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From: MIT
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  • Min 20 and I still understand what he's talking about lol

  • ill be in this in my junior year of high school

    .-,

  • i feel myself getting smarter.

  • Good, I like that you share this video Dot product., I wish success always

  • Nice Video Dot productThat You Share , So Very Nice Thanks You

  • I Really Like The Video Dot product From Your

  • Your Video Is Very Useful Sharing Lecture 01 Dot product.

  • Comment removed

  • 20 people picked #6

  • I'm surprised. I didn't know that I found math so fascinating when I'm not under tremendous pressure to know it so quickly. I'm studying vector calc over the break so that I can have an easy time with it this coming semester.

  • Oh, they make things so much simpler at good schools where people are smarter and have an easier time making connections that are actually not that obvious.

    Like I didn't get any explanation about the intuitive aspect of dot product in my classes...

    -.-

  • should have gone to MIT...(sigh)

    

  • @tangman093090 you would've gone if you could have.

  • I find it to be so funny when he says that the word orthogonality is just a complicated word from Greek that means that things are perpendicular - to me its just the other way around!

    This wasn't really what i was looking for but i watched the whole thing just cause he explains things so nice! Respect!

  • also wer will mit mia schreiben

  • His gr8. "Any questionzzz."

  • nice accent ....

  • Professore: "How many of you actually knew about vectors before that?"

    Class: -______________- ... seriously?

  • He's teaching at Berkeley this semester!! I always see him before my Linear Algebra class

  • This helped a lot! MIT is truly amazing to put these videos online.

  • @xxjash100xx If you liked this Calculus stuff you might also like this number pattern. Check it out! "Speed maths- Multiplying without multiplying". Click on my username and check the vid. Cheers.

  • This is too easy. MIT sucks.

  • @jay1wo this is lecture 1 of a calc 1 class hes kinda doing a review here and MIT does NOT suck.. you're just mad cus you didn't get in

  • I'm a freshman in college and I'm only taking BASIC ALGEBRA

  • I'm a freshman in college and I'm only taking BASIC algebra

  • I love this guy's accent.

  • ...way better than the lecture at Case

  • How is his proof for dot product not circular logic? If you believe the law of cosines... then that is a proof for the dot product. If you believe in the dot product, then that's proof for law of cosine. WTF?

  • @hunglikehuang you weren't paying close enough attention to the French Man. Some girl actually asked that question...i think he should have done it out, but basically the answer to your question is:

    lAl dot lBl = lAl lBl cos (theta) the second formula is multiplying the lengths of vectors A and B, the first is multiplying the 'components'

  • @hunglikehuang

    Lol, you must accept one or the other, but not make an explanation about how you can get to that point from simpler math.

    I agree, it would have made it simpler, but I'm not complaining because this is as simple as it gets in a college lecture. Maybe it's somewhere else on the internet.

  • So it's 3:20am, I'm sitting on the bowl and I figure, let me look up some multivariable calculus... and here I am.

  • i learned this in 6th grade in my country lol

  • @dhairumian

    this is a REVIEW, take a look at lecture 10 or 20, we will see if you learned this in 6th grade also...

  • @slimmerikje not in 6th grade but in 10th grade :p

  • @dhairumian

    stupid

  • thank you soo much for making me see vectors as a reality!

  • That is by far the best explanations on dot product in YouTube!

    By the way, have you heard of the new type of (discrete) derivativative from 2010? You should try and search it on YouTube: "Eureka! a new approach to calculus". This video depicts a simple kind of derivative.

  • although i really admire MIT OCW, what bothers me is that the majority of videos covers easier undergraduate stuff. i would like to see more advanced lessons if there are any filmed.

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  • At 23:31 the captions make a mistake, I think the professor meant: "in terms of expanding, factoring and so on", not vectoring..

  • To think that I have to do 2 more years of classes before I get to do this fun. I can't wait :D

  • Wht school is it

  • @harmansingh101 it is MIT, an ivy league school and arguably the best school on the planet, its the school that Matt Damon's character went to in Good Will Hunting. I would say it is recognized as the best school among most Ivy League students but I'm not positive, there is no doubt that it is on the level of Harvard, Princeton and Tokyo University.

  • @quangngy Theoretically, yes, Ivy League is still the best. In practice there is reasonable doubt about a few chinese and indian universities already being able to overtake these in scientific work quantity and perhaps match in quality of work that's been publicated. Ivies still hold prestige but that's about to change my dear.

  • @pedroissler This is fascinating, but can you elaborate on this further? Quantity and quality of what? Instruction? Research? Both? What human resources are they using or importing to make this happen and from where are they getting it? This is a great reply by the way.

  • @quangngy Both India and China have more people than us and, therefore, more civic needs. They need more engineers than we do, to build homes, powergrids, roads, sewage systems, bridges, dams, usines and everything related... Also, they're developing nations, so there's the need to catch up, which translates into more work to be done by everyone. It is polemic whether we need or not that many engineers, some say we'd have a lot of unemployment if we were to push so hard, some say they're what

  • @quangngy keeps this country's economic engine running and we should go for it and put forth more competition towards chinese and indian manufacture. Well our strength nowadays isn't really the production of goods such as cars, semiconductors, electronic components or anything related, but rather the cutting edge technology that we can assemble from these once high-tech finished goods, now largely made in Asia. Apple profits from designing of the ipod not it's manufacture if you know what I mean

  • @quangngy So our greatest strength is quality over quantity. Asia has been able to deliver a large number of graduated engineers but the technological prowess, we still got it. What I really mean is: will we be able to maintain that high tech superiority (which is powered mainly by those ivy league schools)? Because India and China combined have 3 billion people or so. Maybe what I said won't happen tomorrow or the very next week or, hey, maybe it'll never happen and everything will end up

  • @quangngy as yet another promise. But they are graduating 150 000 engineers a year or so and we're putting up just half of it. But again for the aforementioned reasons and not because we're going to be steamrolled very soon by a beast-like China. I believe closer cooperation with the french, the british, the germans the italians will be the answer for maintaining the West's technological superiority. We should consolidate existing alliances while also keeping a steady eye for the pace of China.

  • @quangngy They're not here yet, but somewhere along the way all these people in chinese and indian universities will start to wonder whether they are talking about feasiable goals, and feeding realistic dreams, or whether both their countries have problems deeper rooted and will completely overtake the western world in the next century, and not in 50/60 years like many prophets have announced. No one knows how this is going to end but, until then, I'm still coming to MIT's channel for lectures.

  • @quangngy To cut a long story short: they haven't catched up YET, and there is doubt whether they will ever. But there's that possibility, and that's probably what's going to happen too, because economic power very often is translated into tech prowess and political might. All in all, the world's fate is still uncertain.

  • @pedroissler caught not catched

  • @ihateloudbitches o well, thanks

  • The world turns, the fates still spin the webs of men's lives.

  • simply amazing :)

  • BORING PROFESSOR

  • good teacher except for his accent...

  • "You haven't seen the law of cosines before?"

    They got into MIT, i certainly hope they've seen it before

  • Lol, this is easy.

    I'm going to Uni this year and was super nervous that I wasn't going to be able to manage the maths. I can sleep calmly now :)

  • @FreddoX1

    this is just a review of vectors. the course becomes more difficult in the next lectures. if you understand this it does not mean you can handle multivariable calculus. certainly not!

  • i think 19 people didn't understand this lecture =)

    Nice vid btw

  • goddangit! metu calculus lectures are waaay harder than this :P

  • it took 5 months to my teacher to explain this 30 minutes video

  • At 31:40, I thought he was saying "sine" instead of "sign". That confused me for a bit haha.

  • this guy teaches well!

  • @944Nima You need a minimum of precalc. Students usually don't skip multi calc (though they can) because very very few highschools teach mv calc, though they offer an advanced standing exam to skip it if you learned however you did.

  • Great gift to our country and the world, there is even a pause button and rewind that no college offers, I can think of no better way for the US government to spend one billion dollars then to sponsor a few thousand videos like these so that people who cant afford so many years in a good college can still get a solid education, for the time being thank you MIT.

  • @lenlen1010 do you realize how much subsidies american universities get? the federal government gives our uni's lots of money.

  • Very nice video. Good introduction to vectors.

  • wow. im in 8th grade and i got this (well how to solve the first segment on vectors). and i was just looking at this video for kicks. and THOSE idiots got into MIT!!??

  • @PlushChronicles calling the students "those idiots" is pushing it. You have to know a little bit more than just "getting a first intro lecture" to get into MIT. :)

  • @PlushChronicles Thats a bit reductive to call MIT students idiots. Especially after just watching ONE video of ONE course. Getting into MIT involves a cumulative understanding in EVERY subject taught in school. In reality, your comment makes you look like the idiot because the general consensus is aware of this fact, and you aren't.

  • @10243406 not actual idiots. i was actually responding to another person's comment. i was being somewhat exaggerated.

  • @PlushChronicles courses are easy; psets are intermediate; but summer research is damn hard.

  • Really? College ADULTS don't know the law of cosines? How the fuck do THEY get into MIT?

  • I watched a few episodes of this in high school a little over a year ago, and just realized that I have him as a teacher next semester at UC Berkeley.

    This is awesome.

  • I have just completed your 18.01 course and am now starting Multivariable Calculus. This is just as clear and well taught as the previous course. I think we have entered a new age of higher education where institutions such as MIT take the lead to post entire courses online free for all of whom are willing to learn. I look forward to seeing more advance courses in Mathematics, Physics and indeed all other disciplines uploaded in the future. From the bottom of my heart, thank you MIT.

  • Haha, I'm only 11 and I totally understand all of this! Thanks Prof. Auroux, you helped me a lot with understanding multivariable calculus at the age of 11!

    Did I mention that I'm only 11?

  • @HerlockSholmes123

    this lecture is not about multivariable calculus. it is just a review of vectors. multivariable calculus comes later.

  • Jesus Crhist, this is MIT level freshman,..? My god I see the department of education has done a good job of fucking your education system

  • @leonidas512 this course is not for math major, so it's kinda easy.

  • @dawncoming , easy? must be a new definition of easy..I didnt know you could major in womens studies at MIT, LOOOL

  • @leonidas512 try reading the second volume of Apostol. then you'll find how easy this course is.

  • its funny how Lady Gaga is a related video...

  • :D understand this review and got his projection questions right so far at 8th grade. Pretty cool that we covered this in Saxon Geometry and by using common sense and a little luck you can expand so much furthur.

  • 19 people payed tuition to hear this lecture

  • i was lost at 0:00

  • This professor writes on the chalkboard like that commercial with the UPS dude drawing shit on the white board

  • this is a great lecture. the way he handled the law of cosines off the cuff was brilliant.

  • damn thats some niceeeeeee chalk

  • i got lost at 3:32

  • see OnyxCode and try to decipher it !

  • what is his name `?

  • @gjeni7 It's in the beginning of the video. 

  • too french accnet

  • @ 25:03

    How is she attending MIT?

  • 9:00 cough....Distance Formula.....Cough

  • thank you

  • To the people complaining about this being too easy for MIT, or about them learning this material before: IT'S REVIEW! If you know this already, then you are completely free to move on to the next lecture. No one is forcing you to watch this, if you don't want to.

  • @HunterDX77M Thank you, I don't get why people can't understand that Lec 1 stands for the first lecture lol

  • @HunterDX77M It's actually not review. Its part of the material for calc 3.

  • Excellent! 

  • o.O i am doing this in high school...

  • @Rale1993PBmaster i know me to

  • mannnnnnnnnn profs. with accents...

  • Parlez-vous français?

  • I learned this in seventh grade. Seriously.

  • @rmhism Who Takes Calculus In Seventh Grade ?

    Better Yet , Who *Teaches* It ?

  • @sgba17 Taught myself from a book I found at the public library.

  • hahahah I don't see one blonde in the class.

  • @yamborghini3 2:40, girl on the left.

  • @GretneRebirth hmmm, I skipped past the easy vector parts lol.

    but she kinda looks golden brown, not typical paris hilton blonde colour. it could be the lighting making her blonde.

  • Does the teacher have a French accent?

  • @Aquarius199 German I think

  • @Aquarius199 my bad, that's definitely French

  • I would love a board like this. My actual teachers write so fast and they just erase the whole thing before I have time to copy. (I write slow)

  • I've seen 13 lectures of "Multivariable Calculus" and all of "Linear Algebra" so far and I don't believe that those people are students of MIT and these lectures are real MIT lectures? Every question posed by the audience makes me think "omg, how can he/she doesn't get it?" And the material of lectures - it's so so easy.

    The lectures are of course very nice, but why are they so simplified? I really don't believe that the level there is so low. [i know my english is not perfect, sorry for that]

  • @raffk Get off your high horse. Get into MIT and then we'll talk.

  • @raffk I don't want to come off as an ultimate smarthead, but I have been asking myself the very same question for quite some time now...

  • Lol, damn. Teachers like this make class so much more interesting!

  • In a lot of classes that come with college, I think a lot of undergrads can relate to the frustration in dealing with concepts that the professor "thinks you should know already", when in reality, you see the course description (and even maybe the title of the course), you find that THING (for lack of better words) is, in fact what you should already know :D ...(hopefully I convey my message clearly; it's the result of not-even-a-semester spent at an engineering university can do)

  • Please God help me get use to french accent

  • @FaildEscape hahahaha i have trouble getting over his creeper looking face. in no way am i implying he's a good/bad teacher, he just looks like a creeper imo.

  • @boblelan I would say so....

  • pretty much the same as i learned at my school in The Netherlands

  • Ze Vectaire.... love it

  • How can somebody who has never learned about or heard of a vector go to MIT? That's outrageous.

  • To think, somewhere in there are four kids who go to Las Vegas every weekend together..

  • These lectures are the EXACT lesson plans of my multivariable calculus class in Im taking in highschool! Im so glad I found these if i ever need hep.

  • @genomstic Why the hell are you taking multivariable calculus in high school

  • Am I the only one who thinks that his writing on the board is very efficient and clear?

  • @jillybooty no, i am with you

  • @jillybooty

    Nope, I think so, too.

  • haha, déjà vu. He's at UCB now teaching Math 53 (multivariable calculus) and his lectures are pretty much the same as this =D

  • GOOD

  • SIGN BETWEEN A.B WILL ALSO BE POSITIVE IF ANGLE THETA LIES BETWEEN 270 DEGREE TO 360 DEGREE( OPEN INTERVAL) .

  • SIGN BETWEEN A.B WILL ALSO BE POSITIVE IF ANGLE THETA LIES BETWEEN 270 DEGREE TO 360 DEGREE( OPEN INTERVAL)

  • He is a beast. 

  • I don't understand how people can end up in MIT, one of the most illustrious tech universities in the world, without having heard of vectors, or the cosine rule.

  • @horrabletypoe it's just a quick review, dude.. gets the mind working after being on the beach alll summer

  • @horrabletypoe You think it matters? You really don't have to be overly smart to go to a school as great as MIT. You just have to show them you have the persistence to learn from their staff. Obviously, you cannot be overly stupid either.

  • @horrabletypoe I'm not a fan of people making those kind of comments, but I agree! ><

  • he's fabulous

  • Hi, this is a wonderful lecture and very nice effort to spread the knowledge.

    Can i know which movie camera was used by you to record this lecture?

    I want to purchase one movie camera for recording lecture....Can you help me?

    Thank you

  • @zikriya25 This was recorded using professional equipment (and with a lot of post-processing). Not the kind of camera you can just bring to lecture and film your professor with.

  • Thank you MIT, you guys are the best in spreading knowledge to human kind =)) This is epic!!! I feel like being a student of one of the top institute in the world without paying extremely high tuition!

  • very good lecture

  • Those are some of the most beastly chalkboards I have ever seen.

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  • i understood shit from this...im more confused

  • This is making sense, even though I haven't even taken Geometry. XD (I'm only 15 and want to go to MIT after High School.)

  • @xkeikoxsanxdesu all the best mate, because its extremely hard to get into MIT even with A++ all round

  • @Kwabz1947 Thanks. ^_^" I plan on getting into some hard places if I can. Do you know what the requirements are for getting into MIT?

  • @xkeikoxsanxdesu quite alot besides the usual insanely high grades...just check out thier websites. These guys only select the best of the best! Thier acceptance rate is 10percent lol.ITS IS EXTREMLY DIFFICLUT to get into M.I.T

  • @Kwabz1947 Sounds easier to get into Harvard at this rate, and that's one of the top 3 Universities in the world (if I'm not mistaken, it's actually #1, while MIT is #9.) What's the site? I'll check it out once I'm done with my homework.

  • @xkeikoxsanxdesu if you can't google and find the site of MIT they probably won't accept you there :P

  • @orfygage . . . Yeah, good point. -goes to google MIT-

  • @xkeikoxsanxdesu Yip...true that but, when it comes to maths, science and technology MIT is best, the website is web.mit.edu

  • @Kwabz1947 Thank you so much. I want to be a doctor, so I think MIT would be a good school to do my Pre Med in. ^_^""

  • Coolest chalkboard ever.

  • @planeshaperman Yeah MIT'S signature chalkboards...

  • I wish probability and combinatorics with Dr. Jerison.

  • Yay professor Auroux. He's at Berkeley now HA go Bears.

  • HAHA.... everyone chose 1 for the 1st question. LOL!!!!!!!

  • @rax7 lol totally hope you're not serious.....

  • these MIT guys are so dumb. length of the vector should be root 14. It seems many have answered 6.

  • @jxcess3891 ...or the cards have two sides?

  • What book are they using for this class?

  • @Sadist102 Above all these comments there is a link to the course materials. Follow that link and select Readings. There you will find the book's author and title.

  • So multivariable calculus requires one to understand vector calculus? Is this Calculus II? My understanding Calculus III focuses more on differential equations and graphing differential equations.

  • I only hope that when I move to MIT next month, I learn as much from lectures in person as I can from watching them on youtube. This was great, I've decided that learning more math is a good way to kill some time this summer =)

  • @eligray wow get a life