variational principle
no piano or audio clips for now. just some rambling about classes.
this sem, my classes have got a lot of "synergy". Two recurring themes are (1) approximating infinite things using a finite basis and trying to do the best you can (2) variational principle.
(1) is really simple but it is the heart of numerical methods, whether numerical linear algebra or PDEs.
(2) is what i think an "oozing with beauty" concept which i first learned in a physics class a few years back. it has huge number of applications, in physics, numerics, PDEs, machine learning, .... the list is probably longer but that's all i know.
very often we differentiate wrt to a finite number of variables. think of a function as represented by infinitely many variables and a functional derivative is a derivative wrt to infinite number of variables. we can even think of the derivative as a row vector.
this sem, my classes have got a lot of "synergy". Two recurring themes are (1) approximating infinite things using a finite basis and trying to do the best you can (2) variational principle.
(1) is really simple but it is the heart of numerical methods, whether numerical linear algebra or PDEs.
(2) is what i think an "oozing with beauty" concept which i first learned in a physics class a few years back. it has huge number of applications, in physics, numerics, PDEs, machine learning, .... the list is probably longer but that's all i know.
very often we differentiate wrt to a finite number of variables. think of a function as represented by infinitely many variables and a functional derivative is a derivative wrt to infinite number of variables. we can even think of the derivative as a row vector.