Release 1.6.5

Signed-off-by: Marcello Seri <[email protected]>

aom.tex

@@ -208,16 +208,16 @@
 \newpage
 
 \begin{fullwidth}
-	~\vfill
-	\thispagestyle{empty}
-	\setlength{\parindent}{0pt}
-	\setlength{\parskip}{\baselineskip}
-	Copyright \copyright\ \the\year\ \thanklessauthor
+  ~\vfill
+  \thispagestyle{empty}
+  \setlength{\parindent}{0pt}
+  \setlength{\parskip}{\baselineskip}
+  Copyright \copyright\ \the\year\ \thanklessauthor
 
-	\par Version 1.6.4 -- \today
+  \par Version 1.6.5 -- \today
 
-	\vfill
-	\small{\doclicenseThis}
+  \vfill
+  \small{\doclicenseThis}
 \end{fullwidth}
 
 \pagenumbering{roman}
@@ -231,9 +231,9 @@ \chapter*{Introduction}
 At the entry for \emph{Mathematical analysis}, our modern source of truth---Wikipedia---says
 
 \begin{quotation}
-	\emph{Mathematical analysis} is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.
+  \emph{Mathematical analysis} is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.
 
-	These theories are usually studied in the context of real numbers and functions. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis. Analysis may be distinguished from geometry; however, it can be applied to any space of mathematical objects that has a definition of nearness (a topological space) or specific distances between objects (a metric space).
+  These theories are usually studied in the context of real numbers and functions. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis. Analysis may be distinguished from geometry; however, it can be applied to any space of mathematical objects that has a definition of nearness (a topological space) or specific distances between objects (a metric space).
 \end{quotation}
 
 \newthought{In this sense}, our course will focus on generalizing the concepts of differentiation, integration and, up to some extent, differential equations to spaces that are more general than the standard Euclidean space.
@@ -254,7 +254,7 @@ \chapter*{Introduction}
 
 An old mathematical joke says that
 \begin{quote}
-	differential geometry is the study of properties that are invariant under change of notation.
+  differential geometry is the study of properties that are invariant under change of notation.
 \end{quote}
 Sadly, this is \emph{funny because it is alarmingly close to the truth}\footnote{Cit. Lee~\cite{book:lee}.}.
 
@@ -287,23 +287,23 @@ \chapter*{Einstein summation convention}
 
 For instance, the expression
 \begin{equation}
-	a^{ij}b_l^k e_i e_k
+  a^{ij}b_l^k e_i e_k
 \end{equation}
 is a shorthand for
 \begin{equation}
-	\sum_{i,k} a^{ij}b_l^k e_i e_k.
+  \sum_{i,k} a^{ij}b_l^k e_i e_k.
 \end{equation}
 
 In general, we will use lower indices for basis of vector spaces\footnote{E.g., $(e_1,\ldots,e_n)$ could be the standard basis of $\R^n$.}, and upper indices for the components of a vector with respect to a basis\footnote{E.g., the $i$th-coordinate $x^i$ of $x\in\R^n$.}.
 \marginnote[10pt]{Since the coordinates of a point $x\in\R^n$ are also its components with respect to the standard basis $(e_1, \ldots, e_n)$, for consistency they will be denoted $(x^1, \ldots, x^n)$ with upper indices.}
 
 Note that an upper index ``in the denominator'' is regarded as a lower index, so the following are to be considered equivalent:
 \begin{equation}
-	\sum_{i} a^i \frac{\partial}{\partial x^i} = a^i \frac{\partial}{\partial x^i}.
+  \sum_{i} a^i \frac{\partial}{\partial x^i} = a^i \frac{\partial}{\partial x^i}.
 \end{equation}
 In fact, the expressions below are all equivalent and commonly used in the differential geometry literature:
 \begin{equation}
-	\sum_{i} a^i \frac{\partial}{\partial x^i} = a^i \frac{\partial}{\partial x^i} = a^i \partial_{x^i} = a^i \partial_i.
+  \sum_{i} a^i \frac{\partial}{\partial x^i} = a^i \frac{\partial}{\partial x^i} = a^i \partial_{x^i} = a^i \partial_i.
 \end{equation}
 
 \chapter{Manifolds}\label{ch:manifolds}
@@ -337,10 +337,10 @@ \chapter{Integration of forms}
 \input{7-integration}
 
 \begin{appendices}
-	\chapter{Lie groups and Lie algebras}\label{appendix:Lie}
-	\input{3b-liegroups}
+  \chapter{Lie groups and Lie algebras}\label{appendix:Lie}
+  \input{3b-liegroups}
 
-	\input{appendices}
+  \input{appendices}
 \end{appendices}
 
 % \begin{appendices}