Justifying the equations in shock wave analysis

[DifferentialGalois]

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.

 

[haruspex]

Are you puzzled at the way the left and right tails become horizontal?

 

[DifferentialGalois]

Are you puzzled at the way the left and right tails become horizontal?

puzzled at everything. may someone start from scratch

 

[nasu]

If most of the video is puzzling, maybe is not the right point for you to start?

 

[DifferentialGalois]

If most of the video is puzzling, maybe is not the right point for you to start?

well most of it requires intuition, no?

 

[haruspex]

I've only looked at the zooming in part so far, and might not get further today, but it does not give me great confidence in the tutor.