Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007

[cjysdny]

Amazing lecturer and good handouts,very clear and easy to follow. Thank you!

[flowewritharoma]

this video is very useful.

[faisalbinaziz1974]

I also kind of like the chalk eraser :-)

[faisalbinaziz1974]

Why does everybody here supposes that teaching Calculus would be a hi fi over the top thing? Why cannot Calculus be taught in a simple manner like this?

[MrMustard12345]

If you're a high school student thinking, "Hey, I know this! MIT/university would be a breeze," then snap out of it: Introductory calculus is an equalizer and MIT, as with other universities, use it to ensure students have a foundation. If you're curious about university, look at the course work, not video lectures, of higher-level classes (exams/assignments). If you start university with an artificial confidence from watching YouTube lectures, you'll undoubtedly be crushed by the reality of it.

[RuthlessPragmatist]

This would be a business calculus course, designed to provide a basic understanding of the concept. A science major would have taken this in high school.

[mongolcopter]

This is the sort of things average British A level students can do with ease towards the end of lower 6th. How can MIT call themselves a world class university if their students are a full 2 years behind British students?

[daehomango10000]

@mongolcopter these students are probably studying other areas, that don't need rigorous math like literature or history, but these courses are core to the curriculum, so it's kinda mandatory even if they don't need calculus. The reason MIT calls itself a world class university is because these students excel at something else (every student excels at their field(s) of study. so i wouldn't say that MIT is 2 years behind British high schoolers.

[UnchartedZodiac]

.... i didnt learn anything and this made me question everything I already know about calculus. The only thing I knew was the polynomal at the end.... but thats for next class =(

[RuthlessPragmatist]

At least he speaks English clearly. Most of my math, computer science, and engineering professors were barely understandable.

[antiFoolishness]

my community college professor is better than this guy!

[Pr3fixProducts]

This seems very fun. Can't wait to start learning this. :D

[ChivalrysDownfall]

So If I go to MIT I get this guys chalk? Pffft I'm in!

[SteveSparx]

professor is lacking comfort in his presentation~indicative of

[globalModValue]

It's 8 am and your are sitting in a calculus class. I hated those days. So glad to be graduated and FREE!

[stavrospod]

this dude says everything so clean and good! I didn't get bored in any minute! amazing!

[Rangers2011WS]

Whats the justification of paying 50k a year to go to MIT? they have to buy bad ass chalk?

[Sheikarthur]

@Rangers2011WS What about paying a bad ass teacher?

[andresmdn22]

What's with the "OMG I KNOW THIS ALREADY!!" comments?

This is the first lecture of single variable calculus, what do you expect?

[FyeMusic]

OMG Yes this is clearly not a hard, hard math class. Most of us took this in high school. But if you want to  watch something more advance go to multi variable or linear algebra.

[itstristanyo]

This is calc 1 you tards, go watch some differential equation videos if you want more advanced stuff...

[perrito94]

This is so basic.

[ohjaysus28]

Any point x =X0 =dy/dx

should be stated to clarify

[NeomiAlannacn28]

hmz bin aus hamburg

[aceone1988]

what the hell is this elementary crap e is teaching

[marksfeir94]

i used to do single variable calculus, but then i took an arrow to the knee.

[thatscientificgeek]

@starofcctv94 because not all functions have a part that says (Number) x X to the fifth power.

[mring001]

Very nice lecture with clear explanations and worked examples. I hope he develops the limit laws with his students early on as well so they can use them with understanding when finding derivatives using the definition of the derivative instead of just remembering a handful of rote algebra tricks.

[starofcctv94]

why doesn't he just use the method of multiplying the power and subtracting 1 from the power? much easier than going through that formula for 1/x.

[wrzazq]

@starofcctv94 He uses that method (Sadosky-Guber table methods) only after he explains how to get the derivatives using formulas. Calculus is both about solving and understanding.

[starofcctv94]

@wrzazq yeah commented half way through the video. I've got to stop doing that.

[vinylshah]

all u dumbos, every journey is started with a single step, and if ur basics are not reviewed and cleared then u cant get to the depth of the subject.

And i think its gud 2 have a quick review of the past.

[TOPDUDEASS]

moi j'ai regardé juste pour le trait de la craie.

et puis ce double tableau !

[TheSunIsBlack]

just because you can do it doesn't mean you can teach it . or conversely just because you can teach it doesn't mean you can do it

[tylertubeism]

@TheSunIsBlack How can you teach it without being able to do it?

[basayork]

What textbook does MIT use for this course?

[mathewheffley121]

Is this seriously a class at MIT? Korean kids learn it when they're like 11...

[julianwerules]

@mathewheffley121 thats not true at all Korea teaches the same math at the same ages as the usa

[vinylshah]

@mathewheffley121 ya korean kids might CRAM that at 11, bt i am sure they dont UNDERSTAND that at 11.

lood dude instead of praising yourself, try proving it.

[mathewheffley121]

@vinylshah how am i praising myself , I'm not korean, nor did i learn it at 11

[beethovensworld]

@mathewheffley121 I don't think this course is for students majoring in mathematics...

[jileel]

wow this is helpful o.o

[yamum806]

lol 04:03 MINDFUCKED!!!

[iHacksorzz]

My prof is fucking horrible we dont even understand what he says, OR what he writes on the board. Fucking York University(canada)

[Mr1990jorge]

he make calculus so boring.......and his teaching skills are so terrible and not fun..

[roniepao]

227,119 people attended a class for free.

[ciganama]

man, I wish I had teacher like that in my community college........

[MrKurtisalive]

great teacher

[paddyeth]

Why are people saying, ohh i did this when i was 2. The main thing is that there are people learning, no matter what age, theres a guy in my lectures at uni who's about 60, we don't all give him crap because he's doing it when he's older than us. If anything there at a disadvantage as your brain learns less easily as you get older.

[BigWuMpa]

@paddyeth it's because people want to feel/ act like they're smarter than mit. Truth is mathematics is mathematics, nobody cares when you learned it, performance and intelligence is the key.

[bcatz454]

lol, this course must be the #1 GPA booster at MIT. You don't get into MIT without learning this is 11th grade or as Canadians say "grade 11".

Easiest course ever at MIT?

[golfer501golfer]

Where was youtube/m.i.t. and internet 12 years ago?

I failed this course, and this would have really helped me pass.

Thanks for nothing!!!!!!!!!!!!!!!!!!!!!!!­!!!

[Jipzorowns]

NOOOOO, I thought it would never happen to me. I wanted to push the like button, I accidentally hit the dislike -_-'. By the way, great video! helped me alot :)

[hutangbabi]

Thank you prof. David. THis is the best lecture on derivative I have seen. Great example the way you take the student into the concept of derivative. Thank you.

[LAnonHubbard]

He's managed to show a lot in such a short period of time. Well done. I'd personally be very confused if I had no exposure to calculus prior to viewing this video, but luckily I'm using it to augment information from books, Khan Academy, etc. Really like the concise proof at the end for higher order powers.

[ArielBendavid]

Thank you MIT.

[Triniloverboi]

He is doing it the hard way.

[interinfinity]

too all of you people who think that just because the first lecture of a MIT calculus class looks simple it would be the same as high school... wait till the midterm and tell me how helpful your 9th grade calculus was

[xxMafia101]

@interinfinity Who takes Calculus in 9th grade?

[claton95]

@xxMafia101 I took it in 5th grade

[raghuveerjha]

@claton95 MIT not meeting your high standards? Disappointed in MIT? What do you expect? Math classes are basically the same no matter where you go. This professor is amazing to be able to teach linear algebra in such a simple and straightforward approach. I absolutely hate it when professors don't break it down for students. If anything, it's an ego trip. So with that said, I applaud Prof. Strang for his both brilliance and humility.

[kestkr]

@SudanCarib MIT=well paying job

[xxjash100xx]

Is this a harder version of calculus? because I thought MIT was too smart to have a calculus class for college... Theres a calculus class at my highscool. Yet again, I might be COMPLETELY off on this comment.

[BigWuMpa]

@xxjash100xx that doesn't make sense. Calculus is an important math and mit gives its students a high quality calculus education. Since mit is a good school it BY NATURE doesn't want its students knowing merely crap calculus learned in high school. Understand now?

[xxjash100xx]

@BigWuMpa yes, thank you.

[southernblaque]

@ThexAristotle SMH thats F'ng frustrating

[ThexAristotle]

I already had calculus but I wish I would have had this professor mine went in circles for a whole class and in the end said "ill just give you the answer tommorrow"

[MrThylakoid]

When he finds the Area for the triangle, why is the answer 2 and not 2XoYo ?

Thank you.

[OM4R7x]

@MrThylakoid I think it's because Yo=1/Xo, so when you take 2Xo(1/Xo) you just get 2

[jvcscasio]

Just loved this class, thousand times better than my teacher, she even forgot that there was a test last week!

[SudanCarib]

MIT= Nerd city

[EconomicLiteracyNow]

Anybody watching this has "gotten into" MIT. Knowledge can't be locked behind walls. These videos make me think of all the retired teachers who racked their brains and combed their school libraries looking for material to give their most gifted students.

[prittwitz1]

Danke schoen! Dass ist gott Geschenken fuer uns in Langemarck.

[tommie997]

I did this in 8th grade...

[ggHaSu]

Why is this in university? Isn't this year 12 stuff

[BigWuMpa]

@ggHaSu some people take learn algebra in university, go figure.

[vampire29queen]

i rlly wanna get into MIT hopefully

[spondulas]

This guy is a great lecturer... Crystal clear explanation...

[TestMonkey254]

My professor sucks (no i did not even get close to MIT) so i think these will be a life saver.

[DelGeeZee]

where do i send my tuition?

[flowewritharoma]

thanks for posting this awesome informative video.

[nickmax123]

saved me $50,000

[JamSamJackx]

that cant be good for his lungs when he erases!

[ofnotandi]

Spoiler alert.... it was the butler. 

[pedobearlover135]

just love how people write on da chalk board

[ttttrigg3r]

Someone help. at 40:55 he explains that 2X0Y0= 2. That is the area of the triangle. How did he go from 2XoYo to 2?

[feitingschatten1]

@ttttrigg3r If you start plugging in numbers, two things will happen. You'll find the answer, and you'll notice a pattern. That pattern points to that, whatever Y is, X is the reciprocal, and visa-versa. Essentially that negates every number, so you always get 2 * 1. Any number times its reciprocal is one, which is how you end up that way. To everyone whose head hurts: you cant get a tangent line at a single point because the slope equation is unusable: thus this 'way', in short, the power rule

[ttttrigg3r]

@feitingschatten1 Thanks mate

[DelGeeZee]

@ttttrigg3r shit if i know

[riyadhelalami]

@ttttrigg3r because Y0 =1/X0

[emau99]

I haven't had a calculus course in nearly 20 years. This was a GREAT way to review this material. Thanks, MIT, an props to everybody involved with the open courseware project!

[bangalorebully]

And anyways, it's a nice idea to begin with the UMKC lecture first and then follow that up with this MIT series to PERFECT the subject......

[bangalorebully]

I hate Chalkboards...reminds one of a real maths classroom..Well, MIT is MIT, maybe the best if not one of the best. But if you find this series hard to follow you can watch "UMKC calculus 1" by Prof R. Delaware (Universty of Missouri)...MIT lectures may be best in content, but when it comes to simplicity,accessibility & quality combined, none beats Prof. Richard Delaware ,especially if you are new to the subject...MIT lectures are somewhat elitist!!

[RPShredow]

8 billion dollar endowment and they still have chalk boards.

[froet213kil]

there're always new things to learn, no matter if you've learned it in your kindergarten.

[Thallod]

best part about these videos is that theres not 20 million retards in the class asking stupid questions leading the professors off into a fucking tangent about nascar or the incredible hulk

[iawesome60]

I have to take Calculus I and Calculus II for my major. My approach to have on any math class is from this analogy. The distance between point a and point b is 300 miles. There are particular exits, turns, and miles of a distance you have to drive to get to your destination. If you make a wrong turn, take a wrong exit, or etcetera; you will not get to your destination. All maths require you to do the EXACT steps to get the right answers and understand the class (plus with practice).

[Thallod]

500 people think they just magically learned Calculus.

[gardnerbm]

he lost me at 7 min lol

[navinsridhar]

want to join in MIT..... :P

[mrzipdisk]

these mit profs are rock stars

[EugenioNS]

This red chalk is very cool. : )

[smallfrye182]

this looks like the 90's

[JohnPeace2]

Dust from the chalks give you cancer. That teacher should probably change to markers soon or he will die at a young senior age.

[fuzzylogic67]

@JohnPeace2 nah, i don't think MIT professors are that ignorant. i mean, it's THE MIT.. so probably they've measured the pros and cons for chalk usage.

[nLoL2]

@JohnPeace2 The carcinogenic effects of chalk are nothing compared to other hazards in daily life- the most it would do is cause respiratory problems after some seriously long inhaling of the material.

[dliberty1988]

e to the u du.

[flowewritharoma]

great video clip

[RespectMyHate]

Calculus is as easy as 1+2=3 you just have to know the rules.

[Coffeeisnecessary]

@RespectMyHate That's good to know. I didn't have the privilege of a Middle / High school education, so I have to begin from the, as my great - grandmother once told me, the bottom up. (: 

[RespectMyHate]

@Coffeeisnecessary But don't get it twisted, your still going to have to study your butt off.

[Xonipher]

Im entering college in a few months, this video eased my nerves because I actually understood it. Thanks MIT!

[mbogomol]

Taking Calculus online this summer....hopefully these will help understand wtf im doing....

[bobob0000]

@mbogomol Calculus online? wow man what a boss.

[yuraaa1990]

Your free lessons is huge donation to since ! thanks a lot

[eNARV1]

@theliberalsoup liberal scum

[homerilias]

No wonder the people at MIT are so good, with theese explainations... when I remember how hard I had to bite this.

[combatsinaloa]

Why the fuck do we take calculus ??? We dont use it in Our lifes Man ???

[WongeneKIM]

@combatsinaloa Calculus is fun! :)

[quantomic1106]

@combatsinaloa Why the fuck do we have technology??? We dont use it in Our lifes Man??

[Dobbs8816]

@combatsinaloa Lol what prompted you to search for calculus on youtube in your free time if you hate it so much?

[bobbyfearfactor]

How could you get into MIT without having already taken AP Calculus in high school?

[Samuray116]

@bobbyfearfactor If you don't get a 5 on the AP Calculus exam, you have to take the course over again in MIT

[WowhesNeat]

Lol, that power proof was unnecessary... A simple example would suffice.

[Kronuserus]

these videos are getting me through calc II in university. im very appreciative XD

[sylphida]

thank you thank you thank you MIT!

[caracaes]

but I said nope! There's only one way to find that slope! And now I, I'll derive...

[PlasmaPrestige]

This professor has managed to turn something simple into something convoluted, and I'm not in college either.

[TheLiberalSoup]

how do you get into fucking MIT without knowing the DEFINITION OF A FUCKING DERIVATIVE. Im a freshman in HIGH SCHOOL and I know this shit. come on, world, you've really let yourself go

[judigar]

thanks 4 helping me!

[stangGTKKK187]

i learned all this back in 10th grade

[aandgpointlessvideos]

@stangGTKKK187 me in ninth lol

[ilya150]

@stangGTKKK187

You still didn't get into MIT... :)

[mrzipdisk]

@stangGTKKK187 cool story bro

[fingerboy18]

I was surprised that MIT offered Calc I. I thought you needed AP Calc to even get accepted.

[karticaHAACKER]

Thanks thanks thanks!!! I want have my PhD at MIT! Please add more courses....

[TheBigIg]

Is this the same as a pre calculus course?

[vagabond197979]

nerds!

[ladicius]

i love chalkboards.

[utube2605]

@ladicius I prefer dry erase boards but chalkboards are cool too :)

[googoo2u5]

Holy shit I have to learn this stuff in 10th grade I'm toast!!!!!!

[JimmyKudoDetective2]

@googoo2u5 where in the same toster then fuck highschool! JK high school asome

[TheSeantague]

is anyone else annoyed how he says "x zero" instead of "x not?"

[SpoiledLogic]

he kinda assumes everyone is following him and makes things more complicated than they should be, but he's still good i like MIT professors so much!!!

[KARTTIKEYA1]

it simplifies the basic need

[KARTTIKEYA1]

i just u knw so much grateful to u

[lighthammer2531]

Thank you so much for this post.

[jadlerhalofan]

My current teacher at Purdue sucks compared to this guy. It's like an academic woodstock on youtube these days. Can you make an MIT extension in Indiana for people without a lot of funds but a great hunger for knowledge?

[DMXP100]

This is absolutely perfect for my AP Calculus course.

[behnamasid]

This lecturer is awesome. 

[itsRAWRtime007]

couldnt they use some sort of powerpoint presentation instead of writting down all of these stuff on the blackboard ?

[Poleschs]

@itsRAWRtime007 Conservative learning for the win!

[itsRAWRtime007]

@Poleschs i was just saying that he doesn't need to write down everything he says, but of course math formulas and graphs must be written down :D i totally agree with that one ;)

[itsRAWRtime007]

couldnt they used some sort of powerpoint presentation instead of writting down all of these stuff on the blackboard ?

[SF1010]

Perfect lecture!

[edmundstoiberderdepp]

what did he calculate with f'(xo)=-1/xo^2? is that the slope of the tangent? that's a hyperbula, isn't it?

[Theiammadmad]

This guy assume that you know math but if you go to MIT you do know math :)

[xHzDxKING]

yes i agree this teacher is very good he digs into the solutions and the problems is very forwards and desrciptive with it giving lots of details to it,which makes him a really good teacher.You see it doesn't matter on the student its more of the teacher to amuse the student into the teaching of the lesson really,that of course and the student willing to learn,but like i said,more to the teacher like this one who sorta grasps the lesson and breaks it down properly.Very Good Vid.

[Chaossspirit]

??Why is the area of the triangle 2?How do you go from 2xoyo to 2?

[jmcsweeney]

@Chaossspirit yo = 1/xo, so xoyo = xo/xo =1 and 2 xoxo = 2

[Chaossspirit]

@jmcsweeney why thank you

[MatosEnvy]

I play hopscotch with that chalk and he plays calculus.

[13Puebla13]

13 people hate CALCULUS!!!!!

[BorgKing001]

this is made up

[jchan12345]

My 11 years old daughter loves to watch it.