Lecture 15, 18.300, Thu Mar 31, 2022.
Summary
New topic: Gas Dynamics, Acoustics, and Strings.
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#050  Recall 1-D Euler eqns of Gas Dynamics.
      Explain BC for a pipe: close end and open end.
#051  Polytropic gases and gamma-gas law.
#050  Shallow water wave equations: rectangular channel & flat horizontal
      bottom. BC at closed end, or when discharging into a lake.
Derive characteristic form:
  rho_t + u*rho_x + rho*u_x = 0  times +/- c/rho
  plus
  u_t + u*u_x + (c^2/rho)*rho_x = 0
  --->   (u_t + C*u_x) +/- (rho_t + C*rho_x) = 0  \ Characteristic form.
  where  C = u =/- c  [characteristic speeds].    /
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