If anyone uses these, we can make them lighter-weight this way. Here's an example template: Alpine template https://github.com/Silex/docker-emacs/blob/master/images.yml

• Chapter 1
  • Equations
  • Concluding.
• Chapter 2

\begin{equation}
\begin{split}
x &= 10 \cr
y &= 10
\end{split}
\end{equation}

Chapter 1

This is an example of how we might structure an org-mode file that can export out to Github flavored Markdown, or to a PDF.

First, let's get some code loaded up and written.

(load "ch1/utils.scm")

(define (p->r local)
  (let* ((polar-tuple (coordinate local))
         (r (ref polar-tuple 0))
         (phi (ref polar-tuple 1))
         (x (* r (cos phi)))
         (y (* r (sin phi))))
    (up x y)))

(define (spherical->rect local)
  (let* ((spherical-tuple (coordinate local))
         (r (ref spherical-tuple 0))
         (theta (ref spherical-tuple 1))
         (phi (ref spherical-tuple 2)))
    (up (* r (sin theta) (cos phi))
        (* r (sin theta) (sin phi))
        (* r (cos theta)))))

This block will generate a LaTeX version of the code I've supplied:

(->tex-equation
 ((+ (literal-function 'c)
     (D (literal-function 'z)))
  't)
 "eq:masterpiece")

\begin{equation}
c\left( t \right) + Dz\left( t \right)
\label{eq:masterpiece}
\end{equation}

You can even reference these with equation numbers, like Equation \eqref{eq:masterpiece} above.

(up 1 2 't)

#|
(up 1 2 t)
|#

Equations

Here's a test of (a = bc) and more [ \alpha_t ] equations:

(and again) this is a thing.

[ e^{i\pi} = -1 ]

[ \int_0^\infty e^{-x^2} dx = \frac{\sqrt{\pi}}{2} ]

Concluding.

This is the rest of the goods.

Chapter 2

Testing a second's output.

Exercise:

Derive Lagrange's equations for Lagrangians that depend on accelerations. In particular, show that the Lagrange equations for Lagrangians of the form \(L(t, q, \dot{q}, \ddot{q})\) with \(\ddot{q}\) terms are

\begin{equation}
\label{eq:1-10-action}
S[q](t_a, t_b) = \int_{t_a}^{t_b} L(t, x, v, a) dx
\end{equation}

\begin{equation}
\begin{aligned}
\int_{t_a}^{t_b} & ((DL) \circ \Gamma[q]) \delta_\eta\Gamma[q] = \cr
& \int_{t_a}^{t_b} 0 + (\partial_1L + \Gamma[q])\eta + (\partial_2L + \Gamma[q])D\eta + \ldots \
\end{aligned}
\end{equation}

Action for a Lagrangian that takes acceleration. The derivation will work for higher derivatives too:

On macOS (11.1), XQuartz (tried both 2.7.1 and 2.8.0_beta3) is not opening when running the following in the Docker scheme terminal:

1 ]=> (show-expression (+ 'alpha 't))
(+ alpha t)

;No return value.

XQuartz->Preferences->Security has both of the following checked: "Authenticate connections" and "Allow connections from network clients"

"xdvi" is correctly installed (working in OSX Terminal), and XQuartz is set as the default X11 application. Restarted OSX as well.