What Are the Key Equations in Shock Wave Analysis?

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    Integrals Shock wave
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DifferentialGalois
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Homework Statement
I don't understand anything they do after 1:26 constructing the first diagram ("the zooming in part") and devising the integral.
Relevant Equations
provided here from 1:26 ONWARDS: https://www.youtube.com/watch?v=er512TwsxNM&t=86s
the attempted is the above ex. i needa justify why and figure out the reason behind those relevant equations.
 
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haruspex said:
Are you puzzled at the way the left and right tails become horizontal?
puzzled at everything. may someone start from scratch
 
nasu said:
If most of the video is puzzling, maybe is not the right point for you to start?
well most of it requires intuition, no?