Exploring Shock Waves: A Mathematical Analysis

  • #1
DifferentialGalois
68
25
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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  • #2
Are you puzzled at the way the left and right tails become horizontal?
 
  • #3
haruspex said:
Are you puzzled at the way the left and right tails become horizontal?
puzzled at everything. may someone start from scratch
 
  • #4
If most of the video is puzzling, maybe is not the right point for you to start?
 
  • #5
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?
 
  • #6
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.
 
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1. What is the purpose of "Exploring Shock Waves: A Mathematical Analysis"?

The purpose of this book is to provide a comprehensive mathematical analysis of shock waves, which are sudden and dramatic changes in the properties of a fluid or gas caused by a high-speed disturbance. This analysis can help scientists and engineers better understand and predict the behavior of shock waves in various contexts, such as in supersonic flight, explosions, and astrophysical phenomena.

2. Who is the target audience for this book?

This book is primarily intended for scientists and engineers who have a background in mathematics and are interested in studying shock waves. It may also be useful for graduate students or advanced undergraduate students in related fields.

3. What mathematical concepts are covered in this book?

This book covers a wide range of mathematical concepts, including calculus, differential equations, linear algebra, and complex analysis. It also introduces more advanced topics such as shock wave theory, numerical methods, and asymptotic analysis.

4. Are there any real-world applications of the mathematical analysis presented in this book?

Yes, there are many real-world applications of shock wave analysis, such as in aerodynamics, combustion, and high-energy physics. This book provides a theoretical foundation for understanding and solving problems related to shock waves in these and other fields.

5. Is this book suitable for self-study?

While this book is primarily intended for use in a classroom setting, it can also be used for self-study. It includes numerous examples, exercises, and solutions to help readers grasp the concepts and apply them to real-world problems. However, a strong background in mathematics is recommended for self-study.

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