Calculus 1: Max-Min Problems (30 of 30) Derive Snell's Law Using Least Time
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- Опубликовано: 30 сен 2024
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In this video I will derive Snell's Law using least time or minimizing time dv/dt=?.
First video in this series can be seen at:
• Calculus 1: Max-Min Pr...
At 7:20 you forgot to raise the denominator to the 1/2 power. Nice proof regardless!
I think the natural question would be:
Why is it that light would try to take the fastest path?
- Physics enthusiast
The "why" questions are usual the most difficult to answer. But most often the answer can be found when you think about it in terms of energy. In nature most things will take the path requiring the least amount of energy, including light
What a wonderful man and teacher. These people who give of themselves to educate others are the true heroes.
Happy New Year Professor. Thank you so very much for explaining this thoroughly and for not missing a step. I really appreciate this.
You are welcome. Note that most of the work is done by my wife behind the scenes, filming, editing, producing, and uploading the videos as well as all the thumbnails. Without her these videos wouldn't exist.
@@MichelvanBiezen We also appreciate your wife for all the hard work she puts into these videos, so whenever we say thanks we meant for your entire team even if not stated explicitly. I believe she is also a professor so next we will say thanks Professors.
Hello, by setting the derivative = 0 we only prove that the final result is a critical point. How can we prove that it is a minimum value and not a maximum nor a horizontal inflection point?
Thank you.
By taking the second derivative to determine the concavity.
The great video! Thank you so much.
Glad you liked it!
Thank you,I just love the math presented in here
Dear sir , thanks for your usual great videos. I didn't think one could prove this without the calculus of variations.......I must be over thinking things!
just have no idea how that equation created so far. Thank you so much!
simply brilliant
Really good video, thanks
wow!!!! Thank you that was awesome.
Super awesome!
Any videos for second order derivative?
Yes, we have videos on higher order derivatives.
amazing Sir!!!
Can we do the Arthmatic mean dealing max-min problems?
why dt/dx equal to 0?
It is NOT equal to zero. But when we take a derivative and we set it equal to zero, then when we solve for the variable, we find the minimum or maximum of the function. (It is the technique used to find the minimum or maximum of a function)
Why is it that the time taken to travel the path should be minimized?
Everything in nature tends to the lowest energy or the path of least resistance
I am from India , but in my life this is first forenier video which is awesome, fully understandable...thank s sir