Lecture 17, 18.300, Thu Apr 7, 2022.
Summary
Continue with Gas Dynamics, Acoustics, and Strings.
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#053 Finish. General case, Y_t + A(x, y)*Y_x = F(x, u),
     where A is real diagonalizable [hyperbolic system].
     Do further review of linear algebra [case A self-adjoint].
#054 Done in prior lecture(s).
#055 Back to characteristics for Isentropic Gas Dynamics.
     Show how they interact, in general. Cannot solve them independently
     of each other.
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Introduce Riemann invariants. NOTE: this is in the supplementary notes
to problem set #5.
Describe how to ``in principle'' solve the equation in small dt steps,
using the characteristics. From this introduce the notions:
--- DOMAIN OF DEPENDENCE. \  See #056.5
--- DOMAIN OF INFLUENCE.  /
Note that, in particular, if the initial conditions are non-trivial only
in some interval [a, b], the solution will remain trivial both
--- ahead of the fastest characteristic starting at x = b.
--- behind the slowest characteristic starting at x = b.

    CHECK THE PICTURE IN: Lecture17_finite_speed_of_propagation
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#056 Simple waves.
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