A few minor fixes, use dash for theorem names with multiple authors, add

an unstable example in limit cycle section, along with figure.

ch-eigenvalue-probs.tex

@@ -2,7 +2,7 @@ \chapter{More on eigenvalue problems} \label{SL:chapter}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
-\section{Sturm-Liouville problems}
+\section{Sturm--Liouville problems}
 \label{slproblems:section}
 
 \sectionnotes{2 lectures\EPref{, \S10.1 in \cite{EP}}\BDref{,
@@ -91,7 +91,7 @@ \subsection{Boundary value problems}
 \end{example}
 
 The so-called 
-\emph{\myindex{Sturm-Liouville problem}}%
+\emph{\myindex{Sturm--Liouville problem}}%
 \footnote{Named after the French mathematicians
 \href{https://en.wikipedia.org/wiki/Jacques_Charles_Fran\%C3\%A7ois_Sturm}{Jacques Charles Fran\c{c}ois Sturm}
 (1803--1855) and
@@ -120,7 +120,7 @@ \subsection{Boundary value problems}
 \begin{theorem} \label{sl:slregthm}
 Suppose $p(x)$, $p'(x)$, $q(x)$ and $r(x)$ are continuous on $[a,b]$
 and suppose $p(x) > 0$ and $r(x) > 0$ for all $x$ in $[a,b]$.
-Then the Sturm-Liouville problem \eqref{sl:slprob}
+Then the Sturm--Liouville problem \eqref{sl:slprob}
 has an increasing sequence of eigenvalues
 \begin{equation*}
 \lambda_1 < \lambda_2 < \lambda_3 < \cdots 
@@ -138,8 +138,8 @@ \subsection{Boundary value problems}
 
 Problems satisfying the hypothesis of the
 theorem are called
-\emph{regular Sturm-Liouville problems\index{regular Sturm-Liouville problem}}%
-\index{Sturm-Liouville problem!regular}
+\emph{regular Sturm--Liouville problems\index{regular Sturm--Liouville problem}}%
+\index{Sturm--Liouville problem!regular}
 and we will only consider such problems here.
 That is, a regular problem is one where
 $p(x)$, $p'(x)$, $q(x)$ and $r(x)$ are continuous, $p(x) > 0$, $r(x) > 0$,
@@ -154,7 +154,7 @@ \subsection{Boundary value problems}
 
 \begin{example}
 The problem $y''+\lambda y$, $0 < x < L$, $y(0) = 0$, and $y(L) = 0$
-is a regular Sturm-Liouville problem.  $p(x) = 1$, $q(x) = 0$, $r(x) = 1$,
+is a regular Sturm--Liouville problem.  $p(x) = 1$, $q(x) = 0$, $r(x) = 1$,
 and we have $p(x) = 1 > 0$ and $r(x) = 1 > 0$.
 The eigenvalues are $\lambda_n = \frac{n^2 \pi^2}{L^2}$ and eigenfunctions
 are $y_n(x) = \sin(\frac{n\pi}{L} x)$.  All eigenvalues are nonnegative as
@@ -179,7 +179,7 @@ \subsection{Boundary value problems}
 & hy(0)- y'(0) = 0, \quad y'(1)  = 0, \quad h > 0.
 \end{align*}
 
-These equations give a regular Sturm-Liouville problem.
+These equations give a regular Sturm--Liouville problem.
 
 \begin{exercise}
 Identify $p, q, r, \alpha_j, \beta_j$ in the example above.
@@ -260,7 +260,7 @@ \subsection{Orthogonality}
 
 We have seen the notion of orthogonality before.  For example,
 we have shown that $\sin (nx)$ are orthogonal for distinct $n$ on $[0,\pi]$.
-For general Sturm-Liouville problems we will need a more general setup.
+For general Sturm--Liouville problems we will need a more general setup.
 Let $r(x)$
 be a \emph{\myindex{weight function}} (any function, though generally we will
 assume it is positive) on $[a,b]$.  Two functions $f(x)$, $g(x)$
@@ -288,10 +288,10 @@ \subsection{Orthogonality}
 think of a change of variables such that $d\xi = r(x)~ dx$.
 
 We have the following orthogonality property of eigenfunctions of a
-regular Sturm-Liouville problem.
+regular Sturm--Liouville problem.
 
 \begin{theorem}
-Suppose we have a regular Sturm-Liouville problem
+Suppose we have a regular Sturm--Liouville problem
 \begin{align*}
 &\frac{d}{dx} \left( p(x) \frac{dy}{dx} \right)
 - q(x) y + \lambda r(x) y = 0 , \\
@@ -314,12 +314,12 @@ \subsection{Orthogonality}
 \subsection{Fredholm alternative}
 
 The \emph{Fredholm alternative} theorem we talked about before
-holds for all regular Sturm-Liouville problems.
+holds for all regular Sturm--Liouville problems.
 We state it here for completeness.
 
 \begin{theorem}[Fredholm alternative]%
-\index{Fredholm alternative!Sturm-Liouville problems}
-Suppose that we have a regular Sturm-Liouville problem.
+\index{Fredholm alternative!Sturm--Liouville problems}
+Suppose that we have a regular Sturm--Liouville problem.
 Then either
 \begin{align*}
 &\frac{d}{dx} \left( p(x) \frac{dy}{dx} \right)
@@ -395,15 +395,15 @@ \subsection{Eigenfunction series}
 
 \begin{theorem}
 Suppose $f$ is a piecewise smooth continuous function on $[a,b]$.  If $y_1,
-y_2, \ldots$ are eigenfunctions of a regular Sturm-Liouville problem,
+y_2, \ldots$ are eigenfunctions of a regular Sturm--Liouville problem,
 one for each eigenvalue,
 then there exist real constants $c_1, c_2, \ldots$ given by \eqref{sl:cm}
 such that
 \eqref{sl:fdecomp} converges and holds for $a < x < b$.
 \end{theorem}
 
 \begin{example}
-Take the simple Sturm-Liouville problem
+Take the simple Sturm--Liouville problem
 \begin{align*}
 & y'' + \lambda y = 0, \quad 0 < x < \frac{\pi}{2} , \\
 & y(0) =0, \quad y'\left(\frac{\pi}{2}\right) = 0 .
@@ -483,7 +483,7 @@ \subsection{Exercises}
 \end{exercise}
 
 \begin{exercise}
-Suppose that you had a Sturm-Liouville problem on the interval
+Suppose that you had a Sturm--Liouville problem on the interval
 $[0,1]$ and came up with
 $y_n(x) = \sin (\gamma n x)$, where $\gamma > 0$ is some constant.
 Decompose $f(x) = x$, $0 < x < 1$ in terms of these eigenfunctions.
@@ -495,7 +495,7 @@ \subsection{Exercises}
 y^{(4)}+\lambda y = 0, \quad y(0) = 0, \quad y'(0) = 0, \quad y(1) = 0, \quad
 y'(1) = 0 .
 \end{equation*}
-This problem is not a Sturm-Liouville problem, but the idea is the same.
+This problem is not a Sturm--Liouville problem, but the idea is the same.
 \end{exercise}
 
 \begin{exercise}[more challenging]
@@ -522,7 +522,7 @@ \subsection{Exercises}
 }
 
 \begin{exercise}
-Put the following problems into the standard form for Sturm-Liouville
+Put the following problems into the standard form for Sturm--Liouville
 problems, that is, find $p(x)$, $q(x)$, $r(x)$,
 $\alpha_1$,
 $\alpha_2$,

ch-first-order-ode.tex

@@ -2468,7 +2468,7 @@ \section{Numerical methods: Euler's method}
 
 In real applications we would not use a simple method such as Euler's.  The
 simplest method that would probably be used in a real application is the
-standard Runge-Kutta method (see exercises).  That is a
+standard Runge--Kutta method (see exercises).  That is a
 \myindex{fourth order method},
 meaning that if we halve the interval, the error generally
 goes down by a factor of 16 (it is fourth order as $\nicefrac{1}{16} =
@@ -2553,7 +2553,7 @@ \subsection{Exercises}
 \end{exercise}
 
 The simplest method used in practice is the
-\emph{\myindex{Runge-Kutta method}}.
+\emph{\myindex{Runge--Kutta method}}.
 Consider $\frac{dy}{dx}=f(x,y)$, $y(x_0) = y_0$,
 and a step size $h$.  Everything is the same as in Euler's method, except
 the computation of $y_{i+1}$ and $x_{i+1}$.
@@ -2572,7 +2572,7 @@ \subsection{Exercises}
 \begin{exercise}
 Consider $\dfrac{dy}{dx} = yx^2$, $y(0)=1$.
 \begin{tasks}
-\task Use Runge-Kutta (see above) with step sizes $h=1$ and $h=\nicefrac{1}{2}$
+\task Use Runge--Kutta (see above) with step sizes $h=1$ and $h=\nicefrac{1}{2}$
 to approximate $y(1)$.
 \task Use Euler's method with $h=1$ and
 $h=\nicefrac{1}{2}$.

ch-higher-order-ode.tex

@@ -223,7 +223,7 @@ \subsection{Exercises}
 
 Equations of the form $a x^2 y'' + b x y' + c y = 0$ are called
 \emph{Euler's equations\index{Euler's equation}} or
-\emph{Cauchy-Euler equations\index{Cauchy-Euler equation}}.
+\emph{Cauchy--Euler equations\index{Cauchy--Euler equation}}.
 They are solved by trying
 $y=x^r$ and solving for $r$ (assume that $x \geq 0$ for simplicity).
 
@@ -723,7 +723,7 @@ \subsection{Exercises}
 \end{exercise}
 
 \begin{exercise}
-Let us revisit the Cauchy-Euler equations\index{Cauchy-Euler equation} of
+Let us revisit the Cauchy--Euler equations\index{Cauchy--Euler equation} of
 \exercisevref{sol:eulerex}.  Suppose now
 that ${(b-a)}^2-4ac < 0$.  Find a formula for the general solution
 of $a x^2 y'' + b x y' + c y = 0$.  Hint: Note that $x^r = e^{r \ln x}$.

ch-intro.tex

@@ -194,7 +194,7 @@ \subsection{Typical types of courses}
 
 The chapter on
 Laplace transform (\chapterref{LT:chapter}),
-the chapter on Sturm-Liouville (\chapterref{SL:chapter}),
+the chapter on Sturm--Liouville (\chapterref{SL:chapter}),
 the chapter on power series (\chapterref{ps:chapter}),
 and the chapter on nonlinear systems (\chapterref{nlin:chapter}),
 are more or less interchangeable, and can be treated as ``topics''.

ch-laplace.tex

@@ -1747,7 +1747,7 @@ \subsection{Three-point beam bending}
 of length $L$, resting on two simple supports at the ends.  Let $x$ denote
 the position on the beam, and let $y(x)$ denote the deflection of the beam in
 the vertical direction.  The deflection $y(x)$ satisfies the
-\emph{\myindex{Euler-Bernoulli equation}}%
+\emph{\myindex{Euler--Bernoulli equation}}%
 \footnote{Named for the Swiss mathematicians
 \href{https://en.wikipedia.org/wiki/Jacob_Bernoulli}{Jacob Bernoulli}
 (1654--1705),