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.
"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
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.
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...........:-)
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.
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.
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!!!!!!!
ha ha fruit flies newton apple tree apples don't fly see-d you season. dichotomy imago dio imago dei iod. biology philosophical tree. ottffssent~! deciduous tree periodic table temperature some fruit fly fruition gravity grab it. witch which. chop chop chop go the maple seeds pin-e nuts cashews god b-less Nicolas tesla 369 . philosophical three ops tree ottffssent~! L-ove Leonardo da vinci egg seed parallel ect.
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
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!
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
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
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.
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
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.
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 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!
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'
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.
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.
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.
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.
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.
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.
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" :)
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?
I suppose you are plus minus 12 years old. So my answer is: you can divide or multiply right equality by any expression which is not zero and you receive right equality . And when you divide by some expression (by x in this case) you have to concern the case x=0 afterwards.
3x^2=2x if you cancel the x's and are left with 3x=2 ---> x=2/3 i've never seen that way of solving quadratic equations before? could someone tell me what it's called, does it always work? My mind just got blown THANKS
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
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?
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.
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!
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.
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.
@@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!
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.
