mirror of
https://git.lyx.org/repos/lyx.git
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a15303b938
Especially after the change to use semantic linefeeds (7b23c76b), the diffs are large and it's hard to figure out what diff is the result of the linefeed change and which diff is the result of an edit. By updating the docs, it will make the edits easier to understand from the diff. This commit used the LyX binary to write the new .lyx files since lyx2lyx does not apply semantic linefeeds. I used the following command: ./development/tools/updatedocs.py [path to 'lyx' binary] A few documents were not updated (e.g., the command sequence used failed because a dialog about a missing dependency was shown). I did not update Additional.lyx for any language since it is undergoing changes. I also didn't change anything in doc/fr since JP is working on some of those. I also didn't change doc/ru since it appears Yuriy already updated those.
1603 lines
27 KiB
Plaintext
1603 lines
27 KiB
Plaintext
#LyX 2.4 created this file. For more info see https://www.lyx.org/
|
||
\lyxformat 612
|
||
\begin_document
|
||
\begin_header
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||
\save_transient_properties true
|
||
\origin /systemlyxdir/examples/Books/
|
||
\textclass tufte-book
|
||
\use_default_options true
|
||
\maintain_unincluded_children no
|
||
\language english
|
||
\language_package default
|
||
\inputencoding utf8
|
||
\fontencoding auto
|
||
\font_roman "default" "default"
|
||
\font_sans "default" "default"
|
||
\font_typewriter "default" "default"
|
||
\font_math "auto" "auto"
|
||
\font_default_family default
|
||
\use_non_tex_fonts false
|
||
\font_sc false
|
||
\font_roman_osf false
|
||
\font_sans_osf false
|
||
\font_typewriter_osf false
|
||
\font_sf_scale 100 100
|
||
\font_tt_scale 100 100
|
||
\use_microtype false
|
||
\use_dash_ligatures false
|
||
\graphics default
|
||
\default_output_format pdf2
|
||
\output_sync 0
|
||
\bibtex_command bibtex
|
||
\index_command default
|
||
\float_placement class
|
||
\float_alignment class
|
||
\paperfontsize default
|
||
\spacing single
|
||
\use_hyperref true
|
||
\pdf_bookmarks true
|
||
\pdf_bookmarksnumbered false
|
||
\pdf_bookmarksopen true
|
||
\pdf_bookmarksopenlevel 1
|
||
\pdf_breaklinks false
|
||
\pdf_pdfborder true
|
||
\pdf_colorlinks false
|
||
\pdf_backref false
|
||
\pdf_pdfusetitle true
|
||
\papersize default
|
||
\use_geometry true
|
||
\use_package amsmath 1
|
||
\use_package amssymb 1
|
||
\use_package cancel 1
|
||
\use_package esint 1
|
||
\use_package mathdots 1
|
||
\use_package mathtools 1
|
||
\use_package mhchem 1
|
||
\use_package stackrel 1
|
||
\use_package stmaryrd 1
|
||
\use_package undertilde 1
|
||
\cite_engine natbib
|
||
\cite_engine_type authoryear
|
||
\biblio_style plain
|
||
\use_bibtopic false
|
||
\use_indices false
|
||
\paperorientation portrait
|
||
\suppress_date false
|
||
\justification true
|
||
\use_refstyle 0
|
||
\use_minted 0
|
||
\use_lineno 0
|
||
\notefontcolor #0000ff
|
||
\index Index
|
||
\shortcut idx
|
||
\color #008000
|
||
\end_index
|
||
\secnumdepth 2
|
||
\tocdepth 2
|
||
\paragraph_separation indent
|
||
\paragraph_indentation default
|
||
\is_math_indent 0
|
||
\math_numbering_side default
|
||
\quotes_style english
|
||
\dynamic_quotes 0
|
||
\papercolumns 1
|
||
\papersides 1
|
||
\paperpagestyle default
|
||
\tablestyle default
|
||
\tracking_changes false
|
||
\output_changes false
|
||
\change_bars false
|
||
\postpone_fragile_content false
|
||
\html_math_output 0
|
||
\html_css_as_file 0
|
||
\html_be_strict false
|
||
\docbook_table_output 0
|
||
\docbook_mathml_prefix 1
|
||
\end_header
|
||
|
||
\begin_body
|
||
|
||
\begin_layout Standard
|
||
\begin_inset Note Note
|
||
status open
|
||
|
||
\begin_layout Plain Layout
|
||
|
||
\series bold
|
||
Note
|
||
\series default
|
||
:
|
||
To be able to view your file as PDF you must have the \SpecialChar LaTeX
|
||
-package
|
||
\family sans
|
||
fpl
|
||
\family default
|
||
installed to your \SpecialChar LaTeX
|
||
system.
|
||
If you are using MiK\SpecialChar TeX
|
||
,
|
||
you will automatically be asked to install this package when previewing your file,
|
||
if you are using \SpecialChar TeX
|
||
Live,
|
||
use \SpecialChar TeX
|
||
Live's package manager.
|
||
\end_layout
|
||
|
||
\begin_layout Plain Layout
|
||
|
||
\series bold
|
||
Note 2
|
||
\series default
|
||
:
|
||
If you wish to compile to PDF with plain \SpecialChar LaTeX
|
||
(instead of pdf\SpecialChar TeX
|
||
),
|
||
there is currently a bug in the Tufte class that causes errors.
|
||
You can add the class option 'nols' (put this in the
|
||
\begin_inset Quotes eld
|
||
\end_inset
|
||
|
||
Custom
|
||
\begin_inset Quotes erd
|
||
\end_inset
|
||
|
||
field of Document\SpecialChar menuseparator
|
||
Settings \SpecialChar menuseparator
|
||
Document Class) to get rid of the errors,
|
||
but this also removes letterspacing,
|
||
an important part of the Tufte design.
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Title
|
||
Tufte Examples
|
||
\end_layout
|
||
|
||
\begin_layout Author
|
||
Fake Author
|
||
\begin_inset Note Note
|
||
status open
|
||
|
||
\begin_layout Plain Layout
|
||
author of this example file:
|
||
Jason Waskiewicz
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\begin_inset CommandInset toc
|
||
LatexCommand tableofcontents
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Chapter
|
||
The Features of the Tufte-book Class
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
In this document,
|
||
it was endeavored to show some of the features of the
|
||
\family sans
|
||
Tufte-book
|
||
\family default
|
||
class.
|
||
In the first chapter,
|
||
their use is outlined.
|
||
In the second chapter,
|
||
their use through a handout that was created in a calculus class is demonstrated.
|
||
\end_layout
|
||
|
||
\begin_layout Section
|
||
Features
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
The
|
||
\family sans
|
||
Tufte-book
|
||
\family default
|
||
class is based on the work of
|
||
\noun on
|
||
Edward Tufte
|
||
\noun default
|
||
.
|
||
It provides the same functionality as the
|
||
\family sans
|
||
Tufte-handout
|
||
\family default
|
||
class with book-specific additions.
|
||
Tufte's documents consist of a rather narrow column of text and a wide column of margin notes and margin figures.
|
||
This is to improve readability.
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
The features provided by this format include:
|
||
\end_layout
|
||
|
||
\begin_layout Itemize
|
||
Margin figures
|
||
\end_layout
|
||
|
||
\begin_layout Itemize
|
||
Ordinary figures in text with captions in margins
|
||
\end_layout
|
||
|
||
\begin_layout Itemize
|
||
Full width figures and text when needed
|
||
\end_layout
|
||
|
||
\begin_layout Itemize
|
||
\begin_inset Quotes eld
|
||
\end_inset
|
||
|
||
Footnotes
|
||
\begin_inset Quotes erd
|
||
\end_inset
|
||
|
||
in margins
|
||
\end_layout
|
||
|
||
\begin_layout Itemize
|
||
Limited layers of sections and subsections
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
In this sample document,
|
||
some of these features are demonstrated.
|
||
For a full demonstration,
|
||
visit the tufte-latex website:
|
||
|
||
\begin_inset Flex URL
|
||
status collapsed
|
||
|
||
\begin_layout Plain Layout
|
||
|
||
https://tufte-latex.github.io/tufte-latex/
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
.
|
||
\end_layout
|
||
|
||
\begin_layout Section
|
||
Page Layout
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
Tufte's margins are
|
||
\begin_inset Quotes eld
|
||
\end_inset
|
||
|
||
ragged right
|
||
\begin_inset Quotes erd
|
||
\end_inset
|
||
|
||
rather than justified.
|
||
\begin_inset Flex Sidenote
|
||
status open
|
||
|
||
\begin_layout Plain Layout
|
||
To get justified text,
|
||
add the option
|
||
\emph on
|
||
justified
|
||
\emph default
|
||
to the
|
||
\emph on
|
||
Custom
|
||
\emph default
|
||
field in
|
||
\family sans
|
||
Document\SpecialChar menuseparator
|
||
Settings\SpecialChar menuseparator
|
||
Document Class
|
||
\family default
|
||
.
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
Ragged right text is used in most of his works,
|
||
but the class option
|
||
\emph on
|
||
justified
|
||
\emph default
|
||
is provided to change this.
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
Tufte also formats his pages asymmetrically.
|
||
This means that the marginalia appear on the right side on each page,
|
||
whether odd or even.
|
||
If you prefer,
|
||
you can change that and have symmetric layout,
|
||
as common in traditional book typography,
|
||
by using the
|
||
\emph on
|
||
symmetric
|
||
\emph default
|
||
class option.
|
||
\begin_inset Flex Sidenote
|
||
status open
|
||
|
||
\begin_layout Plain Layout
|
||
To create a symmetric layout,
|
||
add the option
|
||
\emph on
|
||
symmetric
|
||
\emph default
|
||
to the
|
||
\emph on
|
||
Custom
|
||
\emph default
|
||
field in
|
||
\family sans
|
||
Document\SpecialChar menuseparator
|
||
Settings\SpecialChar menuseparator
|
||
Document Class
|
||
\family default
|
||
.
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
Finally,
|
||
Tufte does not number his chapters or his sections.
|
||
If you like to refer to sections by number,
|
||
move the
|
||
\emph on
|
||
Numbering
|
||
\emph default
|
||
slider in
|
||
\family sans
|
||
Document\SpecialChar menuseparator
|
||
Settings\SpecialChar menuseparator
|
||
Numbering & TOC
|
||
\family default
|
||
to the very right (as done in this document).
|
||
\begin_inset Flex Marginnote
|
||
status collapsed
|
||
|
||
\begin_layout Plain Layout
|
||
marginnote
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Section
|
||
Figures
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
Tufte uses ordinary figure floats such as the following:
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\begin_inset Float figure
|
||
placement document
|
||
alignment document
|
||
wide false
|
||
sideways false
|
||
status open
|
||
|
||
\begin_layout Plain Layout
|
||
\begin_inset Box Boxed
|
||
position "t"
|
||
hor_pos "c"
|
||
has_inner_box 1
|
||
inner_pos "t"
|
||
use_parbox 0
|
||
use_makebox 0
|
||
width "100col%"
|
||
special "none"
|
||
height "1in"
|
||
height_special "totalheight"
|
||
thickness "0.4pt"
|
||
separation "3pt"
|
||
shadowsize "4pt"
|
||
framecolor "black"
|
||
backgroundcolor "none"
|
||
status open
|
||
|
||
\begin_layout Plain Layout
|
||
Imagine your favorite figure inside this box instead of this boring text.
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\begin_inset Caption Standard
|
||
|
||
\begin_layout Plain Layout
|
||
An ordinary figure float.
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
Furthermore,
|
||
he uses margin figures,
|
||
as shown in Fig.
|
||
\begin_inset space ~
|
||
\end_inset
|
||
|
||
|
||
\begin_inset CommandInset ref
|
||
LatexCommand ref
|
||
reference "fig:margin-figure"
|
||
nolink "false"
|
||
|
||
\end_inset
|
||
|
||
.
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\begin_inset VSpace 5theight%
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\begin_inset Float marginfigure
|
||
placement document
|
||
alignment document
|
||
wide false
|
||
sideways false
|
||
status open
|
||
|
||
\begin_layout Plain Layout
|
||
\begin_inset Box Boxed
|
||
position "t"
|
||
hor_pos "c"
|
||
has_inner_box 1
|
||
inner_pos "t"
|
||
use_parbox 0
|
||
use_makebox 0
|
||
width "100col%"
|
||
special "none"
|
||
height "1in"
|
||
height_special "totalheight"
|
||
thickness "0.4pt"
|
||
separation "3pt"
|
||
shadowsize "4pt"
|
||
framecolor "black"
|
||
backgroundcolor "none"
|
||
status open
|
||
|
||
\begin_layout Plain Layout
|
||
Imagine your favorite photograph of a squirrel inside this box instead of this boring text.
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\begin_inset Caption Standard
|
||
|
||
\begin_layout Plain Layout
|
||
A margin figure.
|
||
\begin_inset CommandInset label
|
||
LatexCommand label
|
||
name "fig:margin-figure"
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\begin_inset Note Greyedout
|
||
status open
|
||
|
||
\begin_layout Plain Layout
|
||
|
||
\series bold
|
||
Note:
|
||
|
||
\series default
|
||
If you are using margin figures or tables you must use the default float placement option in the document settings under
|
||
\family sans
|
||
Float
|
||
\begin_inset space ~
|
||
\end_inset
|
||
|
||
Placement
|
||
\family default
|
||
.
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
In the same vein,
|
||
the
|
||
\family sans
|
||
Tufte-book
|
||
\family default
|
||
class allows the use of tables,
|
||
both in the margins and in the text.
|
||
The margin tables are recommended for a small set of data to illustrate a concept such as
|
||
\begin_inset Quotes eld
|
||
\end_inset
|
||
|
||
Look,
|
||
distance-time data is quadratic when the object is falling.
|
||
\begin_inset Quotes erd
|
||
\end_inset
|
||
|
||
More detailed data such as flame test results and comments should be put in a full-width table instead.
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
Finally,
|
||
|
||
\family sans
|
||
Tufte-book
|
||
\family default
|
||
provides a full-width figure.
|
||
This one takes up the entire width of the page,
|
||
i.
|
||
\begin_inset space \thinspace{}
|
||
\end_inset
|
||
|
||
e.,
|
||
text and margin.
|
||
See Fig.
|
||
\begin_inset space ~
|
||
\end_inset
|
||
|
||
|
||
\begin_inset CommandInset ref
|
||
LatexCommand ref
|
||
reference "fig:full-width-figure"
|
||
nolink "false"
|
||
|
||
\end_inset
|
||
|
||
for an example.
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\begin_inset Float figure
|
||
placement document
|
||
alignment document
|
||
wide true
|
||
sideways false
|
||
status open
|
||
|
||
\begin_layout Plain Layout
|
||
\begin_inset Box Boxed
|
||
position "t"
|
||
hor_pos "c"
|
||
has_inner_box 1
|
||
inner_pos "t"
|
||
use_parbox 0
|
||
use_makebox 0
|
||
width "100line%"
|
||
special "none"
|
||
height "1in"
|
||
height_special "totalheight"
|
||
thickness "0.4pt"
|
||
separation "3pt"
|
||
shadowsize "4pt"
|
||
framecolor "black"
|
||
backgroundcolor "none"
|
||
status open
|
||
|
||
\begin_layout Plain Layout
|
||
Imagine your favorite photograph of a squirrel inside this box instead of this boring text.
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\begin_inset VSpace defskip
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Plain Layout
|
||
\begin_inset Caption Standard
|
||
|
||
\begin_layout Plain Layout
|
||
A full-width figure.
|
||
\begin_inset CommandInset label
|
||
LatexCommand label
|
||
name "fig:full-width-figure"
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Section
|
||
Working with Text
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
One of the most prominent and distinctive features of this style is the extensive use of sidenotes.
|
||
There is a wide margin to provide ample room for sidenotes and small figures.
|
||
Any footnotes will automatically be converted to sidenotes.
|
||
\begin_inset Foot
|
||
status open
|
||
|
||
\begin_layout Plain Layout
|
||
This is a sidenote that was entered using a
|
||
\family typewriter
|
||
footnote
|
||
\family default
|
||
.
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
Alternatively,
|
||
you can also use the
|
||
\family typewriter
|
||
Sidenote
|
||
\family default
|
||
inset directly;
|
||
you'll find it in the
|
||
\family sans
|
||
Insert\SpecialChar menuseparator
|
||
Custom Insets
|
||
\family default
|
||
menu.
|
||
\begin_inset Flex Sidenote
|
||
status open
|
||
|
||
\begin_layout Plain Layout
|
||
This is a sidenote that was entered using a
|
||
\family typewriter
|
||
sidenote
|
||
\family default
|
||
.
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
If you like to place ancillary information in the margin without the sidenote mark (the superscript number),
|
||
you can use the
|
||
\family typewriter
|
||
Marginnote
|
||
\family default
|
||
inset.
|
||
|
||
\begin_inset Flex Marginnote
|
||
status open
|
||
|
||
\begin_layout Plain Layout
|
||
This is Tufte's margin note.
|
||
Notice that there isn't a number preceding the note,
|
||
and there is no number in the main text where this note was written.
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
The normal margin note will work as well,
|
||
but it will look rather odd.
|
||
\begin_inset Marginal
|
||
status open
|
||
|
||
\begin_layout Plain Layout
|
||
This is a normal margin note.
|
||
Don't use it.
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\begin_inset Flex NewThought
|
||
status open
|
||
|
||
\begin_layout Plain Layout
|
||
Another useful
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
innovation is Tufte's
|
||
\family typewriter
|
||
NewThought
|
||
\family default
|
||
character style (
|
||
\family sans
|
||
Edit\SpecialChar menuseparator
|
||
TextStyle\SpecialChar menuseparator
|
||
NewThought
|
||
\family default
|
||
).
|
||
It introduces new thoughts by means of small caps,
|
||
as demonstrated in this paragraph.
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
The Tufte document classes include two new character styles and some improvements on existing commands for letterspacing.
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
When setting strings of
|
||
\begin_inset Flex AllCaps
|
||
status open
|
||
|
||
\begin_layout Plain Layout
|
||
ALL CAPS
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
or
|
||
\begin_inset Flex SmallCaps
|
||
status open
|
||
|
||
\begin_layout Plain Layout
|
||
small caps
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
,
|
||
the letterspacing—
|
||
that is,
|
||
the spacing between the letters—
|
||
should be increased slightly.
|
||
\begin_inset CommandInset citation
|
||
LatexCommand cite
|
||
key "Bringhurst2005"
|
||
literal "true"
|
||
|
||
\end_inset
|
||
|
||
The
|
||
\emph on
|
||
AllCaps
|
||
\emph default
|
||
character style (
|
||
\family sans
|
||
Edit\SpecialChar menuseparator
|
||
TextStyle\SpecialChar menuseparator
|
||
AllCaps
|
||
\family default
|
||
) has proper letterspacing for strings of
|
||
\begin_inset Flex AllCaps
|
||
status open
|
||
|
||
\begin_layout Plain Layout
|
||
FULL CAPITAL LETTERS
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
,
|
||
and the
|
||
\emph on
|
||
SmallCaps
|
||
\emph default
|
||
character style (
|
||
\family sans
|
||
Edit\SpecialChar menuseparator
|
||
TextStyle\SpecialChar menuseparator
|
||
SmallCaps
|
||
\family default
|
||
) has letterspacing for
|
||
\begin_inset Flex SmallCaps
|
||
status open
|
||
|
||
\begin_layout Plain Layout
|
||
small capital letters
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
.
|
||
These commands will also automatically convert the case of the text to upper- or lowercase,
|
||
respectively.
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
The normal
|
||
\emph on
|
||
Small Caps
|
||
\emph default
|
||
shape has also been redefined to include letterspacing.
|
||
Its case is left as is,
|
||
however.
|
||
This allows one to use both uppercase and lowercase letters:
|
||
|
||
\shape smallcaps
|
||
The Initial Letters Of The Words In This Sentence Are Capitalized.
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
Finally,
|
||
the
|
||
\emph on
|
||
Full Width
|
||
\emph default
|
||
paragraph environment provides a paragraph layout that stretches across the main text block and the sidenotes area:
|
||
\end_layout
|
||
|
||
\begin_layout Full Width
|
||
Lorem ipsum dolor sit amet,
|
||
consectetuer adipiscing elit.
|
||
Ut purus elit,
|
||
vestibulum ut,
|
||
placerat ac,
|
||
adipiscing vitae,
|
||
felis.
|
||
Curabitur dictum gravida mauris.
|
||
Nam arcu libero,
|
||
nonummy eget,
|
||
consectetuer id,
|
||
vulputate a,
|
||
magna.
|
||
Donec vehicula augue eu neque.
|
||
Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas.
|
||
Mauris ut leo.
|
||
Cras viverra metus rhoncus sem.
|
||
Nulla et lectus vestibulum urna fringilla ultrices.
|
||
Phasellus eu tellus sit amet tortor gravida placerat.
|
||
Integer sapien est,
|
||
iaculis in,
|
||
pretium quis,
|
||
viverra ac,
|
||
nunc.
|
||
Praesent eget sem vel leo ultrices bibendum.
|
||
Aenean faucibus.
|
||
Morbi dolor nulla,
|
||
malesuada eu,
|
||
pulvinar at,
|
||
mollis ac,
|
||
nulla.
|
||
Curabitur auctor semper nulla.
|
||
Donec varius orci eget risus.
|
||
Duis nibh mi,
|
||
congue eu,
|
||
accumsan eleifend,
|
||
sagittis quis,
|
||
diam.
|
||
Duis eget orci sit amet orci dignissim rutrum.
|
||
\end_layout
|
||
|
||
\begin_layout Section
|
||
References
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
References are placed alongside their citations as sidenotes,
|
||
as well.
|
||
This can be accomplished using the normal citation command.
|
||
\begin_inset Foot
|
||
status collapsed
|
||
|
||
\begin_layout Plain Layout
|
||
The previous section includes a citation.
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
The complete list of references may also be printed automatically by using
|
||
\family sans
|
||
Insert\SpecialChar menuseparator
|
||
Lists/TOC\SpecialChar menuseparator
|
||
Bib\SpecialChar TeX
|
||
|
||
\begin_inset space ~
|
||
\end_inset
|
||
|
||
Bibliography
|
||
\family default
|
||
(see the end of this document for an example.) If you do not want to print a bibliography at the end of your document,
|
||
place the
|
||
\family sans
|
||
Bib\SpecialChar TeX
|
||
|
||
\begin_inset space ~
|
||
\end_inset
|
||
|
||
Bibliography
|
||
\family default
|
||
inset inside a \SpecialChar LyX
|
||
note and use the \SpecialChar LaTeX
|
||
command
|
||
\family typewriter
|
||
|
||
\backslash
|
||
nobibliography
|
||
\family default
|
||
the text.
|
||
\end_layout
|
||
|
||
\begin_layout Chapter
|
||
Calculation of Volume:
|
||
Sections 2.12–2.13
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
Imagine taking a function like
|
||
\begin_inset Formula $y=\sqrt{x}$
|
||
\end_inset
|
||
|
||
and rotating it in 3 dimensions around the x-axis.
|
||
The resulting shape would look somewhat like a cup (on its side).
|
||
Interestingly,
|
||
integration empowers us to do exactly this and to find out how much water that cup could hold.
|
||
\end_layout
|
||
|
||
\begin_layout Section
|
||
Visualizing Rotation
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\begin_inset Float marginfigure
|
||
placement document
|
||
alignment document
|
||
wide false
|
||
sideways false
|
||
status open
|
||
|
||
\begin_layout Plain Layout
|
||
\begin_inset Box Boxed
|
||
position "t"
|
||
hor_pos "c"
|
||
has_inner_box 1
|
||
inner_pos "t"
|
||
use_parbox 0
|
||
use_makebox 0
|
||
width "100col%"
|
||
special "none"
|
||
height "1in"
|
||
height_special "totalheight"
|
||
thickness "0.4pt"
|
||
separation "3pt"
|
||
shadowsize "4pt"
|
||
framecolor "black"
|
||
backgroundcolor "none"
|
||
status open
|
||
|
||
\begin_layout Plain Layout
|
||
I had a graph of the square root function here.
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\begin_inset Caption Standard
|
||
|
||
\begin_layout Plain Layout
|
||
\begin_inset CommandInset label
|
||
LatexCommand label
|
||
name "mar:A-graph-of"
|
||
|
||
\end_inset
|
||
|
||
A graph of
|
||
\begin_inset Formula $f(x)=\sqrt{x}$
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\begin_inset Float marginfigure
|
||
placement document
|
||
alignment document
|
||
wide false
|
||
sideways false
|
||
status open
|
||
|
||
\begin_layout Plain Layout
|
||
\begin_inset Box Boxed
|
||
position "t"
|
||
hor_pos "c"
|
||
has_inner_box 1
|
||
inner_pos "t"
|
||
use_parbox 0
|
||
use_makebox 0
|
||
width "100col%"
|
||
special "none"
|
||
height "1in"
|
||
height_special "totalheight"
|
||
thickness "0.4pt"
|
||
separation "3pt"
|
||
shadowsize "4pt"
|
||
framecolor "black"
|
||
backgroundcolor "none"
|
||
status open
|
||
|
||
\begin_layout Plain Layout
|
||
Here I rotated the square root function and then drew a disk on the figure to illustrate how I would calculate the volume of the figure.
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\begin_inset Caption Standard
|
||
|
||
\begin_layout Plain Layout
|
||
\begin_inset CommandInset label
|
||
LatexCommand label
|
||
name "mar:rotated"
|
||
|
||
\end_inset
|
||
|
||
A graph of
|
||
\begin_inset Formula $f(x)=\sqrt{x}$
|
||
\end_inset
|
||
|
||
rotated about the x-axis and with additional remarks for integration.
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
Figure
|
||
\begin_inset CommandInset ref
|
||
LatexCommand ref
|
||
reference "mar:A-graph-of"
|
||
nolink "false"
|
||
|
||
\end_inset
|
||
|
||
shows the plot of the function
|
||
\begin_inset Formula $f(x)=\sqrt{x}.$
|
||
\end_inset
|
||
|
||
Now,
|
||
imagine that we rotate that function about the x-axis.
|
||
The resulting figure would be somewhat like figure
|
||
\begin_inset CommandInset ref
|
||
LatexCommand ref
|
||
reference "mar:rotated"
|
||
nolink "false"
|
||
|
||
\end_inset
|
||
|
||
.
|
||
This is akin to a cup lying on its side.
|
||
For the sake of clarity,
|
||
the artist (me) drew a circle on the end of the figure to show that it is indeed rotated.
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
Now,
|
||
suppose we wished to find the volume of the figure.
|
||
When we integrated the original square root function to find its area,
|
||
we imagined a series of rectangles inside the figure.
|
||
Their height was
|
||
\begin_inset Formula $h=f(x)$
|
||
\end_inset
|
||
|
||
and their width was
|
||
\begin_inset Formula $dx$
|
||
\end_inset
|
||
|
||
.
|
||
Since height multiplied by width was the area of each rectangle,
|
||
we summed these areas and rewrote this as
|
||
\begin_inset Formula $\int\,f(x)\,dx$
|
||
\end_inset
|
||
|
||
,
|
||
or,
|
||
in this specific case,
|
||
|
||
\begin_inset Formula $\int\,\sqrt{x}\,dx$
|
||
\end_inset
|
||
|
||
.
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
To find the volume of our rotated figure the prodecure is quite similar.
|
||
Begin by rotating each rectangle about the x-axis.
|
||
This creates a series of cylinders.
|
||
\begin_inset Flex Sidenote
|
||
status collapsed
|
||
|
||
\begin_layout Plain Layout
|
||
The text refers to these cylinders as "disks".
|
||
This is standard practice in all the Calculus books I checked.
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
Then,
|
||
we can find the volume of each cylinder/disk.
|
||
The basic formula is:
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\begin_inset Formula
|
||
\[
|
||
V=hA
|
||
\]
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\noindent
|
||
where
|
||
\begin_inset Formula $h$
|
||
\end_inset
|
||
|
||
is the height of the cylinder (width of the rectangle)
|
||
\begin_inset Formula $dx$
|
||
\end_inset
|
||
|
||
.
|
||
The area of each figure is a circle where
|
||
\begin_inset Formula $A=\pi r^{2}$
|
||
\end_inset
|
||
|
||
.
|
||
The radius in this case is the function
|
||
\begin_inset Formula $f(x)$
|
||
\end_inset
|
||
|
||
.
|
||
By substitution
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\begin_inset Formula
|
||
\[
|
||
A=\pi f^{2}(x)
|
||
\]
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\noindent
|
||
In our specific case,
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\begin_inset Formula
|
||
\begin{eqnarray*}
|
||
A & = & \pi\left(\sqrt{x}\right)^{2}\\
|
||
& = & \pi x
|
||
\end{eqnarray*}
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
To calculate the volume of one disk,
|
||
we have
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\begin_inset Formula
|
||
\[
|
||
V=\pi x\,dx
|
||
\]
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\noindent
|
||
or,
|
||
in the general case
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\begin_inset Formula
|
||
\[
|
||
V=\pi f^{2}(x)\,dx
|
||
\]
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
To find the volume of the figure between points
|
||
\begin_inset Formula $a$
|
||
\end_inset
|
||
|
||
and
|
||
\begin_inset Formula $b$
|
||
\end_inset
|
||
|
||
we sum the volumes by means of integration:
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\begin_inset Formula
|
||
\begin{equation}
|
||
\int_{a}^{b}\,\pi f^{2}(x)\,dx
|
||
\end{equation}
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\noindent
|
||
In the specific example,
|
||
over the interval
|
||
\begin_inset Formula $[0,4]$
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\begin_inset Formula
|
||
\begin{eqnarray*}
|
||
\int_{0}^{4}\,\pi x\,dx & = & \pi\int_{0}^{4}\,x\,dx\\
|
||
& = & \pi\left.\left(\frac{x^{2}}{2}\right)\right|_{0}^{4}\\
|
||
& = & \pi\left(\frac{4^{2}}{2}-0\right)\\
|
||
& = & 8\pi
|
||
\end{eqnarray*}
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\begin_inset Flex NewThought
|
||
status open
|
||
|
||
\begin_layout Plain Layout
|
||
Suppose I drill
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
a special hole down the length of the cup we just worked with.
|
||
It is made with a quadratic shaped bit.
|
||
\begin_inset Flex Sidenote
|
||
status collapsed
|
||
|
||
\begin_layout Plain Layout
|
||
I have no idea how I'd do this in real life,
|
||
but I'm making a point.
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
I find that the hole the bit makes can be modeled with the function
|
||
\begin_inset Formula $g(x)=\frac{x^{2}}{16}$
|
||
\end_inset
|
||
|
||
.
|
||
I would need to subtract the volume of the material removed from the volume of the entire
|
||
\begin_inset Quotes eld
|
||
\end_inset
|
||
|
||
cup
|
||
\begin_inset Quotes erd
|
||
\end_inset
|
||
|
||
.
|
||
Each individual cylinder would become like a
|
||
\begin_inset Quotes eld
|
||
\end_inset
|
||
|
||
washer
|
||
\begin_inset Quotes erd
|
||
\end_inset
|
||
|
||
.
|
||
To get the area of one washer,
|
||
I would use the formula
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\begin_inset Float marginfigure
|
||
placement document
|
||
alignment document
|
||
wide false
|
||
sideways false
|
||
status open
|
||
|
||
\begin_layout Plain Layout
|
||
\begin_inset Box Boxed
|
||
position "t"
|
||
hor_pos "c"
|
||
has_inner_box 1
|
||
inner_pos "t"
|
||
use_parbox 0
|
||
use_makebox 0
|
||
width "100col%"
|
||
special "none"
|
||
height "1in"
|
||
height_special "totalheight"
|
||
thickness "0.4pt"
|
||
separation "3pt"
|
||
shadowsize "4pt"
|
||
framecolor "black"
|
||
backgroundcolor "none"
|
||
status open
|
||
|
||
\begin_layout Plain Layout
|
||
Here I used RLPlot to draw the square root function and the quadratic function.
|
||
Then I used Inkscape to shade the area between them.
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\begin_inset Caption Standard
|
||
|
||
\begin_layout Plain Layout
|
||
The functions
|
||
\begin_inset Formula $f(x)$
|
||
\end_inset
|
||
|
||
and
|
||
\begin_inset Formula $g(x)$
|
||
\end_inset
|
||
|
||
and the area left by
|
||
\begin_inset Formula $f(x)-g(x)$
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\begin_inset Formula
|
||
\begin{eqnarray*}
|
||
A_{washer} & = & A_{cup}-A_{drill}\\
|
||
& = & \pi f^{2}(x)-\pi g^{2}(x)\\
|
||
& = & \pi\left(f^{2}(x)-g^{2}(x)\right)
|
||
\end{eqnarray*}
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
The volume of each washer would be
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\begin_inset Formula
|
||
\begin{eqnarray*}
|
||
V_{washer} & = & A_{washer}\,dx\\
|
||
& = & \pi\left(f^{2}(x)-g^{2}(x)\right)\,dx
|
||
\end{eqnarray*}
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\noindent
|
||
Then,
|
||
by summing the volumes of all the washers between points
|
||
\begin_inset Formula $a$
|
||
\end_inset
|
||
|
||
and
|
||
\begin_inset Formula $b$
|
||
\end_inset
|
||
|
||
,
|
||
the integral is derived:
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\begin_inset Formula
|
||
\begin{equation}
|
||
\int_{a}^{b}\,\pi\left(f^{2}(x)-g^{2}(x)\right)\,dx
|
||
\end{equation}
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
In the case of our quadratic drill bit::
|
||
\begin_inset Float marginfigure
|
||
placement document
|
||
alignment document
|
||
wide false
|
||
sideways false
|
||
status open
|
||
|
||
\begin_layout Plain Layout
|
||
\begin_inset Box Boxed
|
||
position "t"
|
||
hor_pos "c"
|
||
has_inner_box 1
|
||
inner_pos "t"
|
||
use_parbox 0
|
||
use_makebox 0
|
||
width "100col%"
|
||
special "none"
|
||
height "1in"
|
||
height_special "totalheight"
|
||
thickness "0.4pt"
|
||
separation "3pt"
|
||
shadowsize "4pt"
|
||
framecolor "black"
|
||
backgroundcolor "none"
|
||
status open
|
||
|
||
\begin_layout Plain Layout
|
||
This was the rotated set of 2 functions.
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\begin_inset Caption Standard
|
||
|
||
\begin_layout Plain Layout
|
||
The cup with a quadratic hole drilled down its length
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\begin_inset Formula
|
||
\begin{eqnarray*}
|
||
\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\\
|
||
& = & \pi\left(\int_{0}^{4}\,x\,dx-\int_{0}^{4}\,\frac{x^{4}}{256}\,dx\right)\\
|
||
& = & \pi\left(\left.\left(\frac{x^{2}}{2}\right)\right|_{0}^{4}-\left.\left(\frac{x^{5}}{1280}\right)\right|_{0}^{4}\right)\\
|
||
& = & \pi\left(\left(\frac{4^{2}}{2}-0\right)-\left(\frac{4^{5}}{1280}-0\right)\right)\\
|
||
& = & \pi\left(8-0.8\right)\\
|
||
& = & 7.2\pi
|
||
\end{eqnarray*}
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Section
|
||
Homework
|
||
\end_layout
|
||
|
||
\begin_layout Itemize
|
||
p114:
|
||
1,
|
||
4,
|
||
5,
|
||
6,
|
||
8,
|
||
10,
|
||
12,
|
||
15
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\begin_inset CommandInset bibtex
|
||
LatexCommand bibtex
|
||
bibfiles "../biblioExample"
|
||
options "plainnat"
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\end_body
|
||
\end_document
|