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Back MatterReference


This is some notation introduced in the article.

Symbol Description Location
\(\int_a^b\,f(x)\,dx\) definite integral of \(f(x)\) Paragraph
\(\int\,f(x)\,dx\) indefinite integral of \(f(x)\) Definition 2.2
\(\rho\) this symbol could be used for lots of things, but we are just trying to make a super-long description to get it to wrap within the column where it belongs, which is sometimes set to a fixed width to accomodate really complicated explanations Paragraph
\(\nabla\) gradient operator Paragraph

AppendixBSolutions to Selected Exercises



This is an exercise in an “Exercises” subdivision at the level of a subsubsection. There is no question other than if the numbering is appropriate. Here is a self-referential link: Exercise

The subsubsection has no title in the source, so one is provided automatically, and will adjust according to the language of the document.


Exercises11.4More Exercises





Exercise1An Exercise in a Section

Exercises can appear in a “section” of their own. You need to give the section a title, even if it seems obvious what to call it. Individual exercises may have titles, as you choose. Problem: How should we hide solutions?

Exercise42aAn Exercise with a Hard-Coded Problem Number

Compute the definite integral \(\definiteintegral{2}{4}{x^2}{x}\text{,}\) not as an approximate value from a Riemann sum, but as an exact value based of the limit by using the Fundamental Theorem.


Can you prove Corollary 4.1 directly? If not consider that a problem could have several parts, which should be formatted as a second-level list, since the problems normally get numbered at the top level.

  1. Why is this result a Corollary?

  2. Could you interchange the Theorem and Corollary?

Hint 1Hint 2AnswerSolution

AppendixCList of Results

We had an automatic list of theorems for just one section, back in Subsection 25.6. Here we expand to include corollary in our space-delimited list of elements and we request divisions (headings) at each subsection and section. The default scope is the entire document, which is appropriate here in the backmatter. There are many subsections with no results, so we set the empty attribute to no to suppress them, though this is the default behavior (yes being the other option to see divisions with no list items). These lists are most valuable if you are in the practice of giving items titles.

Section2The Fundamental Theorem

Theorem 2.1 The Fundamental Theorem of Calculus

Section4An Interesting Corollary

Subsection4.1Second Version of FTC

Section20Program Listings

Section25Advanced Numbering


Theorem 25.1 First Theorem
Theorem 25.2 Second Theorem


Theorem 25.3 First Theorem
Theorem 25.4 Second Theorem
Theorem 25.5 First Theorem
Theorem 25.6 Second Theorem


Theorem 25.7 First Theorem
Theorem 25.8 Second Theorem


Theorem 25.9 Good Numbered Theorem One
Theorem 25.10 Good Numbered Theorem Two
Theorem 25.11 First Theorem
Theorem 25.12 Second Theorem
Theorem 25.13 First Theorem
Theorem 25.14 Second Theorem
Theorem 25.15 Bad Numbered Theorem One
Theorem 25.16 Bad Numbered Theorem Two


Theorem 25.17 First Theorem
Theorem 25.18 Second Theorem


There is an index manufactured at the end of the back matter. So we are talking about it here, rather than within the index, which is an impossibility. It contains some sample entries, and is not meant to be comprehensive. Look at the source of this XML file, searching on <index>, to see how they are written. They may be placed inside of a a variety of structures, and their location greatly influences the cross-references produced in the HTML version of the index.

The version of the index is more traditional, using page numbers to reference locations. A newer package is used to create the index, and so there is no extra intermediate step required to process the index. The one downside of this convenience is that index entries may not be placed in the back colophon (which is the only subdivision that may follow the index).

There is an index entry about multicolumn lists which spans more than one page. This requires doubly-linked index entries, the first has the index content and points to the xml:id of the second. The second is an empty element, but points back to the xml:id of the first entry. So each has a marker and a reference, which allows the span of the index topic to cut across XML boundaries in the source. This is the mechanism to produce a page range in the index. See the source of this article for syntax details.

Bully Pulpit: Index Headings

Professionals do not capitalize the headings (entries) of an index, unless it is a proper noun (name, place, etc.). We do not provide any enforcement of this advice, nor any assistance. It is your responsibility to provide quality source material in this regard.


Most all of the index entries below to page 2 (PDF output) are just from a suite of non-sensical tests. These are harder to recognize in the HTML output.


Tom Judson, Abstract Algebra: Theory and Applications.
David C. Lay, Subspaces and Echelon Forms. The College Mathematics Journal, January 1993, 24 no. 1, 57–62.


A, see also Hsee Fsee GSection
B, see also C
C, see D
activity, Exploration
assemblage, Subsection
asymptote graphics language, Paragraph
autoname, Paragraph
canceling a term, Paragraph
cancelto macro, Paragraph
sorted as if “Cat”, Section
shades, List
repurposed from proposition, Paragraph
description list, Paragraph
exploration, Exploration
fill-in blank, Exercise
Fundamental Theorem of Calculus, Theorem
GeoGebra, Subsection
investigation, Exploration
Led Zeppelin video, Figure
list, Paragraph
description, Paragraph
ordered, Subsection
unordered, Subsection
listing, Paragraph
multicolumn, Paragraph
mixed-content emphasized, Section
numerical, see Sage integrationsee Sage
numerical integration
cell, see SageSection
numerics, see also Sage
ordered list, Subsection
siunitx, Paragraph
normal, Paragraph
opens with list, Paragraph
problem, Paragraph
program listing, Paragraph
question, Paragraph
sorted as if “Quorum”, Section
quotations, Paragraph
within a section, References
rename an environment, Exploration
\(\rho\)–fibers, Section
integration, Section
cell, Section
numerical, Section
Sage cell
with a title, Paragraphs
Sage cells
linking, Subsection
Sage plots, Subsection
siunitx package, Paragraph
strange colors, ItemItem
structured-content emphasized, Section
test: buried in theorem/statement/p, Theorem
Underdown, Jason, Paragraph
units, Paragraph
Z (sort as A), Section
A (sort as Z), Section
unordered list, Subsection
URLs, Paragraph
verbatim text, use sortby, Section
YouTube, Paragraph
YouTube videos, Paragraph


This article was authored in PreTeXt.