotes and small figures.
606 Any footnotes will automatically be converted to sidenotes.
610 \begin_layout Plain Layout
611 This is a sidenote that was entered using a
620 Alternatively, you can also use the
624 inset directly; you'll find it in the
626 Insert\SpecialChar \menuseparator
630 \begin_inset Flex Sidenote
633 \begin_layout Plain Layout
634 This is a sidenote that was entered using a
646 \begin_layout Standard
647 If you like to place ancillary information in the margin without the sidenote
648 mark (the superscript number), you can use the
654 \begin_inset Flex Marginnote
657 \begin_layout Plain Layout
658 This is Tufte's margin note.
659 Notice that there isn't a number preceding the note, and there is no number
660 in the main text where this note was written.
665 The normal margin note will work as well, but it will look rather odd.
666 \begin_inset Marginal
669 \begin_layout Plain Layout
670 This is a normal margin note.
679 \begin_layout Standard
680 \begin_inset Flex NewThought
683 \begin_layout Plain Layout
689 innovation is Tufte's
695 Edit\SpecialChar \menuseparator
696 TextStyle\SpecialChar \menuseparator
700 It introduces new thoughts by means of small caps, as demonstrated in this
705 \begin_layout Standard
706 The Tufte document classes include two new character styles and some improvement
707 s on existing commands for letterspacing.
710 \begin_layout Standard
711 When setting strings of
712 \begin_inset Flex AllCaps
715 \begin_layout Plain Layout
722 \begin_inset Flex SmallCaps
725 \begin_layout Plain Layout
731 , the letterspacing---that is, the spacing between the letters---should
732 be increased slightly.
733 \begin_inset CommandInset citation
745 Edit\SpecialChar \menuseparator
746 TextStyle\SpecialChar \menuseparator
749 ) has proper letterspacing for strings of
750 \begin_inset Flex AllCaps
753 \begin_layout Plain Layout
765 Edit\SpecialChar \menuseparator
766 TextStyle\SpecialChar \menuseparator
769 ) has letterspacing for
770 \begin_inset Flex SmallCaps
773 \begin_layout Plain Layout
774 small capital letters
780 These commands will also automatically convert the case of the text to
781 upper- or lowercase, respectively.
784 \begin_layout Standard
789 shape has also been redefined to include letterspacing.
790 Its case is left as is, however.
791 This allows one to use both uppercase and lowercase letters:
793 The Initial Letters Of The Words In This Sentence Are Capitalized.
796 \begin_layout Standard
801 paragraph environment provides a paragraph layout that stretches across
802 the main text block and the sidenotes area:
805 \begin_layout Full Width
806 Lorem ipsum dolor sit amet, consectetuer adipiscing elit.
807 Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae, felis.
808 Curabitur dictum gravida mauris.
809 Nam arcu libero, nonummy eget, consectetuer id, vulputate a, magna.
810 Donec vehicula augue eu neque.
811 Pellentesque habitant morbi tristique senectus et netus et malesuada fames
814 Cras viverra metus rhoncus sem.
815 Nulla et lectus vestibulum urna fringilla ultrices.
816 Phasellus eu tellus sit amet tortor gravida placerat.
817 Integer sapien est, iaculis in, pretium quis, viverra ac, nunc.
818 Praesent eget sem vel leo ultrices bibendum.
820 Morbi dolor nulla, malesuada eu, pulvinar at, mollis ac, nulla.
821 Curabitur auctor semper nulla.
822 Donec varius orci eget risus.
823 Duis nibh mi, congue eu, accumsan eleifend, sagittis quis, diam.
824 Duis eget orci sit amet orci dignissim rutrum.
827 \begin_layout Section
831 \begin_layout Standard
832 References are placed alongside their citations as sidenotes, as well.
833 This can be accomplished using the normal citation command.
837 \begin_layout Plain Layout
838 The previous section includes a citation.
846 \begin_layout Standard
847 The complete list of references may also be printed automatically by using
850 Insert\SpecialChar \menuseparator
851 Lists/TOC\SpecialChar \menuseparator
858 (see the end of this document for an example.) If you do not want to print
859 a bibliography at the end of your document, place the
867 inset inside a LyX note and use the LaTeX command
876 \begin_layout Chapter
877 Calculation of Volume: Sections 2.12–2.13
880 \begin_layout Standard
881 Imagine taking a function like
882 \begin_inset Formula $y=\sqrt{x}$
885 and rotating it in 3 dimensions around the x-axis.
886 The resulting shape would look somewhat like a cup (on its side).
887 Interestingly, integration empowers us to do exactly this and to find out
888 how much water that cup could hold.
891 \begin_layout Section
895 \begin_layout Standard
896 \begin_inset Float marginfigure
901 \begin_layout Plain Layout
902 \begin_inset Box Boxed
912 height_special "totalheight"
915 \begin_layout Plain Layout
916 I had a graph of the square root function here.
922 \begin_inset Caption Standard
924 \begin_layout Plain Layout
925 \begin_inset CommandInset label
927 name "mar:A-graph-of"
932 \begin_inset Formula $f(x)=\sqrt{x}$
948 \begin_layout Standard
949 \begin_inset Float marginfigure
954 \begin_layout Plain Layout
955 \begin_inset Box Boxed
965 height_special "totalheight"
968 \begin_layout Plain Layout
969 Here I rotated the square root function and then drew a disk on the figure
970 to illustrate how I would calculate the volume of the figure.
976 \begin_inset Caption Standard
978 \begin_layout Plain Layout
979 \begin_inset CommandInset label
986 \begin_inset Formula $f(x)=\sqrt{x}$
989 rotated about the x-axis and with additional remarks for integration.
1002 \begin_layout Standard
1004 \begin_inset CommandInset ref
1006 reference "mar:A-graph-of"
1010 shows the plot of the function
1011 \begin_inset Formula $f(x)=\sqrt{x}.$
1014 Now, imagine that we rotate that function about the x-axis.
1015 The resulting figure would be somewhat like figure
1016 \begin_inset CommandInset ref
1018 reference "mar:rotated"
1023 This is akin to a cup lying on its side.
1024 For the sake of clarity, the artist (me) drew a circle on the end of the
1025 figure to show that it is indeed rotated.
1028 \begin_layout Standard
1029 Now, suppose we wished to find the volume of the figure.
1030 When we integrated the original square root function to find its area,
1031 we imagined a series of rectangles inside the figure.
1033 \begin_inset Formula $h=f(x)$
1037 \begin_inset Formula $dx$
1041 Since height multiplied by width was the area of each rectangle, we summed
1042 these areas and rewrote this as
1043 \begin_inset Formula $\int\, f(x)\, dx$
1046 , or, in this specific case,
1047 \begin_inset Formula $\int\,\sqrt{x}\, dx$
1053 \begin_layout Standard
1054 To find the volume of our rotated figure the prodecure is quite similar.
1055 Begin by rotating each rectangle about the x-axis.
1056 This creates a series of cylinders.
1057 \begin_inset Flex Sidenote
1060 \begin_layout Plain Layout
1061 The text refers to these cylinders as "disks".
1062 This is standard practice in all the Calculus books I checked.
1067 Then, we can find the volume of each cylinder/disk.
1068 The basic formula is:
1071 \begin_layout Standard
1072 \begin_inset Formula
1082 \begin_layout Standard
1085 \begin_inset Formula $h$
1088 is the height of the cylinder (width of the rectangle)
1089 \begin_inset Formula $dx$
1093 The area of each figure is a circle where
1094 \begin_inset Formula $A=\pi r^{2}$
1098 The radius in this case is the function
1099 \begin_inset Formula $f(x)$
1106 \begin_layout Standard
1107 \begin_inset Formula
1117 \begin_layout Standard
1119 In our specific case,
1122 \begin_layout Standard
1123 \begin_inset Formula
1125 A & = & \pi\left(\sqrt{x}\right)^{2}\\
1134 \begin_layout Standard
1135 To calculate the volume of one disk, we have
1138 \begin_layout Standard
1139 \begin_inset Formula
1149 \begin_layout Standard
1151 or, in the general case
1154 \begin_layout Standard
1155 \begin_inset Formula
1165 \begin_layout Standard
1166 To find the volume of the figure between points
1167 \begin_inset Formula $a$
1171 \begin_inset Formula $b$
1174 we sum the volumes by means of integration:
1177 \begin_layout Standard
1178 \begin_inset Formula
1180 \int_{a}^{b}\,\pi f^{2}(x)\, dx
1188 \begin_layout Standard
1190 In the specific example, over the interval
1191 \begin_inset Formula $[0,4]$
1197 \begin_layout Standard
1198 \begin_inset Formula
1200 \int_{0}^{4}\,\pi x\, dx & = & \pi\int_{0}^{4}\, x\, dx\\
1201 & = & \pi\left.\left(\frac{x^{2}}{2}\right)\right|_{0}^{4}\\
1202 & = & \pi\left(\frac{4^{2}}{2}-0\right)\\
1211 \begin_layout Standard
1212 \begin_inset Flex NewThought
1215 \begin_layout Plain Layout
1221 a special hole down the length of the cup we just worked with.
1222 It is made with a quadratic shaped bit.
1223 \begin_inset Flex Sidenote
1226 \begin_layout Plain Layout
1227 I have no idea how I'd do this in real life, but I'm making a point.
1232 I find that the hole the bit makes can be modeled with the function
1233 \begin_inset Formula $g(x)=\frac{x^{2}}{16}$
1237 I would need to subtract the volume of the material removed from the volume
1239 \begin_inset Quotes eld
1243 \begin_inset Quotes erd
1247 Each individual cylinder would become like a
1248 \begin_inset Quotes eld
1252 \begin_inset Quotes erd
1256 To get the area of one washer, I would use the formula
1259 \begin_layout Standard
1260 \begin_inset Float marginfigure
1265 \begin_layout Plain Layout
1266 \begin_inset Box Boxed
1276 height_special "totalheight"
1279 \begin_layout Plain Layout
1280 Here I used RLPlot to draw the square root function and the quadratic function.
1281 Then I used Inkscape to shade the area between them.
1287 \begin_inset Caption Standard
1289 \begin_layout Plain Layout
1291 \begin_inset Formula $f(x)$
1295 \begin_inset Formula $g(x)$
1298 and the area left by
1299 \begin_inset Formula $f(x)-g(x)$
1315 \begin_layout Standard
1316 \begin_inset Formula
1318 A_{washer} & = & A_{cup}-A_{drill}\\
1319 & = & \pi f^{2}(x)-\pi g^{2}(x)\\
1320 & = & \pi\left(f^{2}(x)-g^{2}(x)\right)
1328 \begin_layout Standard
1329 The volume of each washer would be
1332 \begin_layout Standard
1333 \begin_inset Formula
1335 V_{washer} & = & A_{washer}\, dx\\
1336 & = & \pi\left(f^{2}(x)-g^{2}(x)\right)\, dx
1344 \begin_layout Standard
1346 Then, by summing the volumes of all the washers between points
1347 \begin_inset Formula $a$
1351 \begin_inset Formula $b$
1354 , the integral is derived:
1357 \begin_layout Standard
1358 \begin_inset Formula
1360 \int_{a}^{b}\,\pi\left(f^{2}(x)-g^{2}(x)\right)\, dx
1368 \begin_layout Standard
1369 In the case of our quadratic drill bit::
1370 \begin_inset Float marginfigure
1375 \begin_layout Plain Layout
1376 \begin_inset Box Boxed
1386 height_special "totalheight"
1389 \begin_layout Plain Layout
1390 This was the rotated set of 2 functions.
1396 \begin_inset Caption Standard
1398 \begin_layout Plain Layout
1399 The cup with a quadratic hole drilled down its length
1412 \begin_layout Standard
1413 \begin_inset Formula
1415 \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\\
1416 & = & \pi\left(\int_{0}^{4}\, x\, dx-\int_{0}^{4}\,\frac{x^{4}}{256}\, dx\right)\\
1417 & = & \pi\left(\left.\left(\frac{x^{2}}{2}\right)\right|_{0}^{4}-\left.\left(\frac{x^{5}}{1280}\right)\right|_{0}^{4}\right)\\
1418 & = & \pi\left(\left(\frac{4^{2}}{2}-0\right)-\left(\frac{4^{5}}{1280}-0\right)\right)\\
1419 & = & \pi\left(8-0.8\right)\\
1428 \begin_layout Standard
1432 \begin_layout Section
1436 \begin_layout Itemize
1437 p114: 1, 4, 5, 6, 8, 10, 12, 15
1440 \begin_layout Standard
1441 \begin_inset CommandInset bibtex
1443 bibfiles "biblioExample"