MIT courses are not about teaching simple things in a complicated way which ordinary ppl do not understand. It is about teaching complicated things in a simple way where ppl get an extra 'dimension' of understanding. THank you Sir for an excellent lecture and thanks to MIT initiative to provide these courses online for rest of the world.
Amazing how Professor Gilbert can explain the key ideas clearly. He is by far the best teacher I ever had. A lot of the concepts he explain I usually learned them by memory now I can see the big picture.
This is a Hats off to the Calculus Master. Durring my engineering this was just a night mare. I now love calculus after viewing the three parts of this vedio series. Thanks to you. To increase the reach to remotest areas of the world there are lots of breakages that happen during the sessions. It would be good if these vedios could be available for lower bandwidth connections too. A BIG THANK YOU!
Strange truly deserves a Medal of Honor of sorts for his monumental contributions to the advancement and dissemination of mathematical knowledge and intuitions in these MIT series. The Internet has created a whole new and accessible dimension of learning not available to the previous generations of students.
The maxima of "like" function for this video is infinte. This video kept on giving me "aww" moments. Thankyou sir. I always wondered why we need to take the derivative of x and assign to 0. I will always be indebted to you.
I wish I had had a teacher like Strang in high school. The example of the way to drive to MIT are great ways to explain why you would use these derivatives in real life. Great course! Thank you.
This is a Hats off to the Calculus Master. Durring my engineering this was just a night mare. I now love calculus. Thanks to you. To increase the reach to remotest areas of the world there are lots of breakages that happen during the sessions. It would be good if these vedios could be available for lower bandwidth connections too. A BIG THANK YOU!
I saw concave and convex curves, and thought this lecture might be too difficult for me. Then, he explained it so easily and well, and I’m very satisfied having watched this. Thanks a lot!
God bless you Mr. Strang!! Thank you very much for your efforts... I am taking a second look at calculus as I prepare for graduate school and your videos have been most helpful! Thank you!!!!!!!
I never thought i could finish this 38mins video lecture. but once i started to watch its really hard to close the video. Thank you for this excellent lecture Sir and also thanks to MIT for this initiative.
MIT OpenCourseWare Max and Min and Second Derivative 'Professor Strang Chapters. The Second Derivative: The derivative of the derivative. Subtitles: Jimmy Ren.' 2:10 min ... acceleration 2:56 min ... Newton's Law, F = ma
The first and second derivative as combination of zero positive and negative bending as it oscillstes between convex and concave planes differentiated by that an be applied in digital communication developed by Nyquist further developed by shannon where the basic first and second derivative as otherwise may be a function of basic digital functions. Inspired by MIT course offered by this professor. Sankaravelayudhan Nandakumar
The triangulated surface in modili form is derived at in between maxima and minima around the point of inflection in between with increase in frequency of transition as applicable entropy equation in understanding the hydrogen attraction and repulsion in boson gas as a function of interactive magneticfield over electricfield as Hall's interpretation. A definition on electron gap in between atom and nucleus could be arrived at the interpretation of first derivative and sevond derivative based on the sign of the sevond derivative Sankarabrlayudhan Nandakumar.
Sorry i should have watched the last 40 seconds to know the answer to my silly question now :)..the answer is there....great video and wonderful lecturer
The oscillation becoming bending down convex and bending down a concave with inflexion point at which the sign of bending oscillate between concave and convex producing positive and negative energy.
Really Very Nice Smooth Teaching :) Btw, been French, looks to me that the French name for calculus is way much meaningful as it is "analyse" (analysis), which is about "cutting in (little) peaces" etymologically, which goes very well imho with the concepts of "dx" and "dy" :)
"Why move myself 20 miles to MIT when I can, with a click of the mouse, move not 20 inches and absorb the same knowledge." ~The wise musings of an unemployed student drowning in debt
I'm having trouble understanding the word problem at 26:27. I don't understand *why* the fastest time is where the first derivative of the graph is zero. What is the actual graph, and why does the derivative of zero (where the first graph's slope is zero?) mean the fastest time when solving the equation?
It is because the function "time it takes to arrive at work" reaches either a min or a max point when its first derivative is equal to zero. We don't know what its graph looks like, but we do know that its value must reach a min or max when its derivative is zero. So when the value of this function is minimum, the time it takes to arrive at work is minimum, because it is what the value of this function represent, the time it takes to arrive at work.
Very nice explanation.superb.minutest of minutest study is knowledge.h ow?how?every thing is from mind.Mind is full of equation.while going to bed you must shake your head violently then only equations shall fall down you will get sleep.
I have now attended Walter Lewin's Physicd class, Susskind at Stanford and Yale Physics and now Mathematics at MIT! I am thrilled to learn from the greatest lecturers/ professors of the day - this is an opportunity I would not have otherwise and it means everything to me. I've learned so much! My sincerest gratitude to you all for these lessons.
No kidding, it looks like the biggest problem with getting a good professor is getting one that's not arrogant, presents the facts in a logical way and the best professors will incidentally get you to use the best practices without even having to stress it.
The conflection points becomes the square comfogurstoon points pave the way for basic figitsl numbers while denfing the pulses in between zeros and ones in signal sending in computstionsl digitsal mathematics.
@@user-qj4zr1pj9y Hi. I was the original poster (though have a different account now). Yes, I still remember what the lectures taught me. Probably because I have found it useful in my job. Maths (I'm from UK) is awesome!
while looking for the min time, you use the deriv=0, but that applies for both the min and the max, why assume that what you found was the min and not the max, without using the second deriv, or by studying the monotony of the function ???
the lecturer in the last 40-50 seconds explain this point ......he explained that he should have calculated the second derivative at this point to show that the second derivative is positive , and hence its bending upward at this point , so its a minimum.....please watch the last minute of the lecture....regards
you can only do that if the formula for the equation is in the form ax^2 +bx = 0 in this form we can presume that one anwer has to be zero, and it is simple algebra to find out the second number. You would have not seen this very often because most equations we work with are in the form ax^2 + bx + c = 0 this c value muddles it up and means you can not do what he did.
When differentiating for the second time your found the two roots as 2/3 and 0. I understand how you got 2/3 but a bit shaky on how you got 0 without the graph. A bit of help would be nice...
if your talking about the 3x^2-2x if you factor it you can pull out a 'x' and a '3x-2' and if you solve for x for both of them you get 0 for 'x' and you get 2/3 for '3x-2'
i could say the same as zik667, my teacher had a post doctor at a french institution at math teaching and still hadnot that good didactics. MIT rules, i wish i could study over there. Im brazilian and i have my engineer course at UFSC - Santa Catarina Brazil
Great example, but If the b was to be smaller than x then there should be an "absolute value sign" on the right side, because one cannot lessen the time by driving backwards, right?🙂 But this wouldn't matter since it always take longer to overshoot and drive back.
If i'm looking for minimum time, then why to set first derivative of time function to zero? Why not setting time function itself directly to zero? Why deferentiation is required ?
Reason #1: The time function itself is never zero. You will always need some time > 0 to drive from Home to MIT, no matter which way you choose. Reason #2: You are not looking for the point where time is zero. You are looking for the point where time is minimum.
Thank you for this video......just a question , in the end problem why we assume that the answer is the minimum time and not the max time?.....any suggestions?
Interesting he talks about inflection point in the US economy in 2010 and thinks we might be turning around (as an example).......it has now happened...........:-)
It was originally arrived at using limits. You can probably find the proof (which is quite simple actually) in any introduction to derivatives lecture.
Jolly Jokress its called the "power rule"! (1st) you take the exponent(power) down from its position, and multiply it times whatever coefficient and/or variable that is there already. (2nd) you reduce what the original exponent was by 1-whole integer, to get what the new exponent(power) will be. Power Rule formula: nx^n-1 ex: x^2 derivative= 2x^1 or 2x ex: x^3 derivative= 3x^2 ex: x^1/2 derivative= 1/2x^-1/2 hint: [1- (1/2)= -1/2] ex: 12x^3 = 36x^2 ex: 2x^5 = 10x^4 and that's the basis of the "Power Rule" used when necessary in calculus differentiation😊😊😊😊
You should read up on infinitesimals. This it the cornerstone of derivatives and calculus. Newton discovered it and used ‘h’ whereas Leibnitz used ‘delta’ and published it. there’s a whole history there which is fascinating too. However it is very simple in principle and worth reading as it will clear up how this whole derivative thing works.
Brilliant lecture! One question, I can't figure out why a/sqrt3 = 30 degrees. On the unit circle, cosx of 30 is sqrt3/2, and sine of 30 degrees is 1/2. Anybody?
a = cos 30 x = sin 30 x = a / sqrt 3 ----------------- sin 30 = cos 30 / sqrt 3 Note that as he said this holds only for a speed ratio of 2/1 which is build in and hidden in sqrt 3. Actually it's x = a / sqrt( (60/30)^2 -1). He lost that somewhere during the process.
what about the 3rd derivative test?....(used specifically when 2nd derivative is zero, giving no clue as to gradient and concavity - as you MAY or MAY NOT have an inflection pt. when f''=0 e.g. straight line). Cool thing about that test is that when the modulus of it >0, we have an inflection point (rising if > 0, falling if
How did the professor see that x=2/3 at 17:30? obviously one of the possible solutions is that x=0 but how did he see that the second solution was 2/3 without factoring or using the quadratic formula?
![Lp. Сердце Вселенной #60 РОЖДЕНИЕ ЛОЛОЛОШКИ [Финал] • Майнкрафт](http://i.ytimg.com/vi/YoR0pAV9FVQ/mqdefault.jpg)
MIT courses are not about teaching simple things in a complicated way which ordinary ppl do not understand. It is about teaching complicated things in a simple way where ppl get an extra 'dimension' of understanding. THank you Sir for an excellent lecture and thanks to MIT initiative to provide these courses online for rest of the world.
Tomsci K very true.
I got really emotional seeing Professor Strang talk. Seeing a person devoting a lifetime to math and teaching itself is touching and inspiring.
I have had the same reaction, actually. Btw he just recently retired at age 88. End of an era.
This is called a genius because I don't know about others but this presentation is massive and therefore you are the teacher of MIT.Thanks a lot.
This wasn't even part of what I was looking for but I watched the whole thing, I enjoyed this lecture because he's a great Prof.
Amazing how Professor Gilbert can explain the key ideas clearly. He is by far the best teacher I ever had. A lot of the concepts he explain I usually learned them by memory now I can see the big picture.
It's like watching a superhero of calculus at it's best. Thank you, Sir!
No Matter what Technology advances, need of such brilliant teachers will always be felt
Holy cow, 38 minutes with you on UA-cam did more good then 2 hours with the book. THANK YOU SO MUCH
34:02 "Drive at a 30 degrees, hope there's a road going that way. Sorry about that point" LOL this guy is genius and funny at the same time :D
This is a Hats off to the Calculus Master. Durring my engineering this was just a night mare. I now love calculus after viewing the three parts of this vedio series. Thanks to you.
To increase the reach to remotest areas of the world there are lots of breakages that happen during the sessions. It would be good if these vedios could be available for lower bandwidth connections too.
A BIG THANK YOU!
No words for this man's teaching.Really loved it.
Strange truly deserves a Medal of Honor of sorts for his monumental contributions to the advancement and dissemination of mathematical knowledge and intuitions in these MIT series. The Internet has created a whole new and accessible dimension of learning not available to the previous generations of students.
The maxima of "like" function for this video is infinte. This video kept on giving me "aww" moments. Thankyou sir. I always wondered why we need to take the derivative of x and assign to 0. I will always be indebted to you.
I wish I had had a teacher like Strang in high school. The example of the way to drive to MIT are great ways to explain why you would use these derivatives in real life. Great course! Thank you.
This is a Hats off to the Calculus Master. Durring my engineering this was just a night mare. I now love calculus. Thanks to you.
To increase the reach to remotest areas of the world there are lots of breakages that happen during the sessions. It would be good if these vedios could be available for lower bandwidth connections too.
A BIG THANK YOU!
I saw concave and convex curves, and thought this lecture might be too difficult for me. Then, he explained it so easily and well, and I’m very satisfied having watched this. Thanks a lot!
Thanks. One of the most simple, and brilliant explanations regarding this subject.
excellent explanation, you could be in a regular university, but you could watch classes from the best teachers in the world. Thanks MIT
Doing my masters in Econ Science and I still come to watch these intuition classes by Prof Gilbert.
Legendary!
the greatest calculus teacher in the whole wide world
God bless you Mr. Strang!! Thank you very much for your efforts...
I am taking a second look at calculus as I prepare for graduate school and your videos have been most helpful! Thank you!!!!!!!
DR. Strang thank you for another excellent lecture on classical selection of max and min problems in calculus.
Most beautiful way to define double derivative test. Hats off to you sir.
I have been studying from you sir the main topics in calculus, thank you!
I never thought i could finish this 38mins video lecture. but once i started to watch its really hard to close the video. Thank you for this excellent lecture Sir and also thanks to MIT for this initiative.
MIT OpenCourseWare
Max and Min and Second Derivative
'Professor Strang
Chapters.
The Second Derivative: The derivative of the derivative.
Subtitles: Jimmy Ren.'
2:10 min ... acceleration
2:56 min ... Newton's Law, F = ma
Thank you very much Dr. Strang, wish I had you back when I took calculus.
'If I knew where we were (22:58) mathematics would even more useful than it is...which would be hard to do!' This guy is fantastic.
this man play beautiful mathematical music ,
the exact definition of deep learning
What a teaching style
"And there's a sign of hope. It started bending up."
Thank you, professor. This is amazingly clear.
hats off for gilbert strang
Thank you! I am doing a condensed 8 week course that is kicking my ass and this is making it all "tangible"!
I really enjoy your videos. You're helping me through my Business Calculus class at Brockport College this semester.
I love calculus, It is great exercise for the brain. I love the logic and the patterns.
This man, has explained this very well!! Thank you for this video!!
Thank you for this video!! Very well done. I understand soooo much better.
if i could afford the mit's fees i definitely would have been a part of that institute which is the best in the world.
I can't resist to myself to watch these explanations.
Excellence and hard work personified!!
nice lecture ...really I highly influenced ....because of its simplicity and graphical interpretation......
The first and second derivative as combination of zero positive and negative bending as it oscillstes between convex and concave planes differentiated by that an be applied in digital communication developed by Nyquist further developed by shannon where the basic first and second derivative as otherwise may be a function of basic digital functions. Inspired by MIT course offered by this professor.
Sankaravelayudhan Nandakumar
This guy is an amazing teacher.
this videos are enough for gate exam without practice,i love this lectures
The triangulated surface in modili form is derived at in between maxima and minima around the point of inflection in between with increase in frequency of transition as applicable entropy equation in understanding the hydrogen attraction and repulsion in boson gas as a function of interactive magneticfield over electricfield as Hall's interpretation. A definition on electron gap in between atom and nucleus could be arrived at the interpretation of first derivative and sevond derivative based on the sign of the sevond derivative
Sankarabrlayudhan Nandakumar.
Many thanks, you are excellent, so simple so clear
Great work, Professor!
This video/topic is important to understand the Laplacian in multivariable calculus
Sorry i should have watched the last 40 seconds to know the answer to my silly question now :)..the answer is there....great video and wonderful lecturer
The oscillation becoming bending down convex and bending down a concave with inflexion point at which the sign of bending oscillate between concave and convex producing positive and negative energy.
Really Very Nice Smooth Teaching :)
Btw, been French, looks to me that the French name for calculus is way much meaningful as it is "analyse" (analysis), which is about "cutting in (little) peaces" etymologically, which goes very well imho with the concepts of "dx" and "dy" :)
"Why move myself 20 miles to MIT when I can, with a click of the mouse, move not 20 inches and absorb the same knowledge."
~The wise musings of an unemployed student drowning in debt
how did it go?
I'm having trouble understanding the word problem at 26:27. I don't understand *why* the fastest time is where the first derivative of the graph is zero. What is the actual graph, and why does the derivative of zero (where the first graph's slope is zero?) mean the fastest time when solving the equation?
It is because the function "time it takes to arrive at work" reaches either a min or a max point when its first derivative is equal to zero. We don't know what its graph looks like, but we do know that its value must reach a min or max when its derivative is zero. So when the value of this function is minimum, the time it takes to arrive at work is minimum, because it is what the value of this function represent, the time it takes to arrive at work.
Very nice explanation.superb.minutest of minutest study is knowledge.h ow?how?every thing is from mind.Mind is full of equation.while going to bed you must shake your head violently then only equations shall fall down you will get sleep.
Prof Strang is COOL! love the videos
Very good point to point explanation
divide x on both sides (3x^2)/x=(2x)/x,
then simplify to get 3x=2,
then divide each side by three to solve for x, x=2/3
Thank you so much for uploading these courses..
Great lecture Prof - thank you!
Thanks MIT!!
I love me some ♡Calculus♡
I have now attended Walter Lewin's Physicd class, Susskind at Stanford and Yale Physics and now Mathematics at MIT!
I am thrilled to learn from the greatest lecturers/ professors of the day - this is an opportunity I would not have otherwise and it means everything to me. I've learned so much!
My sincerest gratitude to you all for these lessons.
The good Dr. needs to switch to de-caf. Excellent presentation.
No kidding, it looks like the biggest problem with getting a good professor is getting one that's not arrogant, presents the facts in a logical way and the best professors will incidentally get you to use the best practices without even having to stress it.
The conflection points becomes the square comfogurstoon points pave the way for basic figitsl numbers while denfing the pulses in between zeros and ones in signal sending in computstionsl digitsal mathematics.
Thanks Professor Strang.
Do you stil remember what you have learned from these lectures ? 😄
@@user-qj4zr1pj9y Hi. I was the original poster (though have a different account now). Yes, I still remember what the lectures taught me. Probably because I have found it useful in my job. Maths (I'm from UK) is awesome!
@@newbarker523 Good for you !! Yaa Maths is awesome when you learn from Gilbert.!!
The combustion graph follow a sin and cos curve follow maximum and minimum.
Thus maxima and minima points with combustion inflexions follow a sine curve and cos curve.
Appreciated with impressive lecture!
while looking for the min time, you use the deriv=0, but that applies for both the min and the max, why assume that what you found was the min and not the max, without using the second deriv, or by studying the monotony of the function ???
the lecturer in the last 40-50 seconds explain this point ......he explained that he should have calculated the second derivative at this point to show that the second derivative is positive , and hence its bending upward at this point , so its a minimum.....please watch the last minute of the lecture....regards
you can only do that if the formula for the equation is in the form ax^2 +bx = 0
in this form we can presume that one anwer has to be zero, and it is simple algebra to find out the second number. You would have not seen this very often because most equations we work with are in the form ax^2 + bx + c = 0 this c value muddles it up and means you can not do what he did.
Thanks a lot for sharing your knowledge!
@ 8:56 spoken like a true Mathematician!
thanks for graphical explanation.
how. do. you. explain. so. well.
Will you help me how did you get to the 30 degrees?
🙏 మీరు చేస్తున్న సేవకు ధన్యవాదములు🙏
Thank you, great job explaining.
When differentiating for the second time your found the two roots as 2/3 and 0. I understand how you got 2/3 but a bit shaky on how you got 0 without the graph. A bit of help would be nice...
if your talking about the 3x^2-2x if you factor it you can pull out a 'x' and a '3x-2' and if you solve for x for both of them you get 0 for 'x' and you get 2/3 for '3x-2'
Thank you so much 🙏
this guy is great!
hi youre cute
i could say the same as zik667, my teacher had a post doctor at a french institution at math teaching and still hadnot that good didactics. MIT rules, i wish i could study over there. Im brazilian and i have my engineer course at UFSC - Santa Catarina Brazil
First class teacher.
Nice lecture 👍👍👍
Love this, I've subscribed. Thanks for sharing; Jesus Christ Bless
Pure gold!
Great example, but If the b was to be smaller than x then there should be an "absolute value sign" on the right side, because one cannot lessen the time by driving backwards, right?🙂 But this wouldn't matter since it always take longer to overshoot and drive back.
best explanation
Good one bruh..was a bit skeptic at first due to,too much fidgeting of yours...but the last problem was cool
what's up doc? a very relaxing informative lecture. thanks. B+)
If i'm looking for minimum time, then why to set first derivative of time function to zero?
Why not setting time function itself directly to zero?
Why deferentiation is required ?
Reason #1: The time function itself is never zero. You will always need some time > 0 to drive from Home to MIT, no matter which way you choose.
Reason #2: You are not looking for the point where time is zero. You are looking for the point where time is minimum.
@@wbaumschlager great 👍, zero time means stay at home no need to drive.
What's the name of this wonderful teacher
Gilbert Strang
Thank you for this video......just a question , in the end problem why we assume that the answer is the minimum time and not the max time?.....any suggestions?
Interesting he talks about inflection point in the US economy in 2010 and thinks we might be turning around (as an example).......it has now happened...........:-)
Check out the Elliot Wave Theory to see some beautiful market behaviour analysis and predictions. Calculus, fractals, wave theory... sexy stuff. :)
you are brilliant! thanks a lot mate
Can someone please tell me why the rule of derivative is valid? Why is x^2 always 2x and x^3 always 3x^2 ... derived??? THX!
It was originally arrived at using limits. You can probably find the proof (which is quite simple actually) in any introduction to derivatives lecture.
Jolly Jokress its called the "power rule"! (1st) you take the exponent(power) down from its position, and multiply it times whatever coefficient and/or variable that is there already.
(2nd) you reduce what the original exponent was by 1-whole integer, to get what the new exponent(power) will be.
Power Rule formula: nx^n-1
ex: x^2 derivative= 2x^1 or 2x
ex: x^3 derivative= 3x^2
ex: x^1/2 derivative= 1/2x^-1/2
hint: [1- (1/2)= -1/2]
ex: 12x^3 = 36x^2
ex: 2x^5 = 10x^4
and that's the basis of the "Power Rule" used when necessary in calculus differentiation😊😊😊😊
U can use first principle to get d answer...
You should read up on infinitesimals. This it the cornerstone of derivatives and calculus. Newton discovered it and used ‘h’ whereas Leibnitz used ‘delta’ and published it. there’s a whole history there which is fascinating too. However it is very simple in principle and worth reading as it will clear up how this whole derivative thing works.
Look here.... tutorial.math.lamar.edu/Classes/CalcI/DefnOfDerivative.aspx
Brilliant lecture! One question, I can't figure out why a/sqrt3 = 30 degrees. On the unit circle, cosx of 30 is sqrt3/2, and sine of 30 degrees is 1/2. Anybody?
a = cos 30
x = sin 30
x = a / sqrt 3
-----------------
sin 30 = cos 30 / sqrt 3
Note that as he said this holds only for a speed ratio of 2/1 which is build in and hidden in sqrt 3. Actually it's x = a / sqrt( (60/30)^2 -1). He lost that somewhere during the process.
Wowwwww!!
Great 👍👌👍👌👍👌👍👌👍
Thank You!
what about the 3rd derivative test?....(used specifically when 2nd derivative is zero, giving no clue as to gradient and concavity - as you MAY or MAY NOT have an inflection pt. when f''=0 e.g. straight line). Cool thing about that test is that when the modulus of it >0, we have an inflection point (rising if > 0, falling if
That's true everywhere except when x=0 so you have to be careful doing that.
How did the professor see that x=2/3 at 17:30?
obviously one of the possible solutions is that x=0 but how did he see that the second solution was 2/3 without factoring or using the quadratic formula?
this stuff helps thanks