1 #LyX 2.0 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
15 \font_default_family default
16 \use_non_tex_fonts false
23 \default_output_format default
25 \bibtex_command default
26 \index_command default
27 \paperfontsize default
31 \pdf_bookmarksnumbered false
32 \pdf_bookmarksopen true
33 \pdf_bookmarksopenlevel 1
48 \paperorientation portrait
57 \paragraph_separation indent
58 \paragraph_indentation default
59 \quotes_language english
62 \paperpagestyle default
63 \tracking_changes false
72 \begin_layout Standard
73 \begin_inset Note Note
76 \begin_layout Plain Layout
81 : To be able to view your file as PDF you must have the LaTeX-package
85 installed to your LaTeX system.
86 If you are using MiKTeX, you will automatically be asked to install this
87 package when previewing your file, if you are using TeXLive, use TeXLive's
102 \begin_inset Note Note
105 \begin_layout Plain Layout
106 author of this example file: Jason Waskiewicz
114 \begin_layout Standard
115 \begin_inset CommandInset toc
116 LatexCommand tableofcontents
123 \begin_layout Chapter
124 The Features of the Tufte-book Class
127 \begin_layout Standard
128 In this document, it was endeavored to show some of the features of the
134 In the first chapter, their use is outlined.
135 In the second chapter, their use through a handout that was created in
136 a calculus class is demonstrated.
139 \begin_layout Section
143 \begin_layout Standard
148 class is based on the work of
153 It provides the same functionality as the
157 class with book-specific additions.
158 Tufte's documents consist of a rather narrow column of text and a wide
159 column of margin notes and margin figures.
160 This is to improve readability.
163 \begin_layout Standard
164 The features provided by this format include:
167 \begin_layout Itemize
171 \begin_layout Itemize
172 Ordinary figures in text with captions in margins
175 \begin_layout Itemize
176 Full width figures and text when needed
179 \begin_layout Itemize
180 \begin_inset Quotes eld
184 \begin_inset Quotes erd
190 \begin_layout Itemize
191 Limited layers of sections and subsections
194 \begin_layout Standard
195 In this sample document, some of these features are demonstrated.
196 For a full demonstration, visit the tufte-latex website:
197 \begin_inset Flex URL
200 \begin_layout Plain Layout
202 http://code.google.com/p/tufte-latex
210 \begin_layout Section
214 \begin_layout Standard
216 \begin_inset Quotes eld
220 \begin_inset Quotes erd
223 rather than justified.
224 \begin_inset Flex Sidenote
227 \begin_layout Plain Layout
228 To get justified text, add the option
238 Document\SpecialChar \menuseparator
239 Settings\SpecialChar \menuseparator
247 Ragged right text is used in most of his works, but the class option
251 is provided to change this.
254 \begin_layout Standard
255 Tufte also formats his pages asymmetrically.
256 This means that the marginalia appear on the right side on each page, whether
258 If you prefer, you can change that and have symmetric layout, as common
259 in traditional book typography, by using the
264 \begin_inset Flex Sidenote
267 \begin_layout Plain Layout
268 To create a symmetric layout, add the option
278 Document\SpecialChar \menuseparator
279 Settings\SpecialChar \menuseparator
290 \begin_layout Standard
291 Finally, Tufte does not number his chapters or his sections.
292 If you like to refer to sections by number, move the
298 Document\SpecialChar \menuseparator
299 Settings\SpecialChar \menuseparator
302 to the very right (as done in this document).
303 \begin_inset Flex Marginnote
306 \begin_layout Plain Layout
315 \begin_layout Section
319 \begin_layout Standard
320 Tufte uses ordinary figure floats such as the following:
323 \begin_layout Standard
324 \begin_inset Float figure
329 \begin_layout Plain Layout
330 \begin_inset Box Boxed
340 height_special "totalheight"
343 \begin_layout Plain Layout
344 Imagine your favorite figure inside this box instead of this boring text.
352 \begin_layout Plain Layout
353 An ordinary figure float.
366 \begin_layout Standard
367 Furthermore, he uses margin figures, as shown in Fig.
372 \begin_inset CommandInset ref
374 reference "fig:margin-figure"
381 \begin_layout Standard
382 \begin_inset Float marginfigure
387 \begin_layout Plain Layout
388 \begin_inset Box Boxed
398 height_special "totalheight"
401 \begin_layout Plain Layout
402 Imagine your favorite photograph of a squirrel inside this box instead of
411 \begin_layout Plain Layout
413 \begin_inset CommandInset label
415 name "fig:margin-figure"
432 \begin_layout Standard
433 In the same vein, the
437 class allows the use of tables, both in the margins and in the text.
438 The margin tables are recommended for a small set of data to illustrate
440 \begin_inset Quotes eld
443 Look, distance-time data is quadratic when the object is falling.
444 \begin_inset Quotes erd
447 More detailed data such as flame test results and comments should be put
448 in a full-width table instead.
451 \begin_layout Standard
456 provides a full-width figure.
457 This one takes up the entire width of the page, i.
458 \begin_inset space \thinspace{}
467 \begin_inset CommandInset ref
469 reference "fig:full-width-figure"
476 \begin_layout Standard
477 \begin_inset Float figure
482 \begin_layout Plain Layout
483 \begin_inset Box Boxed
493 height_special "totalheight"
496 \begin_layout Plain Layout
497 Imagine your favorite photograph of a squirrel inside this box instead of
504 \begin_inset VSpace defskip
510 \begin_layout Plain Layout
513 \begin_layout Plain Layout
515 \begin_inset CommandInset label
517 name "fig:full-width-figure"
534 \begin_layout Section
538 \begin_layout Standard
539 One of the most prominent and distinctive features of this style is the
540 extensive use of sidenotes.
541 There is a wide margin to provide ample room for sidenotes and small figures.
542 Any footnotes will automatically be converted to sidenotes.
546 \begin_layout Plain Layout
547 This is a sidenote that was entered using a
556 Alternatively, you can also use the
560 inset directly; you'll find it in the
562 Insert\SpecialChar \menuseparator
566 \begin_inset Flex Sidenote
569 \begin_layout Plain Layout
570 This is a sidenote that was entered using a
582 \begin_layout Standard
583 If you like to place ancillary information in the margin without the sidenote
584 mark (the superscript number), you can use the
590 \begin_inset Flex Marginnote
593 \begin_layout Plain Layout
594 This is Tufte's margin note.
595 Notice that there isn't a number preceding the note, and there is no number
596 in the main text where this note was written.
601 The normal margin note will work as well, but it will look rather odd.
602 \begin_inset Marginal
605 \begin_layout Plain Layout
606 This is a normal margin note.
615 \begin_layout Standard
616 \begin_inset Flex NewThought
619 \begin_layout Plain Layout
625 innovation is Tufte's
631 Edit\SpecialChar \menuseparator
632 TextStyle\SpecialChar \menuseparator
636 It introduces new thoughts by means of small caps, as demonstrated in this
641 \begin_layout Standard
642 The Tufte document classes include two new character styles and some improvement
643 s on existing commands for letterspacing.
646 \begin_layout Standard
647 When setting strings of
648 \begin_inset Flex AllCaps
651 \begin_layout Plain Layout
658 \begin_inset Flex SmallCaps
661 \begin_layout Plain Layout
667 , the letterspacing---that is, the spacing between the letters---should
668 be increased slightly.
669 \begin_inset CommandInset citation
681 Edit\SpecialChar \menuseparator
682 TextStyle\SpecialChar \menuseparator
685 ) has proper letterspacing for strings of
686 \begin_inset Flex AllCaps
689 \begin_layout Plain Layout
701 Edit\SpecialChar \menuseparator
702 TextStyle\SpecialChar \menuseparator
705 ) has letterspacing for
706 \begin_inset Flex SmallCaps
709 \begin_layout Plain Layout
710 small capital letters
716 These commands will also automatically convert the case of the text to
717 upper- or lowercase, respectively.
720 \begin_layout Standard
725 shape has also been redefined to include letterspacing.
726 Its case is left as is, however.
727 This allows one to use both uppercase and lowercase letters:
729 The Initial Letters Of The Words In This Sentence Are Capitalized.
732 \begin_layout Standard
737 paragraph environment provides a paragraph layout that stretches across
738 the main text block and the sidenotes area:
741 \begin_layout Full Width
742 Lorem ipsum dolor sit amet, consectetuer adipiscing elit.
743 Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae, felis.
744 Curabitur dictum gravida mauris.
745 Nam arcu libero, nonummy eget, consectetuer id, vulputate a, magna.
746 Donec vehicula augue eu neque.
747 Pellentesque habitant morbi tristique senectus et netus et malesuada fames
750 Cras viverra metus rhoncus sem.
751 Nulla et lectus vestibulum urna fringilla ultrices.
752 Phasellus eu tellus sit amet tortor gravida placerat.
753 Integer sapien est, iaculis in, pretium quis, viverra ac, nunc.
754 Praesent eget sem vel leo ultrices bibendum.
756 Morbi dolor nulla, malesuada eu, pulvinar at, mollis ac, nulla.
757 Curabitur auctor semper nulla.
758 Donec varius orci eget risus.
759 Duis nibh mi, congue eu, accumsan eleifend, sagittis quis, diam.
760 Duis eget orci sit amet orci dignissim rutrum.
763 \begin_layout Section
767 \begin_layout Standard
768 References are placed alongside their citations as sidenotes, as well.
769 This can be accomplished using the normal citation command.
773 \begin_layout Plain Layout
774 The previous section includes a citation.
782 \begin_layout Standard
783 The complete list of references may also be printed automatically by using
786 Insert\SpecialChar \menuseparator
787 Lists/TOC\SpecialChar \menuseparator
794 (see the end of this document for an example.) If you do not want to print
795 a bibliography at the end of your document, place the
803 inset inside a LyX note and use the LaTeX command
812 \begin_layout Chapter
813 Calculation of Volume: Sections 2.12–2.13
816 \begin_layout Standard
817 Imagine taking a function like
818 \begin_inset Formula $y=\sqrt{x}$
821 and rotating it in 3 dimensions around the x-axis.
822 The resulting shape would look somewhat like a cup (on its side).
823 Interestingly, integration empowers us to do exactly this and to find out
824 how much water that cup could hold.
827 \begin_layout Section
831 \begin_layout Standard
832 \begin_inset Float marginfigure
837 \begin_layout Plain Layout
838 \begin_inset Box Boxed
848 height_special "totalheight"
851 \begin_layout Plain Layout
852 I had a graph of the square root function here.
860 \begin_layout Plain Layout
861 \begin_inset CommandInset label
863 name "mar:A-graph-of"
868 \begin_inset Formula $f(x)=\sqrt{x}$
884 \begin_layout Standard
885 \begin_inset Float marginfigure
890 \begin_layout Plain Layout
891 \begin_inset Box Boxed
901 height_special "totalheight"
904 \begin_layout Plain Layout
905 Here I rotated the square root function and then drew a disk on the figure
906 to illustrate how I would calculate the volume of the figure.
914 \begin_layout Plain Layout
915 \begin_inset CommandInset label
922 \begin_inset Formula $f(x)=\sqrt{x}$
925 rotated about the x-axis and with additional remarks for integration.
938 \begin_layout Standard
940 \begin_inset CommandInset ref
942 reference "mar:A-graph-of"
946 shows the plot of the function
947 \begin_inset Formula $f(x)=\sqrt{x}.$
950 Now, imagine that we rotate that function about the x-axis.
951 The resulting figure would be somewhat like figure
952 \begin_inset CommandInset ref
954 reference "mar:rotated"
959 This is akin to a cup lying on its side.
960 For the sake of clarity, the artist (me) drew a circle on the end of the
961 figure to show that it is indeed rotated.
964 \begin_layout Standard
965 Now, suppose we wished to find the volume of the figure.
966 When we integrated the original square root function to find its area,
967 we imagined a series of rectangles inside the figure.
969 \begin_inset Formula $h=f(x)$
973 \begin_inset Formula $dx$
977 Since height multiplied by width was the area of each rectangle, we summed
978 these areas and rewrote this as
979 \begin_inset Formula $\int\, f(x)\, dx$
982 , or, in this specific case,
983 \begin_inset Formula $\int\,\sqrt{x}\, dx$
989 \begin_layout Standard
990 To find the volume of our rotated figure the prodecure is quite similar.
991 Begin by rotating each rectangle about the x-axis.
992 This creates a series of cylinders.
993 \begin_inset Flex Sidenote
996 \begin_layout Plain Layout
997 The text refers to these cylinders as "disks".
998 This is standard practice in all the Calculus books I checked.
1003 Then, we can find the volume of each cylinder/disk.
1004 The basic formula is:
1007 \begin_layout Standard
1008 \begin_inset Formula
1018 \begin_layout Standard
1021 \begin_inset Formula $h$
1024 is the height of the cylinder (width of the rectangle)
1025 \begin_inset Formula $dx$
1029 The area of each figure is a circle where
1030 \begin_inset Formula $A=\pi r^{2}$
1034 The radius in this case is the function
1035 \begin_inset Formula $f(x)$
1042 \begin_layout Standard
1043 \begin_inset Formula
1053 \begin_layout Standard
1055 In our specific case,
1058 \begin_layout Standard
1059 \begin_inset Formula
1061 A & = & \pi\left(\sqrt{x}\right)^{2}\\
1070 \begin_layout Standard
1071 To calculate the volume of one disk, we have
1074 \begin_layout Standard
1075 \begin_inset Formula
1085 \begin_layout Standard
1087 or, in the general case
1090 \begin_layout Standard
1091 \begin_inset Formula
1101 \begin_layout Standard
1102 To find the volume of the figure between points
1103 \begin_inset Formula $a$
1107 \begin_inset Formula $b$
1110 we sum the volumes by means of integration:
1113 \begin_layout Standard
1114 \begin_inset Formula
1116 \int_{a}^{b}\,\pi f^{2}(x)\, dx
1124 \begin_layout Standard
1126 In the specific example, over the interval
1127 \begin_inset Formula $[0,4]$
1133 \begin_layout Standard
1134 \begin_inset Formula
1136 \int_{0}^{4}\,\pi x\, dx & = & \pi\int_{0}^{4}\, x\, dx\\
1137 & = & \pi\left.\left(\frac{x^{2}}{2}\right)\right|_{0}^{4}\\
1138 & = & \pi\left(\frac{4^{2}}{2}-0\right)\\
1147 \begin_layout Standard
1148 \begin_inset Flex NewThought
1151 \begin_layout Plain Layout
1157 a special hole down the length of the cup we just worked with.
1158 It is made with a quadratic shaped bit.
1159 \begin_inset Flex Sidenote
1162 \begin_layout Plain Layout
1163 I have no idea how I'd do this in real life, but I'm making a point.
1168 I find that the hole the bit makes can be modeled with the function
1169 \begin_inset Formula $g(x)=\frac{x^{2}}{16}$
1173 I would need to subtract the volume of the material removed from the volume
1175 \begin_inset Quotes eld
1179 \begin_inset Quotes erd
1183 Each individual cylinder would become like a
1184 \begin_inset Quotes eld
1188 \begin_inset Quotes erd
1192 To get the area of one washer, I would use the formula
1195 \begin_layout Standard
1196 \begin_inset Float marginfigure
1201 \begin_layout Plain Layout
1202 \begin_inset Box Boxed
1212 height_special "totalheight"
1215 \begin_layout Plain Layout
1216 Here I used RLPlot to draw the square root function and the quadratic function.
1217 Then I used Inkscape to shade the area between them.
1223 \begin_inset Caption
1225 \begin_layout Plain Layout
1227 \begin_inset Formula $f(x)$
1231 \begin_inset Formula $g(x)$
1234 and the area left by
1235 \begin_inset Formula $f(x)-g(x)$
1251 \begin_layout Standard
1252 \begin_inset Formula
1254 A_{washer} & = & A_{cup}-A_{drill}\\
1255 & = & \pi f^{2}(x)-\pi g^{2}(x)\\
1256 & = & \pi\left(f^{2}(x)-g^{2}(x)\right)
1264 \begin_layout Standard
1265 The volume of each washer would be
1268 \begin_layout Standard
1269 \begin_inset Formula
1271 V_{washer} & = & A_{washer}\, dx\\
1272 & = & \pi\left(f^{2}(x)-g^{2}(x)\right)\, dx
1280 \begin_layout Standard
1282 Then, by summing the volumes of all the washers between points
1283 \begin_inset Formula $a$
1287 \begin_inset Formula $b$
1290 , the integral is derived:
1293 \begin_layout Standard
1294 \begin_inset Formula
1296 \int_{a}^{b}\,\pi\left(f^{2}(x)-g^{2}(x)\right)\, dx
1304 \begin_layout Standard
1305 In the case of our quadratic drill bit::
1306 \begin_inset Float marginfigure
1311 \begin_layout Plain Layout
1312 \begin_inset Box Boxed
1322 height_special "totalheight"
1325 \begin_layout Plain Layout
1326 This was the rotated set of 2 functions.
1332 \begin_inset Caption
1334 \begin_layout Plain Layout
1335 The cup with a quadratic hole drilled down its length
1348 \begin_layout Standard
1349 \begin_inset Formula
1351 \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\\
1352 & = & \pi\left(\int_{0}^{4}\, x\, dx-\int_{0}^{4}\,\frac{x^{4}}{256}\, dx\right)\\
1353 & = & \pi\left(\left.\left(\frac{x^{2}}{2}\right)\right|_{0}^{4}-\left.\left(\frac{x^{5}}{1280}\right)\right|_{0}^{4}\right)\\
1354 & = & \pi\left(\left(\frac{4^{2}}{2}-0\right)-\left(\frac{4^{5}}{1280}-0\right)\right)\\
1355 & = & \pi\left(8-0.8\right)\\
1364 \begin_layout Standard
1368 \begin_layout Section
1372 \begin_layout Itemize
1373 p114: 1, 4, 5, 6, 8, 10, 12, 15
1376 \begin_layout Standard
1377 \begin_inset CommandInset bibtex
1379 bibfiles "biblioExample"