This professor is fantastic! When I listen to him I understand things deeply. (Of course, afterward I realize I have to work a bunch of problems to lock things in, but he sure sets it up darn well.)
The most difficult part of this for me to understand was why separation of variables did not just lead to two separate integrals, like in normal diffeq. I am going to post the reason here to clarify for anyone else who is having trouble He has not only separated the variables, but also the functions that depend on those variables. Normally when you separate variables in diffeq, the variables can ultimately still depend on one another. In this case, his left side cannot depend at all on the right side and vice versa. For this reason, they must both be equal to the same constant. If they are not equal to the same constant, then the equation is invalid as written.
It kind of feels like he gives the solution upfront and then gives the punchline later. To clarify, the factorized solution is the only solution for which taking the modulus of it has the time dependence fall out cleanly as a factor of 1. It is by nature a solution to the differential equation (it is a function of both x and t and has to potential to fulfill the boundary conditions), but it is the stationary solution because the time dependence falls out of the modulus.
Stationery doesn't actually means that its static.. It means that a function can be factorised as a function of time and a function of position Like... F(x, t) = cost × sinx Here cost is a function of t while sin x is a function of x Such a wave can be called stationery If you really want to get to know why it's called stationery try to draw this graph at different times by taking time equal some constant.. You will find that all the particles are doing SHM about a mean position and the wave isn't moving..
A UA-camr spotted that some of the videos were low res. We found that 55 videos were affected, this was one of those videos. They should be all fixed now. :)
This is really very informative and interesting video. Thanks to you for sharing this impressive and useful video with us.The school is really very compulsory until the age of 16 or until the student obtains his Secondary V diploma. Its mission according to guts.pk/shop/ that : to instruct, socialize and qualify the students.
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This professor is fantastic! When I listen to him I understand things deeply. (Of course, afterward I realize I have to work a bunch of problems to lock things in, but he sure sets it up darn well.)
All that background noise,,, AUGHHH. Still thankful to MIT and professors
I learnt quantum mechanics 40 years ago - wish I had learnt it like this!
The most difficult part of this for me to understand was why separation of variables did not just lead to two separate integrals, like in normal diffeq. I am going to post the reason here to clarify for anyone else who is having trouble
He has not only separated the variables, but also the functions that depend on those variables. Normally when you separate variables in diffeq, the variables can ultimately still depend on one another. In this case, his left side cannot depend at all on the right side and vice versa. For this reason, they must both be equal to the same constant. If they are not equal to the same constant, then the equation is invalid as written.
It's the most obvious way to solve linear homogiunus pde's ,
Thanks professor
That was easy to understand
Adoro essas aulas do MIT!
It kind of feels like he gives the solution upfront and then gives the punchline later. To clarify, the factorized solution is the only solution for which taking the modulus of it has the time dependence fall out cleanly as a factor of 1. It is by nature a solution to the differential equation (it is a function of both x and t and has to potential to fulfill the boundary conditions), but it is the stationary solution because the time dependence falls out of the modulus.
What is c in time dependent part
constant
Is there spreading in stationary states ?
if it stationary, why there is time dependency?what means stationary
Stationery doesn't actually means that its static..
It means that a function can be factorised as a function of time and a function of position
Like... F(x, t) = cost × sinx
Here cost is a function of t while sin x is a function of x
Such a wave can be called stationery
If you really want to get to know why it's called stationery try to draw this graph at different times by taking time equal some constant.. You will find that all the particles are doing SHM about a mean position and the wave isn't moving..
it quite hard to understand but good and informative...
what is new with this post that was posted weeks ago, thanks again
A UA-camr spotted that some of the videos were low res. We found that 55 videos were affected, this was one of those videos. They should be all fixed now. :)
thanks for all
Isn't there some way to upload videos with new clean audio?
If you have to make noise do it away from the microphone!
Marvellous....
i'm so fucking stupid
This is really very informative and interesting video. Thanks to you for sharing this impressive and useful video with us.The school is really very compulsory until the age of 16 or until the student obtains his Secondary V diploma. Its mission according to guts.pk/shop/ that : to instruct, socialize and qualify the students.
Poor audio quality!!!!!!!!!!!NO COUGH AGAIN!!!!!!!!!!
can someone give the camera person a cough drop.
It's quite hard for me to understand his way of teaching.. sry