I cannot put in words how helpful this approach of really understanding the theory behind the mathematics is, rather than just memorizing things like the Õ great educational system tells us to do.
PS: After you're done with Differential Calculus, It would be really great if you do the same approach of explaining the theory behind Linear/Multi-linear/Matricial and/or Tensor Algebra. Or maybe get into Stochastic Calculus as it's on the same lines of the current series. Applying your approach to these subjects would be really enlightening since they almost look daunting when you try to get to the bottom of the theory.
Integration is NOT just about finding the AREA but about finding any WHOLE (W) called the Integral (I) given the Individual Components (ICs) called derivatives of that W or I. In brief it's about Individual components (ICs) called derivatives and the WHOLE (W) called the Integral (I) of the given ICs or derivatives Thus if the ICs are individual mini lines, then the W or Integral is the length of the Curve. If the ICs are mini areas the W or I is the Whole Area under the curve. If the ICs are mini volumes then the W or I is the Whole Volume. If the ICs are mini ANYTHING like Charge or Force or Energy etc. then the W or I is the Whole Charge or Force or Energy etc
It is used as a mnemonic for when you start working with more complicated Integrals or differential equations. Right now it may not seem like it does anything, but it will start to become useful when you learn techniques for evaluating more complex functions.
Yoni Smadja dx is the difference between two points . A difference which is almost equal to zero , but not zero . U might say this difference is equal to 1/100 or 1/1000 or 1/100000000 or 1/10000000000 , yes the amount of difference which I mentioned above is very very small and almost equal to zero , but they are still some values which you can see and count. dx is some thing that small that a human can't imagine . It's just a previous point before zero , which is obviously not understandable for humans.you can make any number as small as you can by putting more zeros in ur denominator as I did in above examples, but u can never achieve to a point which is just a previous point before zero. So the conclusion of my comment is that dx which is a difference between two points Let's say difference between points X and a so , dx = x - a Such that x is almost equal to a Which we say in mathematics as" x proceeds to a" . An arrow symbol is used to say this phrase which I don't have here. Than you can say that dx proceeds to zero It's a very beautiful concept in mathematics derived by humans. As we are staying at a same point because x and a are almost equal but at the same time we find a difference at that point. Hope.u get something..
its just the length of each square inside the integral. It gets closer to zero as the squares get smaller because they decrease in length and also more are added to the total integral area.
God will help you. Get supernatural help. God is always on your team. God wants to be a part of your day. God wants to be a part of your schedule. Make room to spend time with Jesus.
I cannot put in words how helpful this approach of really understanding the theory behind the mathematics is, rather than just memorizing things like the Õ great educational system tells us to do.
PS: After you're done with Differential Calculus, It would be really great if you do the same approach of explaining the theory behind Linear/Multi-linear/Matricial and/or Tensor Algebra. Or maybe get into Stochastic Calculus as it's on the same lines of the current series. Applying your approach to these subjects would be really enlightening since they almost look daunting when you try to get to the bottom of the theory.
Is it only me or the video cuts off abruptly at 2:27, I'm frustrated that I can't watch it till the end
Wow he's really mastered the art of drawing a straight line :P
Nick W he used the shift key
@@ishandangi133 Don't ruin the fun maaannn
Lol
That is definitely an integral.
Integration is NOT just about finding the AREA but about finding any WHOLE (W) called the Integral (I) given the Individual Components (ICs) called derivatives of that W or I. In brief it's about Individual components (ICs) called derivatives and the WHOLE (W) called the Integral (I) of the given ICs or derivatives
Thus if the ICs are individual mini lines, then the W or Integral is the length of the Curve. If the ICs are mini areas the W or I is the Whole Area under the curve. If the ICs are mini volumes then the W or I is the Whole Volume. If the ICs are mini ANYTHING like Charge or Force or Energy etc. then the W or I is the Whole Charge or Force or Energy etc
You draw perfect straight lines!!! OMG
What is going on with this video... It says 7 minutes but cuts off at 2? It does the same thing on the app. It cuts off in the middle of him talking.
New drawing tool is slick as hell, Sal!
Thanks for Doing these videos again better
Please can you decrease the size of the cursor, as it distracts and doesn't let concentrate on what you write.
No he needs his CS:GO cross hair. How else is he going to draw perfectly straight lines and tap heads with the wisdom of math?
Very helpful video, please keep doing videos about mathematical theory
Which software you are using ........and hardware.....please tell Khan Sir if possible?
سلام عليكم ورحمه الله وبركاته
First to comment. Once more a very helpful video. Thanks Sal Khan, keep your good work going
Hello calc class
What’s the point of dx??? It seems like it just gets ignored most the time!
It is used as a mnemonic for when you start working with more complicated Integrals or differential equations. Right now it may not seem like it does anything, but it will start to become useful when you learn techniques for evaluating more complex functions.
G...
What is dx?
Yoni Smadja dx is the difference between two points . A difference which is almost equal to zero , but not zero . U might say this difference is equal to 1/100 or 1/1000 or 1/100000000 or 1/10000000000 , yes the amount of difference which I mentioned above is very very small and almost equal to zero , but they are still some values which you can see and count. dx is some thing that small that a human can't imagine . It's just a previous point before zero , which is obviously not understandable for humans.you can make any number as small as you can by putting more zeros in ur denominator as I did in above examples, but u can never achieve to a point which is just a previous point before zero.
So the conclusion of my comment is that dx which is a difference between two points
Let's say difference between points
X and a
so , dx = x - a
Such that x is almost equal to a
Which we say in mathematics as" x proceeds to a" . An arrow symbol is used to say this phrase which I don't have here.
Than you can say that
dx proceeds to zero
It's a very beautiful concept in mathematics derived by humans. As we are staying at a same point because x and a are almost equal but at the same time we find a difference at that point.
Hope.u get something..
its just the length of each square inside the integral. It gets closer to zero as the squares get smaller because they decrease in length and also more are added to the total integral area.
God will help you. Get supernatural help. God is always on your team. God wants to be a part of your day. God wants to be a part of your schedule. Make room to spend time with Jesus.
Unfortunately, God didn't make it past first interview and isn't part of the team.