No guarantee. I am using 'nice' examples to clarify the goal we are after. It is much like saying 'continuous functions have graphs that can be drawn without lifting the pen'. Of course, we are assuming bounded variation there. That is why there is no alternative to a rigorous proof. But that is only a dumb tool. Intuition provides the overall plan, ignoring technicalities.
In showing how to generalize the notion of the derivative to higher dimensions, at 5:00 Prof.Chakraborty brilliantly animates the same equation for one dimension, and introduces the matrix M, the need for which can be easily 'seen', creating an indelible memory in the mind of the student. This same intuition can be carried to the Hessian.
Dear Sir at 15:40, could you please mention what is the guarantee that the lines will be mapped to nice curves? Thank you!
No guarantee. I am using 'nice' examples to clarify the goal we are after. It is much like saying 'continuous functions have graphs that can be drawn without lifting the pen'. Of course, we are assuming bounded variation there. That is why there is no alternative to a rigorous proof. But that is only a dumb tool. Intuition provides the overall plan, ignoring technicalities.
Very clear and easy to understand. Congratulations!
Sir, I would like to request you to make some videos on measure theory, Baire measure, Borel measure etc.
Sir!! You're just a gem!!!❤️❤️
In showing how to generalize the notion of the derivative to higher dimensions, at 5:00 Prof.Chakraborty brilliantly animates the same equation for one dimension, and introduces the matrix M, the need for which can be easily 'seen', creating an indelible memory in the mind of the student.
This same intuition can be carried to the Hessian.
Lovely
So lucid!
Can You explain the geometric interprttn of JACOBIAN??????
Loved your explanation
Glad you liked it
Thank you very much!
Thank you sir, it is explained very clearly
i love this explanatory video very much
Really good
Nicely explained
wow