Haha! That was me too! I was a Linguistics major and then I realized that with only 8 more math credits I'd have a double major in Math and Linguistics! Haha! At least I'm not the only one out there!
That's all I remember from Calc 1, the derivative of x^2 = 2x lol. Of course, that was the "shortcut," but we had to do it with all the dy/dx notation. I remember that I loved doing quotient derivatives for fun. What's wrong with me? Linguistics major BTW.
lol the people who learn single variable calc in MIT are the SPED section of high school. Im going to walk into some dumbass college with advanced calc. lol this is so pathetic,
Herr Professor, Gruess Gott! mehr Danken fuer sein Ausgabe zu uns, dass Deutscher Studentversammlung in Kalifornien. Sein solution zu dies hochwissenschaftlich Mathematikkonzept in dies faehigkeit gibt gross Froehlichkeit zu uns und unser Glaubig. Stern von Afrika zu Sie und sein Schul.
@AbitOnus i was only asking n god mind ur tongue i knw ur jealous maybe ur seat got stolen by an Indian but v cnt help t theres crazy competition in India n it takes balls to get in which u clearly dont have n v are way smarter than u n as we progress v dont leave our basic manners behind like nt abusing women n if u understnd eng in those vids den dnt c them!!
When the professor uses the term "speed"; I believe he should be using the term "velocity". My understanding is that speed = |velocity|. That is speed (magnitude) is always positive, where velocity may be positive or negative (magnitude and direction).
@kc8omg Hello it is not about what you use. It is about how you use it or what you do with it. Mr. White board there are many with one. You will be able to distinguish the difference. Indeed that is the choice of the Professor well you could choose to teach with what you feel is more appropriate.
wow, we need more teachers like this. Period. He gives a clear cur examples that does''t confuse you further like most teachers. I have taken calculus before, but you always need to review if you dont use it often. I found this as not only a review, but I also learned something new. Awesome.
@AnimeBelover they can afford best chalks in the world. these chalks consist about 28% of calcium this why these chalks very tough and u can draw long straight lines. and if someone have trouble with teeth it can be eaten as well. but before u need smash chalks or scrape off whiteboard and mix it with some limon- or other acid. without acid you wont consume calcium. they called also eatable chalks.
51:57 he shows f(x) is related to limit while f(x0) is not related to limit, so:
47:20 why is suddenly EVERYTHING divided by (x - x0) ? Consequently because of that limit applies to EVERYTHING and, in my opinion, it contradicts 51:57
I don't buy the last proof. If one never actually uses x = xzero, a zero never exists. In the limit we don't know if f prime tends to zero, infinity, finite, or undefined. Therefore, we don't know if the final product ever approaches zero.
@SacredSteve he used the product rule for limits (but skipped a step)
1) lim as x tends to xzero( f(x) - f(xzero) )( (x-xzero)/(x-xzero) ) =
2) lim x tends to xzero [ ( f(x) - f(xzero) )/(x-xzero) ][lim x tends to xzero (x-xzero)
in 2) the first lim equals f ' (xzero) by the definition of the derivative
the lim x tends to xzero (x-xzero) is evaluated by substituting x for xzero giving xzero - xzero = o therefore we are given f ' (xzeor)[0] = 0 notice the 2 limits are solved independently
@yalg22@yalg22 1) is not the definition of the derivative since it is multiplied by (x-xzero)
Also, independent limit taking is a neat trick. It really makes no sense intuitively. That is the whole problem with the proof. Without independent limit taking you end up with 0/0 in the limit multiplied by some unknown delta f which also approaches zero in the limit under the assuption of continuity.
@SacredSteve It is the product of the definition of the derivative and x - xzero. so originally he started with f(x) - f(xzero) and multiplied it by (x-xzero)/(x-xzero). That can be written as [ (f(x) - f(xzero)) / (x - xzero)] * (x-xzero) this is the product of the difference quotient (the def of derivative) and x - xzero. Using the limit law known as the product rule for limits (not discussed in this lecture) you write it as the product of 2 limits and solve each 1 independently.
You just said something exactly as he stated it. I know exactly what he did. My whole point is that the logic of solving each limit independently is flawed.
@SacredSteve part 2 response. this is not some magical bs he pulled out of his ass. limit laws have their own proofs and you need to know something called mathematical analysis to understand it fully. Its been a while since I calc 1, but I know the subject of analysis is touched on.
@SacredSteve and my point is that it's not flawed. I said twice already that he used the product rule for limits, which apparently you haven't even bothered looking up before responding back. Why don't you get a book and learn more about limits before you make stupid claims. I'm done with this pointless argument.
Look, your product rule argument is circular. The proof of the product rule "assumes" two things: 1) That the limits exist. 2) that the functions are differentiable (at least around the limits). Continuity can't be proven, if that is the assumption you are beginning with.
@SacredSteve Why are you posting this crazy stuff? Of course the function must be continuous at a point to be differentiable at that point, duh. Continuity can be proven. If lim x-->a f(x) == f(a) then the function is continuous at x=a. There are more rigorous ways to show all of this. It is an intro calc course, and you obviously don't understand that some assumptions must be made in the beginning.
@SacredSteve to be completely rigorous you are correct, he would have to prove that lim[y>x](y - x) = 0, in other words that f(y) = y is continuous. however this is fairly obvious from the graph; the technical proof is part of analysis, and it's quite trivial. he just doesn't want to confuse things at this point by introducing epsilon delta before the students have grasped the intuitive definition of a limit.
In lecture one, he derived what a derivative was. That's because the limit delta f(x) over delta x is the proof of the derivative of f(x), which is in other words f'(x).
The quality of education isn't JUST about how difficult it should be for those complaining how easy it is. Clarity and thoroughness of concepts is far more important then difficulty in my opinion. You can always learn and develop ability to tackle difficulty anytime off of the base idea of the concepts.
Also, genius (everyone is potentially a genius) doesn't come out of any academic institutions. It's an illusion. It comes from within.
Man... what´s this?? MIT??? This is the most basic Mathmatic Analysis you can find around here (PT) !! 1st derivative??!! That´s Pre-University work... Man, I hope, and I know you´re better than this... I envy you´re pratical appliance of things... that´s a plus, but the theory is WAAYYYY to easy to teach through a University degree!
A text that will be suffiecient (if spelled correctly) for this course is CALCULUS
FOR ENGINEERS by DONALD TRIM
from university of manitoba. The course here in the hebrew university is too much hard, because they included logic, group theorem, induction and fields and computing methods first as a preview :(
I'm not sure what text he uses, but if you're looking for a good calc book I would try the one written by Swokowski (Calculus: Fifth Edition). He has passed away so that is the latest one by him, and you can find a used copy for dirt cheap. They do offer a new version of his fifth edition on amazon, but they charge 60 bucks (as opposed to the 3 bucks I paid at a used book store). It's very well written
If you can't get into MIT, go to a state university. The education is the same and cheaper and in today's crummy job market, you're lucky if you get a job even with an MIT degree.
It's been my dream to understand what what each notation, operator means in Math and more so in Calsulus. The geometric and physical interpretations with real life examples helped me experience why is is important to understand and learn Mathematics. I'll be covering all the relevant lectures of Calculus. Thanksa lot :-)
To get into MIT you have to be extremely talented. MIT is a great school, which is #1 in math-related majors, such as engineering. If you didn't take Calc, there is a 95% chance you won't get in unless you have AMAZING science, volunteerism, 4.0 unweighted GPA, all AP classes, and a few years of one language.
Think of the gaussian distribution...if you think this is easy you might be on the higher end of the curve and the questions you think were easy were targeted towards the average student...but because MIT is so selective their a the average for your xyz college will be much lower than that of MIT's for example my honors math at brown was way more challenging in a way too
Is this a real MIT Calc class recording? or a modified version for the public with easier material? I looked at the exams in the link and I was in SHOCK!!
I go to McGill and this is way too easy compared to my uni.. NOT FAIR!!!!!!!
math is pretty universal the numbers aren't different on their campus. Granted less renown colleges have the majority of their freshmen starting higher than calc 1.
have you watched the entire series? after you're through with the entire course, let us know if you feel like MIT students aren't learning calculus as thoroughly as you are...
dang i am in precal class, wanting to get a jump start on calculus, and none of this or lecture one made any sense, he kept talking about limits and derivitaves and even showed examples, but never explained how to get them that well, or even what they were....have the ppl in this class had previous exposure to this stuff?
A derivative is the slope of a line. Like if the line is Y = 2X, the slope is 2, so Y=2 is the derivative of Y=2X. A limit is basically what the graph looks like it is going to do as it gets closer and closer to the limiting value.
Sorry I just meant to be specific. Note that I said the derivative is not JUST the slope of a line. If the function given is a slope.You're right. thats all.
Having g=10 m/s^2 (of course ground acceleration is 9.8 or 9.81 but as he mentioned he chose easy numbers to make the calculations easier) and integrating twice we have the distance travelled by the object so we have the formula of the height h=80-5t^2
he chose the numbers based on convienence...note 4 squared is 16, and 16*5 is 80. and 80/4 is 20. he planned out his numbers, he wasnt trying to be exact...but you are right, 9.81 m/s is the gravitational acc for earth..
(Negative due to that positive direction is chosen upwards; speed is the absolute value |v|, meaning it only cares about the magnitude, not the direction, hence it's a scalar.
I really appreciate what he did at around 25:14-25:18. Kind of a subtle thing, but it's the kind of thing I've noticed my kind of worthless community college teachers don't do--catch themselves making mistakes and then happily correct themselves because it could confuse the student for no reason. A lot of them even get kind of pissy when I point it out. Horrible, terrible people, if you can call them people, those community college teachers.
no acceleration is per second squared so that at the 4th second the pumpkin would be falling at 80m per second this is not the position of the pumkin at that time. this is an mit class?? wow epic FAIL!!!
Wow, YOU totally fail! That is the standard equation for a free fall object, with eighty meters as the height.
Integrate the equation to get Velocity. V = -10(m/s^2)*t. Get it? He is rounding gravity to 10 m/s^2 for simplicity. So at t=4 sec, the velocity is -40 m/s.
There are units in his distance equation which are not usually shown
S = 80 (m) - 5 (m/s^2) * t^2
I hope that this helps you understand a little better.
I would put my two degrees up against a guy who can't find the shift key, anytime. Do you recognize this as one of the motion equations in the vertical direction? y = y0 + Vy0*t + (1/2)*a*t^2 y0 = 80 m, the height of the building Vyo = 0 m/s, the pumpkin starts at rest. a = g = -10 m/s^2 y = h, final pumpkin height Substitute into your eq h = 80 m + 0 /ms * t + (1/2) (-10 m/s^2) * t^2 h = 80 m -5 m/s^2 * t^2 dh/dt = -10 m/s^2 * t Now at t=4 sec dh/dt = -40 m/s, not 80 m/s as you stated.
Phisicists would be offended a bit here :) dS/dt is not SPEED it is VELOCITY. These lectures are really good. Everything is so easy even though it's not in my native language, mind you it was even easier to understand. Good job Prof.
Velocity is a vector. Speed is the magnitude of that vector, or a scalar. What he wrote was not a vector, it was a scalar (he defined it as distance). No one need be offended.
It's been a long time since I took calculus, but didn't the last proof only show that every function that is differentiable has a limit--not that it's continuous?
it is a very good gesture what ppl at mit did they show the world that they will always be a source of knowledge in the modern world i hope that many others will follow their steps too..
I understand this was in high school, and I'll admit, I'm in high school. But still, I believe from what I've seen so far, they go more in depth of what is really happening. The point being that you understand where you get a derivative. Not just knowing how to plug in numbers. Still right now these videos help me even though my high school's calculus teacher goes in just as much depth as this professor.
For all the smartie pants who are saying " wow MIT is dumb look at how easy this is" u can keep living in your momma's basement unitl u find a job at mcdonalds
I want this video on my GW910 unit.
altonmiranda49 5 days ago
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exofficerr 5 days ago
Haha! That was me too! I was a Linguistics major and then I realized that with only 8 more math credits I'd have a double major in Math and Linguistics! Haha! At least I'm not the only one out there!
hulbeje 1 week ago
That's all I remember from Calc 1, the derivative of x^2 = 2x lol. Of course, that was the "shortcut," but we had to do it with all the dy/dx notation. I remember that I loved doing quotient derivatives for fun. What's wrong with me? Linguistics major BTW.
F25Xanatos 1 week ago
Satellite preferably above the earth.
ComeFlyWithMe111 2 weeks ago
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anakmudajaman 2 weeks ago 2
if that many people can do it, so can i
GenghisKhan22 4 weeks ago
This video went viral on Berlin
fryejames12 1 month ago
Taking this in high school. This is the hardest stuff ever.
lilzokiller3 1 month ago
ha komme aus münchen
PalmaLillieod315 1 month ago
Comment removed
lwazzan 1 month ago
I dont even know why I'm watching this ..
MufcATW 1 month ago
9.8ms^2 in the earth's surface.
thomisonnnnn 2 months ago
Is this from a maths course or somthing like physics or engineering
starofcctv94 2 months ago
@starofcctv94 math, first-year college calculus
redrum41987 1 month ago
good lecture
keithl28 2 months ago
lol the people who learn single variable calc in MIT are the SPED section of high school. Im going to walk into some dumbass college with advanced calc. lol this is so pathetic,
MrDanielMaciag 2 months ago
@MrDanielMaciag What's SPED ? and why u gonna enter in a "low" college with advanced calculus ?
astrospace23 2 months ago
ave change
MrIarimma 2 months ago
building you :D
MrIarimma 2 months ago
"When you come, you have to be prepared to clean up afterwards."
Words of Wisdom.
IndigentiaSumEgo 2 months ago
helps me understand what my teacher is actually talking about, thanks :)
charlene19940711 2 months ago
Comment removed
prantare 2 months ago
Great lecture! I have question about MIT though: do they only have ~50min lectures? We have 2x50min at my university.. I'm just curious. :)
prantare 2 months ago
Anybody know if MIT has any tutorials on trignometric functions? I'm having trouble understanding the Trignometric limits.
ksb1995 2 months ago
Whats the point of making everyone go to uni. to do maths?
With this you can now just turn up for exam!!!!!!!!!!!!
golfer501golfer 3 months ago
You mean to say I got up every day, went to university for 9 am(in freezing cold), when I could have done it all from the comfort of my bed.
Damn you m.i.t. / internet , where were you 12 years ago!!!!!!!!!!!!!!!!!!!!!!!!!!!!
golfer501golfer 3 months ago
Love it. Thanks MIT!
LAnonHubbard 3 months ago
Herr Professor, Gruess Gott! mehr Danken fuer sein Ausgabe zu uns, dass Deutscher Studentversammlung in Kalifornien. Sein solution zu dies hochwissenschaftlich Mathematikkonzept in dies faehigkeit gibt gross Froehlichkeit zu uns und unser Glaubig. Stern von Afrika zu Sie und sein Schul.
prittwitz1 4 months ago
@AbitOnus And India has honor students more than America has students.
And how could you think homo sexuality it right and normal rethink it please
riyadhelalami 4 months ago
@riyadhelalami What is this stuff about "right and normal"? Why do you associate here with right or wrong?
hereinweymouth 3 months ago
already know all of this from school
Riesenpuller 4 months ago in playlist MIT 18.01 Single Variable Calculus, Fall 2006
Who needs live teachers anymore when you can just see the whole thing on youtube?
Why pay them to give the same class over & over?
You can just watch whenever you want.
gli7utubeo 4 months ago
@gli7utubeo because paying for it gives one an incentive to continue to pay attention to/ learn the material.
ViciousPancakesr1337 4 months ago
@ViciousPancakesr1337 Not really.
tallswede80 3 months ago in playlist MIT 18.01 Single Variable Calculus, Fall 2006
I <3 Math.My love tends toward infinity as I approach math.
DNYAP 5 months ago
Calculus Previsited for me!! THanks for the lecture absolutel fantastic!!!!!! keka!!!!!!!!!1
adirajuadithya 5 months ago
Gilbert Strang.
Rfish117 6 months ago
Comment removed
kjkunaljindal24 7 months ago
at 17:10 what a noob that child is
kjkunaljindal24 7 months ago 2
@kjkunaljindal24 Yeah.. but everyone forgets stuff and some people catch on faster than others.
mahela1993 5 months ago
@AbitOnus i was only asking n god mind ur tongue i knw ur jealous maybe ur seat got stolen by an Indian but v cnt help t theres crazy competition in India n it takes balls to get in which u clearly dont have n v are way smarter than u n as we progress v dont leave our basic manners behind like nt abusing women n if u understnd eng in those vids den dnt c them!!
lizamarget 7 months ago
26:11 "Stick it in...stick it in...stick it in..." lol
Stick234567 7 months ago
I don't care for this professor. I find him to be too boring. I enjoy math, but this man makes me want to fall asleep.
VFB1210 7 months ago
Nice lecture. I'm here for review and picked up a couple of things I didn't know. Thanks MIT.
LAnonHubbard 8 months ago
Comment removed
lizamarget 8 months ago
@lizamarget yes we do, not everyone gets the chance to study it at 11th grade like you...
casagm1186 8 months ago
@casagm1186 theres crazy competition here so v have no choice but to study all this
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paigeyamariahtha 8 months ago
ah l'm positive all the people in that class got 100% of what he said.
freezzertime 8 months ago
How comes no one asks questions? The dude was flying through this jawn, I'm pretty sure someone HAS to have a question...
KarnSingh214 10 months ago
@KarnSingh214 Its College lol. You don't ask questions in mass lecture.
kprice789 10 months ago
I think he proved the converse but its all good
adidasguy87 10 months ago
who is so so so much foolish to dislike the video]
KARTTIKEYA1 11 months ago
When the professor uses the term "speed"; I believe he should be using the term "velocity". My understanding is that speed = |velocity|. That is speed (magnitude) is always positive, where velocity may be positive or negative (magnitude and direction).
Nice lecture series... Thanks, MIT
jbeyersphd 1 year ago 3
Comment removed
froet213kil 6 months ago
@sententia8 I thought for like 5 mins. on your sentence, and then eventually figured out that it was so non-mathematical! lolzz
a1malik 1 year ago
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joenlbarey 1 year ago
MIT, biggest name in leading edge technological schools... And they don't even have a white board? :-)
kc8omg 1 year ago 3
This has been flagged as spam show
@kc8omg wtf
mit is run by jews
ghiblade 1 year ago
@kc8omg Hello it is not about what you use. It is about how you use it or what you do with it. Mr. White board there are many with one. You will be able to distinguish the difference. Indeed that is the choice of the Professor well you could choose to teach with what you feel is more appropriate.
aikar27Gosavi 1 year ago
@kc8omg IMO the black board is much better.. whiteboards shine too much and the lines are too thin
mahela1993 5 months ago
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jamyacollins 1 year ago
wow, we need more teachers like this. Period. He gives a clear cur examples that does''t confuse you further like most teachers. I have taken calculus before, but you always need to review if you dont use it often. I found this as not only a review, but I also learned something new. Awesome.
10243406 1 year ago 4
And yeah, very quiet class O_O?
AnimeBelover 1 year ago
@AnimeBelover begining of the year... nobody knows nobody
tautologicalnickname 1 year ago
@tautologicalnickname yeah, and seniors are picking on freshguys
caracaes 9 months ago
Hm, MIT got good chalks... =O
AnimeBelover 1 year ago 66
@AnimeBelover they can afford best chalks in the world. these chalks consist about 28% of calcium this why these chalks very tough and u can draw long straight lines. and if someone have trouble with teeth it can be eaten as well. but before u need smash chalks or scrape off whiteboard and mix it with some limon- or other acid. without acid you wont consume calcium. they called also eatable chalks.
reagestme 5 months ago
@AnimeBelover true dat
IvanTripleD 3 months ago
thnx
strangercandy 1 year ago
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nadeeraist 1 year ago
Has any encountered viewing problems with the video?
DraSifisGr 1 year ago
Is this an intro to Calculus? I learned everything this guy is talking about my Freshman year of High School.
Schutzstafell 1 year ago
@Schutzstafell If that was the truth, you would probably be smart enough to know that single variable calculus is basic introductory calculus.
Mrlendo1 1 year ago 23
@sententia8 omg! he really fucking said that. oh man, this guy...
nlytend1 1 year ago
Very good contribution to the student community, but not if I could put the
transcript of 18.01 Single Variable Calculus, thanks
pipch1992 1 year ago
51:57 he shows f(x) is related to limit while f(x0) is not related to limit, so:
47:20 why is suddenly EVERYTHING divided by (x - x0) ? Consequently because of that limit applies to EVERYTHING and, in my opinion, it contradicts 51:57
PRANOOKOO 1 year ago
f(x) = 1 if x is rational, 0 if x is real but not rational
is a much cooler discontinuity. :)
gorgolyt 1 year ago
@gorgolyt
That is completely messing with my mind.
grimshawr 1 year ago
I don't buy the last proof. If one never actually uses x = xzero, a zero never exists. In the limit we don't know if f prime tends to zero, infinity, finite, or undefined. Therefore, we don't know if the final product ever approaches zero.
SacredSteve 1 year ago
@SacredSteve he used the product rule for limits (but skipped a step)
1) lim as x tends to xzero( f(x) - f(xzero) )( (x-xzero)/(x-xzero) ) =
2) lim x tends to xzero [ ( f(x) - f(xzero) )/(x-xzero) ][lim x tends to xzero (x-xzero)
in 2) the first lim equals f ' (xzero) by the definition of the derivative
the lim x tends to xzero (x-xzero) is evaluated by substituting x for xzero giving xzero - xzero = o therefore we are given f ' (xzeor)[0] = 0 notice the 2 limits are solved independently
yalg22 1 year ago
@yalg22 @yalg22 1) is not the definition of the derivative since it is multiplied by (x-xzero)
Also, independent limit taking is a neat trick. It really makes no sense intuitively. That is the whole problem with the proof. Without independent limit taking you end up with 0/0 in the limit multiplied by some unknown delta f which also approaches zero in the limit under the assuption of continuity.
SacredSteve 1 year ago
The whole thing is mathematically un-provable and only rests on the heuristic/intuitive concept of curvilinear continuity.
SacredSteve 1 year ago
@SacredSteve Um, wrong..... There are proofs for what you claim to be unproveable.
bgreeson 1 year ago
@SacredSteve It is the product of the definition of the derivative and x - xzero. so originally he started with f(x) - f(xzero) and multiplied it by (x-xzero)/(x-xzero). That can be written as [ (f(x) - f(xzero)) / (x - xzero)] * (x-xzero) this is the product of the difference quotient (the def of derivative) and x - xzero. Using the limit law known as the product rule for limits (not discussed in this lecture) you write it as the product of 2 limits and solve each 1 independently.
yalg22 1 year ago
You just said something exactly as he stated it. I know exactly what he did. My whole point is that the logic of solving each limit independently is flawed.
SacredSteve 1 year ago
@SacredSteve part 2 response. this is not some magical bs he pulled out of his ass. limit laws have their own proofs and you need to know something called mathematical analysis to understand it fully. Its been a while since I calc 1, but I know the subject of analysis is touched on.
yalg22 1 year ago
@SacredSteve and my point is that it's not flawed. I said twice already that he used the product rule for limits, which apparently you haven't even bothered looking up before responding back. Why don't you get a book and learn more about limits before you make stupid claims. I'm done with this pointless argument.
yalg22 1 year ago
Look, your product rule argument is circular. The proof of the product rule "assumes" two things: 1) That the limits exist. 2) that the functions are differentiable (at least around the limits). Continuity can't be proven, if that is the assumption you are beginning with.
SacredSteve 1 year ago
@SacredSteve Why are you posting this crazy stuff? Of course the function must be continuous at a point to be differentiable at that point, duh. Continuity can be proven. If lim x-->a f(x) == f(a) then the function is continuous at x=a. There are more rigorous ways to show all of this. It is an intro calc course, and you obviously don't understand that some assumptions must be made in the beginning.
bgreeson 1 year ago
@SacredSteve to be completely rigorous you are correct, he would have to prove that lim[y>x](y - x) = 0, in other words that f(y) = y is continuous. however this is fairly obvious from the graph; the technical proof is part of analysis, and it's quite trivial. he just doesn't want to confuse things at this point by introducing epsilon delta before the students have grasped the intuitive definition of a limit.
gorgolyt 1 year ago
17:48 correction on the correction; the average gravitational acceleration is 9.81 m/s^2 :) but who needs to do such an exact calculation :P
AlmightyThor90 1 year ago
@BYMYSYD so f'(x) is actually supposed to be something but he doesn't place it because it's long and anyway it gets multiplied by zero?
multipurpose101 1 year ago
@multipurpose101
Yea, f(x) is any algebraic expression that involves x, but that's all you need to know to make the logic work. and f '(x) is the derivative of f (x)
d/dx [f(x)] = f '(x)
BYMYSYD 1 year ago
47:56
can someone explain to me how he got f'(Xo) ?
multipurpose101 1 year ago
@multipurpose101
In lecture one, he derived what a derivative was. That's because the limit delta f(x) over delta x is the proof of the derivative of f(x), which is in other words f'(x).
its a matter of "plug-and-chug", you could say
BYMYSYD 1 year ago
@BYMYSYD so he plugged in the WHOLE term, which was multiplied with X - Xo, to the derivative formula?
multipurpose101 1 year ago
@multipurpose101
Every time you see ΔX this means the same as (X-Xo); it's basicaly the difference as change
so...
lim f(X)
ΔX->0
is the same as...
lim f(X)
X->Xo
BYMYSYD 1 year ago
@BYMYSYD This is so wrong man....
you mean
(X-Xo) --> 0????
it will make sense if you say what I just wrote...
you CAN NOT bring -Xo over the other side since --> is not >
DUH.
trangnguyen1092 1 year ago
@trangnguyen1092 it's not bringing over to the other side
x approaching Xo = change in x approaching zero
multipurpose101 1 year ago
@BYMYSYD yeah i got how X - Xo became zero but i don't get how the term multiplied with X - Xo became f'(x)
multipurpose101 1 year ago
Wow,there are lots of math geniuses making comments.Just enjoy the lesson dumb fuckers.
jesse10x 1 year ago 2
The quality of education isn't JUST about how difficult it should be for those complaining how easy it is. Clarity and thoroughness of concepts is far more important then difficulty in my opinion. You can always learn and develop ability to tackle difficulty anytime off of the base idea of the concepts.
Also, genius (everyone is potentially a genius) doesn't come out of any academic institutions. It's an illusion. It comes from within.
Rumproast 1 year ago
@Rumproast watch Nat Geo's My Brilliant Brain. There are 3 origins of genius
multipurpose101 1 year ago
Man... what´s this?? MIT??? This is the most basic Mathmatic Analysis you can find around here (PT) !! 1st derivative??!! That´s Pre-University work... Man, I hope, and I know you´re better than this... I envy you´re pratical appliance of things... that´s a plus, but the theory is WAAYYYY to easy to teach through a University degree!
PANGAWD 1 year ago
A text that will be suffiecient (if spelled correctly) for this course is CALCULUS
FOR ENGINEERS by DONALD TRIM
from university of manitoba. The course here in the hebrew university is too much hard, because they included logic, group theorem, induction and fields and computing methods first as a preview :(
good luck MIT anyway! :)
ilanlakan 1 year ago
Does anyone know what text the professor uses?
wendyrosennyc 1 year ago 2
I'm not sure what text he uses, but if you're looking for a good calc book I would try the one written by Swokowski (Calculus: Fifth Edition). He has passed away so that is the latest one by him, and you can find a used copy for dirt cheap. They do offer a new version of his fifth edition on amazon, but they charge 60 bucks (as opposed to the 3 bucks I paid at a used book store). It's very well written
gyhbmjik010011001 1 year ago
If you can't get into MIT, go to a state university. The education is the same and cheaper and in today's crummy job market, you're lucky if you get a job even with an MIT degree.
josecitomadera 2 years ago
Thank you very much, MIT and Professor.
It's been my dream to understand what what each notation, operator means in Math and more so in Calsulus. The geometric and physical interpretations with real life examples helped me experience why is is important to understand and learn Mathematics. I'll be covering all the relevant lectures of Calculus. Thanksa lot :-)
videoloverme 2 years ago 2
these kids aren't laughing at the prof's math jokes at all, i feel so sorry for him :(
hehsaan 2 years ago 3
Is it true that colleges such as MIT wouldnt look at a HS applicant if they didnt take calc in HS?
humper3000 2 years ago
To get into MIT you have to be extremely talented. MIT is a great school, which is #1 in math-related majors, such as engineering. If you didn't take Calc, there is a 95% chance you won't get in unless you have AMAZING science, volunteerism, 4.0 unweighted GPA, all AP classes, and a few years of one language.
TheKhazano 2 years ago
No...If you don't take Calculus you still can get accepted.. Get a good SAT test scores and Standardized subject tests :D Good Luck sir
warisover1234 1 year ago
@warisover1234
Although MIT would kill you if you haven't been exposed to the concepts yet.
SageoftheWest 11 months ago
Think of the gaussian distribution...if you think this is easy you might be on the higher end of the curve and the questions you think were easy were targeted towards the average student...but because MIT is so selective their a the average for your xyz college will be much lower than that of MIT's for example my honors math at brown was way more challenging in a way too
pieceofmind616 2 years ago
Is this a real MIT Calc class recording? or a modified version for the public with easier material? I looked at the exams in the link and I was in SHOCK!!
I go to McGill and this is way too easy compared to my uni.. NOT FAIR!!!!!!!
goodman325 2 years ago
This is only for public demonstration.
elmanmelman 2 years ago
Lol ya, that exam looks easier than my exams, and I'm in AP Calculus AB (high school).
BFWaffy 2 years ago
If you think there are degrees of difficulty with CALC exams, then you really don't understand CALC.
josecitomadera 2 years ago
Lol.. suree.. =))
warisover1234 1 year ago
This is calc 1...
math is pretty universal the numbers aren't different on their campus. Granted less renown colleges have the majority of their freshmen starting higher than calc 1.
tsnr2 2 years ago
it is a real class recording
zantrua 2 years ago
@goodman325 i totaly agree this is insane! My mathematics degree is much much more difficult than this!!!
redzor812 2 years ago
have you watched the entire series? after you're through with the entire course, let us know if you feel like MIT students aren't learning calculus as thoroughly as you are...
ayaz1687 2 years ago
dang i am in precal class, wanting to get a jump start on calculus, and none of this or lecture one made any sense, he kept talking about limits and derivitaves and even showed examples, but never explained how to get them that well, or even what they were....have the ppl in this class had previous exposure to this stuff?
steffanc88 2 years ago
he tells you that t is nx^(n-1) which is a way to find the deri\vative. there are other rules i dont know why he wouldnt go over it.
DylanLaRose 2 years ago
A derivative is the slope of a line. Like if the line is Y = 2X, the slope is 2, so Y=2 is the derivative of Y=2X. A limit is basically what the graph looks like it is going to do as it gets closer and closer to the limiting value.
BFWaffy 2 years ago
The derivative is not just the slope of a line. A function can be non-linear or may have 2 lines which are discontinuous... Refer to lecture 1.
SC074507 2 years ago
I like how the lecturer states in 0:46 that derivative IS a slope.
skandalieros666 2 years ago
Sorry I just meant to be specific. Note that I said the derivative is not JUST the slope of a line. If the function given is a slope.You're right. thats all.
SC074507 2 years ago
hey guys
This formula can be proved easily
Having g=10 m/s^2 (of course ground acceleration is 9.8 or 9.81 but as he mentioned he chose easy numbers to make the calculations easier) and integrating twice we have the distance travelled by the object so we have the formula of the height h=80-5t^2
That is so easy
ifthenandelse 2 years ago
This comment has received too many negative votes show
the bit about 80 - 5t^2 is incorrect
the number 5 is not exactly right.
The gravitational acceleration is actually equal to 9.81 meters per second per second.
(or depending where on earth you are it might be 9,80 but never 10)
johanhendriks 2 years ago
he chose the numbers based on convienence...note 4 squared is 16, and 16*5 is 80. and 80/4 is 20. he planned out his numbers, he wasnt trying to be exact...but you are right, 9.81 m/s is the gravitational acc for earth..
shawnwilliams77 2 years ago
This comment has received too many negative votes show
shut the fuck up
danielzinho020 2 years ago
@Danielzinho020
That's really helpful daniel.
Please enlighten us some more...
johanhendriks 2 years ago
Dude, take it easy. It was was "illustrative" purposes.
gunghojoeno 2 years ago
baptistic: check out the transcripts of this lecture on the course page.. maybe you´ll find it less "sloopy"
Sandstroem82 2 years ago
fuck, did anybody else find the last proof "sloppy"?? i'm guessing he made a mistake
baptistic 2 years ago
yeah Caltech is great
whymytie 2 years ago
You would be supposed to demonstrate the linearity of the derivative
nieves666 2 years ago
you are plain wrong: acceleration is not linear!
(final position) = (initial pos.) + (velocity * time) + (acceleration * time squared).
AND
(final velocity) = (initial velocity) + (acceleration * time).
acceleration vector is the derivative (with respect of time) of the velocity vector.
velocity vector is the derivative (with respect of time) of the position vector.
xxMeStessoxx 2 years ago
The following statement:
"final position) = (initial pos.) + (velocity * time) + (acceleration * time squared)."
is to be replaced with:
"(final position) = (initial pos.) + (initial velocity * time) + (1/2 * acceleration * time squared).".
Sorry.
xxMeStessoxx 2 years ago 2
nvm lol you corrected it.... I hate the new youtube layout.
pattttttrick 2 years ago
Trying to be pedantic?
DaChoozen 2 years ago
In your first equation, the acceleration is divided by 2.
xf = x0 + v* t + a/2 * t²
pattttttrick 2 years ago
Comment removed
tuscaaa 2 years ago
(Negative due to that positive direction is chosen upwards; speed is the absolute value |v|, meaning it only cares about the magnitude, not the direction, hence it's a scalar.
aic6702 2 years ago
I really appreciate what he did at around 25:14-25:18. Kind of a subtle thing, but it's the kind of thing I've noticed my kind of worthless community college teachers don't do--catch themselves making mistakes and then happily correct themselves because it could confuse the student for no reason. A lot of them even get kind of pissy when I point it out. Horrible, terrible people, if you can call them people, those community college teachers.
droe82 2 years ago
Yeah, it should have been s= velocity, and ds/dt=acceleration. The derivative of velocity is acceleration.
schlynn 2 years ago
s is used to represent distance, rather confusingly, but v is used for velocity which clears that one up.
So, v = ds/dt.
cagedkiller360 2 years ago
MIT got lectures online and has a youtube account, that pro man. harvard needs to game up.
lucirz 2 years ago 2
Not Bad. . . It is pretty cool that they make MIT lectures free to the public viewing on the internet. . . Go Georgia Tech. . .
kslick88 2 years ago
Georgia Tech sucks
iridethewave 2 years ago
what doest that have to do with this video?
woodmaster413 2 years ago 2
do u guys have to really write on a blackboard not a whiteboard?
roendm 2 years ago
Well, you have to really write regardless of what you're writing on. It wouldn't be writing otherwise.
honeybbqgrundle 2 years ago
no acceleration is per second squared so that at the 4th second the pumpkin would be falling at 80m per second this is not the position of the pumkin at that time. this is an mit class?? wow epic FAIL!!!
circusboy90210 2 years ago
Wow, YOU totally fail! That is the standard equation for a free fall object, with eighty meters as the height.
Integrate the equation to get Velocity. V = -10(m/s^2)*t. Get it? He is rounding gravity to 10 m/s^2 for simplicity. So at t=4 sec, the velocity is -40 m/s.
There are units in his distance equation which are not usually shown
S = 80 (m) - 5 (m/s^2) * t^2
I hope that this helps you understand a little better.
mugwump666 2 years ago
Oops, I meant differentiate, of course, not integrate.
mugwump666 2 years ago
wich is why he was wrong. you fail this is high school stuff.
circusboy90210 2 years ago
mugwump666 2 years ago
Phisicists would be offended a bit here :) dS/dt is not SPEED it is VELOCITY. These lectures are really good. Everything is so easy even though it's not in my native language, mind you it was even easier to understand. Good job Prof.
Martin060480 2 years ago
if S is displacement then dS/dt is velocity... but he defined S as distance so he is correct in saying that dS/dt is speed...
happyman 2 years ago
Velocity is a vector. Speed is the magnitude of that vector, or a scalar. What he wrote was not a vector, it was a scalar (he defined it as distance). No one need be offended.
mcooper951 2 years ago
This shit may look easy, but that's it. The tests are really hard, they require proofs...
thesloc 2 years ago 3
It's been a long time since I took calculus, but didn't the last proof only show that every function that is differentiable has a limit--not that it's continuous?
petersodgmailcom 2 years ago
It has been a long time and I found a definition of continuous.
petersodgmailcom 2 years ago
it is a very good gesture what ppl at mit did they show the world that they will always be a source of knowledge in the modern world i hope that many others will follow their steps too..
textureArtist 2 years ago 2
I understand this was in high school, and I'll admit, I'm in high school. But still, I believe from what I've seen so far, they go more in depth of what is really happening. The point being that you understand where you get a derivative. Not just knowing how to plug in numbers. Still right now these videos help me even though my high school's calculus teacher goes in just as much depth as this professor.
xbraddo07 2 years ago
For all the smartie pants who are saying " wow MIT is dumb look at how easy this is" u can keep living in your momma's basement unitl u find a job at mcdonalds
sokkakings 2 years ago 2