To anyone considering watching all 35 lectures, do it. Professor Auroux teaches better than anyone I've ever seen before. Everything is structured, thought out, and flows from one topic to the next so effortlessly that you'll be amazed you just sat through 50+ minutes of math.
@@amoghdm159 Kiran, you may be right. Unfortunately , whenever I try to listen to any indian teacher, his or her strong accent makes the lecture unbearable. And I have tried many.
@@kenmeyer100 This is because we "mix" Hindi/Tamil etc. into English. Some years back I was not able to understand American accent as its too fast relative to Indian languages, and Words are not pronounced fully (compared to Indian languages). I could still understand British accent that time though.
Im using this lecture series as a supplemental study aid for my multivariable calculus class right now and couldn't help but talk myself through all the math on my midterm in a heavy french accent. All kidding aside, its incredible how even though this professor is teaching the brightest minds, he explains everything so clearly and logically that anyone could learn a ton from this course. MIT, i think its incredible that you guys post these lectures, your professors have an incredible way of communicating information and I think its extremely noble of you guys to make that accessible to anyone with access to a computer.
+Adia L. Its calculus 3. multivariable is all about 3 dimensional planes. Calculus 3 isnt as bad as Calculus 2....most people will agree that calculus 2 is the toughest of them all....calculus 3 is basically repeating what you all ready learned in calculus 1 and 2 and adding a 3rd dimension (x, y, AND z) to every scenario..
pmnelson81 I hope I will have the same opinion as the many people you describe lol. I took Cal II a year ago, and that was the only time I really struggled in a math class. I'm taking Cal III this fall. I've read that this class doesn't focus as much on the most difficult integrals, but using integrals, derivatives, and vectors to learn new concepts. Luckily, I love this guy's way of teaching. These videos plus brushing up on trig functions should be good preparation. I'm so grateful for MIT's open source work!
+B B I took Calculus 3 last year (or, well, the closest Swedish equivalent to that course anyway - "Multivariable Calculus"), and I remember that this course focused a lot on partial derivatives, tangent planes for 3D graphs, and also several different types of integrals, such as the line and surface integrals, and also a few theorems such as Green's Theorem, Stoke's Theorem and Gauss' Theorem.
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.
One of the best teachers that I've ever seen. I'm from Brazil and I could understand all their classes. Congratulations to the teacher and the institute (MIT). A very good job.
Just Completed the entire course. Multivariable Calculus was always on my mind since my high school days. It was everywhere in electromagnetism, however somehow our teachers got away with 2D versions and some mischief, was just fine. Afterwards I went into Computer Science and never got chance to learn it. I always loved physics, however not knowing vector calculus was embarrassing, it was literally everywhere. Then I decided to do it this summer. Hats off to Professor Auroux, he teaches so smoothly never during the entire course I felt like once I feared it. It was so smooth (plus his board work! you will see what I mean when you take the course :)). I feel so much happy now, Thank you Professor Auroux and MIT for bringing us this wonderful course.
Absolutely incredible. All of my teachers tried to explain this over the course of 3 class periods, keep in mind my classes only have 20 students. He accomplished a thorough, easy to follow explanation in 30 minutes. Absolutely incredible teacher.
This guy is a legend. I love him. The neatness of his lectures is just like the beauty of mathematics, and 18.02 is definitely my favorite MIT open course.
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.
Guys, remember this is simply revision! (its a very international university and people know different things so they make sure everyone knows the basics of everything and then they work them hard) this is to level the playing field, also note that they do this stuff very very quick and so someone who has no experience with them will still struggle (im from the UK btw)
This is multivariable calculus so must be assumed that everyone has at least know linear algebra and dot product induced spaces, even though this is one of the clearest classes I've seen. No surprise in why the MIT is one of the bests :)))
It is 3 am, I am hungry and I should have really taken care of washing today but I watched this 12 year old lecture on calculus instead. No regrets though.
Very good instruction. He goes at a perfect speed: good review pace, but if you don’t know about vectors that well, you can learn it very quickly with this speed. Très bon
I have extreme autism which makes me able to hold more information than 99.9% of the population, I did calculus at 7 years old. Normal people like you are mere insects to me, very simple and easy to manipulate.
This guy is extremely thorough and the "simplicity" of the material is only a testament to his teaching ability. He's teaching vectors, and its not like "mit vectors" would be something different, special, or requiring genius to understand simply because the school has a prestigious reputation. If your school's reputation isn't as recognized as mit's your frustration should be directed towards the morons who can not appreciate anything other than what someone else tells them is the "best."
Yeah that is the great thing about the Internet I mean if you like to learn all this stuff you can literally learn a lot of the stuff they teach at college and more but you have to know where to get the information. If I can't find what I want to learn on the Internet I just do it the old fashioned way which Is going to the library and getting a book on whatever subject I am studying or want to learn. I think that classes should be like this in the future instead of attending class everyday with a teacher that is strict and doesn't even know how to teach well in comparison to other teachers like this man and not to mention waisting valuable time but in this being in a live class and being able to ask questions on problems is always good and useful.
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!
hi my name is eric,i just get to america half years,i'm 12 years old,yesterday is my first day of six grade,and i will watch all of mit 250 math classes,and i will get into mit.
After watching this lecture, all I can say is how truly amazed I am. What a great video! Except for the fact that I couldn't understand one word he was saying( currently taking Tech Math at HS). I mean the camera was on point, his writing was nice, and the students were quite polite. Superb! MIT you surely do not disappoint :D
For those curious, the law of cosines is also called “Al-Kashi’s law” (in France and the Arab and Persian world). Al Kashi was a Persian mathematician (I encourage you to check his wikipedia page). Great lecture! I was genuinely surprised that what students in Syria are taught in 11th grade, Americans learn in university.. To those from other countries, when did you learn dot product? Just curious
In India, a basic idea of the dot product and cross product is provided in the beginning of 11th grade, as a pre-requisite for Physics. However, it is taught in much more detail in 12th grade.
10:00 When I was in U in Helsinki, Finland in 80's in comparable lecture the same question about generilization to higher dimension was asked and our lecturer gave almosty exactly the same answer as in here but augumented it with this: "One should invert a 100*100 matrix once in a lifetime to appriciate the fact that almost all multivariable mathematics can be reduced to two or three dimensions."
Most people will know. But it's usually repeated just to make sure that everyone is on the same page. I mean different teachers and different classes sometimes uses different notations and perspectives so it's good to have a quick walk-through of everything before.
I was so nervous about taking multivariable calculus at my college, because I was failing to understand the vector calculus I was learning at the end of calculus 2. I now realize it's not really that hard because I understand it, and that math minor is mine!
When I got a problem as a student in Maribor from the USA to help solve a problem from postgraduate studies and after I solved it in 5 minutes I never watched what Americans do in mathematics. 1986-7 This professor is a classic European mathematician and not to teach you how to solve everyday problems symbolically so that you are cool.
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 =)
Hooray and big ups to MIT for publishing these high quality videos! Anyone else notice the professor alternates between solid red, blue, green shirts throughout the semester? hehe.
this guys has a point. it's part of being educated, having seen important concepts. He didnt even say "without having *memorized..*" he said *seen. it's not a matter of perfect SAT scores either- why bring that up?
Remember that so long as you do not change length or direction, you can place that vector anywhere. So, take your result somewhere in the top left and move it down and you will see that it aligns with his vector c. He did not explain this well, or he expected it to be review maybe.
@xo20202004 there are lots of videos available from various universities. it depends on what you are looking for. if you are looking for another calculus lecture you can check out ...... Calculus1 Lecture1 its a calculus course offered by the University of Missouri-Kansas City.
@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.
I wasn't just talking about this lecture....I was talking about their practice exams involving the gradients and tangent line equations you build about 1/2 way thru multvariable calculus. MIT is a great school, that teaches you what you need to know for your future. However, I think it is not where you go to college but rather what you do at the college you go to.
... It's called vectors, you'll learn about them later. To add vectors you put them tip to tail and draw a vector from the tail of the first to the tip of the last. So in this case, when you put them tip to tail, it forms a rectangle. Then when you draw the "resultant" vector, it is the diagonal of the rectangle.
i've always had a beef with using an arrow as a notation for vector. an arrow is a "ray", which implies it has a starting point and no end point. a "line segment" would be a better choice for notation because it has a starting point and an end point. i realize that a vector has a direction, but it also has a magnitude which means the vector has a clear end point.
I used this to self-learn Vector calculus in my summer finishing year-1 of basic Multi-Calc in college starting from Lesson-15 to Lesson-29. I also made use of Schaum's Vector Analysis for problems and SJ Colley's Vector Calc as an additional reference. I watched all vids in at min 1.25x finishing it up in 2 weeks time. Dennis Auroux is an absolutely delight and his board-rubbing skills are sooo impressive! His explanations are spectacular & I really enjoyed his emphasis on applications (particularly from physics-inertia, maxwell's eqns etc). One thing I missed was lack of info on the Frenet-Serret Equations which I found awesome in general & the lack of practicing more problems but hey, you could do both on your own like I did! Anyways, 12 years after this vid has been released, I'd still recommend this course with all my heart. It is awesome! Thanks MIT for releasing this to the public & thanks Prof. Auroux for just being an amazing lecturer!
There is a circular argument there in 24:45. Law of cosines used to prove geometric expression of dot product. Geometric expression of dot product used to prove law of cosines.
Quanxiang Loo No in reality the geometric expression of dot product is proven by the law of cosines, and the law of cosines has its own proof. Basically he couldn't be bothered/he didn't have the time to write out the proof of the law of cosines. He knew that some students hadn't seen the law of cosines before, and they wanted proof that it was correct. So what he did was say that if you just accept that the dot product thing is true, then it can act as a proof of the law of cosines. It was basically a shortcut to save time. It was a bit sloppy and unclear, but he wasn't really saying that the geometric expression of a dot product is really the proof of the law of cosines.
I think that is the case too. He should have just said "I won't prove the law of cosines, in the interest of time". It's one thing to say assume A is true and that implies B is true; and another thing to say B is true because I claim A is true, oh and by the way A is true because B is true -.- guess it's just a pet peeve of mine. EDIT: Saying something like that during the lecture may result in those who are not as sharp to think there is no need to look up the proof of the law of cosines (if they didn't already know it).
the education is, it's almost the same everywhere, but you can not overrate the students and the teacher, something you will understand if you look at achievement comparison between universities
nice, we covered a lot of multivariable calculus this year (a first for junior students in Hawaii) it was awesome, but since we also took AP Calculus BC during this year, it was a bit difficult to switch back for the exam and I ended up trying to use MV calc on the BC exam lol. Smart idea to spend time reviewing the course materials ^^
There was nothing new that I had learned by watching this, although I did enjoy it very much. The only thing that I noticed about the section that pertains to the dot product that wasn't mentioned but I feel is just as significant is that it doesn't just check for orthogonality whether two vectors are perpendicular or not, but that it also tests if two vectors either coincide or are parallel! They are parallel or coincide when the dot product yields (-1). This is simply because theta will equal either +/- 180 degrees or +/- PI radians where cos(+/- 180) or cos(+/- PI) yields (-1) because the cosine is an even function.
37:40 Wrong assumption, one of the lengths of the vectors can be 0, in which case angle isn't defined and even though it's perpendicular(by definition of euclidean spaces if I remember correctly) you can't deduce cos theta is 0 from that.
Don't act confused guy, i'm not saying anything about the teaching capabilities if the lecturers or the work they cover at MIT. All i'm saying is that the title of being one of the greatest engineering schools in the world is due to talented students every now and then and a wide range of resources available to them.
same content as my non ivy league university. in fact because the professor is so good here and i had to teach my self everything i would say it was harder.
@xo20202004 i also forgot to mention that you can also type in the name of the college eg. harvard, cambridge, StanfordUniversity, UCBerkeley, nptelhrd, calcommunitycontent etc
Lecture 1: Dot Product
Lecture 2: Determinants
Lecture 3: Matrices
Lecture 4: Square Systems
Lecture 5: Parametric Equations
Lecture 6: Kepler's Second Law
Lecture 7: Exam Review (goes over practice exam 1a at 24 min 40 seconds)
Lecture 8: Partial Derivatives
Lecture 9: Max-Min and Least Squares
Lecture 10: Second Derivative Test
Lecture 11: Chain Rule
Lecture 12: Gradient
Lecture 13: Lagrange Multipliers
Lecture 14: Non-Independent Variables
Lecture 15: Partial Differential Equations
Lecture 16: Double Integrals
Lecture 17: Polar Coordinates
Lecture 18: Change of Variables
Lecture 19: Vector Fields
Lecture 20: Path Independence
Lecture 21: Gradient Fields
Lecture 22: Green's Theorem
Lecture 23: Flux
Lecture 24: Simply Connected Regions
Lecture 25: Triple Integrals
Lecture 26: Spherical Coordinates
Lecture 27: Vector Fields in 3D
Lecture 28: Divergence Theorem
Lecture 29: Divergence Theorem (cont.)
Lecture 30: Line Integrals
Lecture 31: Stokes' Theorem
Lecture 32: Stokes' Theorem (cont.)
Lecture 33: Maxwell's Equations
Lecture 34: Final Review
Lecture 35: Final Review (cont.)
got tired of MITs site, hope you find use of this as well
you are a legend!
not all heroes wear capes
*Holy fucking shit...* Calculus 3 has that many topics?
god bless u
you are one real legend
To anyone considering watching all 35 lectures, do it. Professor Auroux teaches better than anyone I've ever seen before. Everything is structured, thought out, and flows from one topic to the next so effortlessly that you'll be amazed you just sat through 50+ minutes of math.
I read your comment before going through the lectures. Now, I can't agree with you more. He's the best.
Bro come to India I will show u dam better lecturers than the guy who is teaching
@Ajey Chahal you are speaking false
@@amoghdm159 Kiran, you may be right. Unfortunately , whenever I try to listen to any indian teacher, his or her strong accent makes the lecture unbearable. And I have tried many.
@@kenmeyer100 This is because we "mix" Hindi/Tamil etc. into English. Some years back I was not able to understand American accent as its too fast relative to Indian languages, and Words are not pronounced fully (compared to Indian languages). I could still understand British accent that time though.
Im using this lecture series as a supplemental study aid for my multivariable calculus class right now and couldn't help but talk myself through all the math on my midterm in a heavy french accent. All kidding aside, its incredible how even though this professor is teaching the brightest minds, he explains everything so clearly and logically that anyone could learn a ton from this course. MIT, i think its incredible that you guys post these lectures, your professors have an incredible way of communicating information and I think its extremely noble of you guys to make that accessible to anyone with access to a computer.
Is this Calculus 2 or 3 he is talking about?
+Adia L. Vector calculus(this course) is calculus 3
+Adia L. Its calculus 3. multivariable is all about 3 dimensional planes. Calculus 3 isnt as bad as Calculus 2....most people will agree that calculus 2 is the toughest of them all....calculus 3 is basically repeating what you all ready learned in calculus 1 and 2 and adding a 3rd dimension (x, y, AND z) to every scenario..
pmnelson81 I hope I will have the same opinion as the many people you describe lol. I took Cal II a year ago, and that was the only time I really struggled in a math class. I'm taking Cal III this fall. I've read that this class doesn't focus as much on the most difficult integrals, but using integrals, derivatives, and vectors to learn new concepts.
Luckily, I love this guy's way of teaching. These videos plus brushing up on trig functions should be good preparation.
I'm so grateful for MIT's open source work!
+B B
I took Calculus 3 last year (or, well, the closest Swedish equivalent to that course anyway - "Multivariable Calculus"), and I remember that this course focused a lot on partial derivatives, tangent planes for 3D graphs, and also several different types of integrals, such as the line and surface integrals, and also a few theorems such as Green's Theorem, Stoke's Theorem and Gauss' Theorem.
This handwriting is very refreshing.
Vector analysis lecture 1
th-cam.com/video/V-mxulFCbBs/w-d-xo.html
So true. I felt like I was sitting in the class
So neat and not scribbles & random scratches representing letters
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.
are ur kids learning multivariable calculus now? lol 😂
I’m a 10th grader learning this stuff in school
This is the way mathematics should be taught explaining every logical step. Sadly it's lightyears away from the way it's usually taught.
Eternaldream00 really agree, in my countrie Ecuador, teacher sucks!!!!! If this teacher work to Ecuador, people love him because teach very well!.
agreed. memorize this and regurgitate it is the current method.
In the US when they added "Common Core" it went backward lightyears away!
Khan academy is also good
It’s MIT so all the students are really smart and they can easily understand what he’s teaching.
One of the best teachers that I've ever seen. I'm from Brazil and I could understand all their classes. Congratulations to the teacher and the institute (MIT). A very good job.
Just Completed the entire course. Multivariable Calculus was always on my mind since my high school days. It was everywhere in electromagnetism, however somehow our teachers got away with 2D versions and some mischief, was just fine. Afterwards I went into Computer Science and never got chance to learn it. I always loved physics, however not knowing vector calculus was embarrassing, it was literally everywhere. Then I decided to do it this summer. Hats off to Professor Auroux, he teaches so smoothly never during the entire course I felt like once I feared it. It was so smooth (plus his board work! you will see what I mean when you take the course :)). I feel so much happy now, Thank you Professor Auroux and MIT for bringing us this wonderful course.
Absolutely incredible. All of my teachers tried to explain this over the course of 3 class periods, keep in mind my classes only have 20 students. He accomplished a thorough, easy to follow explanation in 30 minutes. Absolutely incredible teacher.
He's a professor at one of the most prestigious STEM-oriented institutions for a reason.
his neatness makes me smile
Aidan Cremin Then my neatness of my professor in real analysis will make your mouth rip for smiling wide.
Trigonometry for AS and A level student th-cam.com/video/-WzZRx4vVxI/w-d-xo.html
I love this lesson and the sound of chalk against that board-this vectors lesson gave me goose pimples, merci beaucoup !
This guy is a legend. I love him. The neatness of his lectures is just like the beauty of mathematics, and 18.02 is definitely my favorite MIT open course.
I have a math degree and I still enjoy these lectures. Auroux is a great lecturer.
Don't forget another great thing about MIT. MIT does thing like share these lectures.
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.
I WISH we had more such professor at my University when I was studing. Prof. Auroux, you are a rare "bird".
Let's take out a moment of Appreciation for the camera man👏👏
Guys, remember this is simply revision!
(its a very international university and people know different things so they make sure everyone knows the basics of everything and then they work them hard)
this is to level the playing field, also note that they do this stuff very very quick and so someone who has no experience with them will still struggle (im from the UK btw)
This is multivariable calculus so must be assumed that everyone has at least know linear algebra and dot product induced spaces, even though this is one of the clearest classes I've seen. No surprise in why the MIT is one of the bests :)))
This Prof's handwriting is unbelievable. It's SO neat!
It is 3 am, I am hungry and I should have really taken care of washing today but I watched this 12 year old lecture on calculus instead. No regrets though.
*Takes a break from studies*
*Accidentally learns more*
dudee sameee! haha
Very good instruction. He goes at a perfect speed: good review pace, but if you don’t know about vectors that well, you can learn it very quickly with this speed. Très bon
Me: maybe they'll teach it differently in the US
MIT: Oh by the way, there's our Frenchiest teacher
Vecteurs
There's something about a French or German accent that sounds more 'mathy.'
@@NoActuallyGo-KCUF-Yourself I'm afraid that only works if your not French yourself ;)
Asians laughing in the corner
this is a great lecture. the way he handled the law of cosines off the cuff was brilliant.
I have extreme autism which makes me able to hold more information than 99.9% of the population, I did calculus at 7 years old. Normal people like you are mere insects to me, very simple and easy to manipulate.
I am so happy I know English, which allows me to understand these lectures🙏🙏🙏🙏
This guy is extremely thorough and the "simplicity" of the material is only a testament to his teaching ability. He's teaching vectors, and its not like "mit vectors" would be something different, special, or requiring genius to understand simply because the school has a prestigious reputation. If your school's reputation isn't as recognized as mit's your frustration should be directed towards the morons who can not appreciate anything other than what someone else tells them is the "best."
Auroux is THE MAN. One of the best professors I've had so far.
Thank's MIT, now I don't have to go to my lectures any more! :)
Yeah that is the great thing about the Internet I mean if you like to learn all this stuff you can literally learn a lot of the stuff they teach at college and more but you have to know where to get the information. If I can't find what I want to learn on the Internet I just do it the old fashioned way which Is going to the library and getting a book on whatever subject I am studying or want to learn. I think that classes should be like this in the future instead of attending class everyday with a teacher that is strict and doesn't even know how to teach well in comparison to other teachers like this man and not to mention waisting valuable time but in this being in a live class and being able to ask questions on problems is always good and useful.
I used to think Princeton's cal 3 is better but this guy is actually the best I've seen.
+heikiu96z we do all this in our 12th in india. and he is doing this in mit.wow!!!
+physics for all I do this in back alley in Mexico and he doing this at mit wow!!!
mister one wow dont worry . he mit will be fine
+physics for all MIT students can skip this by taking exams(APs or ASEs)
That's not true, they can only skip Calculus I by taking APs. Source: math.mit.edu/academics/undergrad/first/ap.php
Remember guys, believe in the law of cosines!!
wat
No, you must believe the law of sines!
Spoder Man. Why use sines when you can use tangents, or an identity of one of the laws.
Emergency Jergens yay a^2 +b^2+c^2-2bcCos(A)
I can barely remember it half the time lmao
Started this course today. Hope to complete it soon. Loving the journey of learning.
I am gonna watch the whole series. What a great teacher man! 👌 Keep it up.
أول عربية استاد رائع و بناء جميل لدرس
2,3,8,9,10,11,12,13,15,16,25 - these are topics needed for economics&finance majors
I just started loving physics after seeing your lecture
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!
it is a fortune to have these videos. thank you
I am actually amazed at how he writes with chalk so fast but maintains cleanness and legibility.
At most colleges and universities this would be Calc 3. At MIT, it is Calc 2 and Differential Equations takes the place of Calc 3.
hi my name is eric,i just get to america half years,i'm 12 years old,yesterday is my first day of six grade,and i will watch all of mit 250 math classes,and i will get into mit.
don’t get too ahead of yourself. There are plenty of other prestigious universities too outside of MIT. But good luck.
So this is from like 15 years ago yet it's exactly what I need now.
After watching this lecture, all I can say is how truly amazed I am. What a great video! Except for the fact that I couldn't understand one word he was saying( currently taking Tech Math at HS). I mean the camera was on point, his writing was nice, and the students were quite polite. Superb! MIT you surely do not disappoint :D
For those curious, the law of cosines is also called “Al-Kashi’s law” (in France and the Arab and Persian world). Al Kashi was a Persian mathematician (I encourage you to check his wikipedia page). Great lecture! I was genuinely surprised that what students in Syria are taught in 11th grade, Americans learn in university.. To those from other countries, when did you learn dot product? Just curious
He was an Arab.
This is also something learned in 11th grade in France.
In India, a basic idea of the dot product and cross product is provided in the beginning of 11th grade, as a pre-requisite for Physics. However, it is taught in much more detail in 12th grade.
10:00 When I was in U in Helsinki, Finland in 80's in comparable lecture the same question about generilization to higher dimension was asked and our lecturer gave almosty exactly the same answer as in here but augumented it with this: "One should invert a 100*100 matrix once in a lifetime to appriciate the fact that almost all multivariable mathematics can be reduced to two or three dimensions."
Hes a class lecturer. I envy anyone who had him in college.
Same here. If he was there in my college I wouldn't have ever failed maths
Most people will know. But it's usually repeated just to make sure that everyone is on the same page. I mean different teachers and different classes sometimes uses different notations and perspectives so it's good to have a quick walk-through of everything before.
Thanks to Prof.Auroux from Korea ! 전기공학을 배우는 분들 중 대학교 1학년 과정에 벡터미적분학을 배우지 않은 분들께 꼭 필요한 수업입니다. 전자기학 수강에 큰 도움이 됩니다. (다른 분야는 잘 모르겠음)
고1인데 학교 못가서 이거보고있네요ㅋㅋ
Thx i am from India and really i am enjoying it
I was so nervous about taking multivariable calculus at my college, because I was failing to understand the vector calculus I was learning at the end of calculus 2. I now realize it's not really that hard because I understand it, and that math minor is mine!
I love his french accent, it makes the class more interesting
Thanks, any other 15 year olds watching these lectures, pretty useful for GR actually
I’m 13
When I got a problem as a student in Maribor from the USA to help solve a problem from postgraduate studies and after I solved it in 5 minutes I never watched what Americans do in mathematics.
1986-7
This professor is a classic European mathematician and not to teach you how to solve everyday problems symbolically so that you are cool.
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 =)
you probably graduated by now but how was it?
I wish I was taught calculus by this guy from the start!
Hooray and big ups to MIT for publishing these high quality videos!
Anyone else notice the professor alternates between solid red, blue, green shirts throughout the semester? hehe.
I’m in highschool watching this and this is soo helpful. Thank you
this guys has a point. it's part of being educated, having seen important concepts. He didnt even say "without having *memorized..*" he said *seen.
it's not a matter of perfect SAT scores either- why bring that up?
EXCELENTE LA CLASE, ME GUSTA MUCHO LA FORMA COMO ABARCA Y EXPLICA TODOS LOS TEMAS, SEGUIRÉ VIENDO ESTOS VIDEOS. M.I.T. LO MEJOR.
Remember that so long as you do not change length or direction, you can place that vector anywhere. So, take your result somewhere in the top left and move it down and you will see that it aligns with his vector c. He did not explain this well, or he expected it to be review maybe.
@xo20202004 there are lots of videos available from various universities. it depends on what you are looking for. if you are looking for another calculus lecture you can check out ......
Calculus1 Lecture1
its a calculus course offered by the University of Missouri-Kansas City.
@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.
I wasn't just talking about this lecture....I was talking about their practice exams involving the gradients and tangent line equations you build about 1/2 way thru multvariable calculus. MIT is a great school, that teaches you what you need to know for your future. However, I think it is not where you go to college but rather what you do at the college you go to.
... It's called vectors, you'll learn about them later. To add vectors you put them tip to tail and draw a vector from the tail of the first to the tip of the last. So in this case, when you put them tip to tail, it forms a rectangle. Then when you draw the "resultant" vector, it is the diagonal of the rectangle.
woow im learning more abt the topics than my actual classes, this prof is da bomb
Thank you very much. I have a hard time with this course. This video helps me a lot.
blackboard/whiteboard so much better than powerpoint!
A course in multivariable calculus and the comments center around the sound of the guy's voice. Nice.
i've always had a beef with using an arrow as a notation for vector. an arrow is a "ray", which implies it has a starting point and no end point. a "line segment" would be a better choice for notation because it has a starting point and an end point. i realize that a vector has a direction, but it also has a magnitude which means the vector has a clear end point.
I used this to self-learn Vector calculus in my summer finishing year-1 of basic Multi-Calc in college starting from Lesson-15 to Lesson-29. I also made use of Schaum's Vector Analysis for problems and SJ Colley's Vector Calc as an additional reference. I watched all vids in at min 1.25x finishing it up in 2 weeks time.
Dennis Auroux is an absolutely delight and his board-rubbing skills are sooo impressive! His explanations are spectacular & I really enjoyed his emphasis on applications (particularly from physics-inertia, maxwell's eqns etc).
One thing I missed was lack of info on the Frenet-Serret Equations which I found awesome in general & the lack of practicing more problems but hey, you could do both on your own like I did!
Anyways, 12 years after this vid has been released, I'd still recommend this course with all my heart. It is awesome! Thanks MIT for releasing this to the public & thanks Prof. Auroux for just being an amazing lecturer!
22:30
Law of cosines
MIT OPEN COURSEWER MEANS KNOWLEDGE FOR THOSE WHO WANT IT.
To think that I have to do 2 more years of classes before I get to do this fun. I can't wait :D
Good refreshment for my calc based physics class. Thanks MIT
I love this logical teaching
His accent is wonderful!
Taking notes on this class using mostly screen captures! Very useable boardwork
There is a circular argument there in 24:45.
Law of cosines used to prove geometric expression of dot product.
Geometric expression of dot product used to prove law of cosines.
Quanxiang Loo No in reality the geometric expression of dot product is proven by the law of cosines, and the law of cosines has its own proof. Basically he couldn't be bothered/he didn't have the time to write out the proof of the law of cosines. He knew that some students hadn't seen the law of cosines before, and they wanted proof that it was correct. So what he did was say that if you just accept that the dot product thing is true, then it can act as a proof of the law of cosines. It was basically a shortcut to save time. It was a bit sloppy and unclear, but he wasn't really saying that the geometric expression of a dot product is really the proof of the law of cosines.
I think that is the case too. He should have just said "I won't prove the law of cosines, in the interest of time".
It's one thing to say assume A is true and that implies B is true; and another thing to say B is true because I claim A is true, oh and by the way A is true because B is true -.- guess it's just a pet peeve of mine.
EDIT: Saying something like that during the lecture may result in those who are not as sharp to think there is no need to look up the proof of the law of cosines (if they didn't already know it).
the education is, it's almost the same everywhere, but you can not overrate the students and the teacher, something you will understand if you look at achievement comparison between universities
He's teaching at Berkeley this semester!! I always see him before my Linear Algebra class
UC Berkely you are trying to say?
nice, we covered a lot of multivariable calculus this year (a first for junior students in Hawaii) it was awesome, but since we also took AP Calculus BC during this year, it was a bit difficult to switch back for the exam and I ended up trying to use MV calc on the BC exam lol. Smart idea to spend time reviewing the course materials ^^
Thanks from the bottom of my heart 🥺
There was nothing new that I had learned by watching this, although I did enjoy it very much. The only thing that I noticed about the section that pertains to the dot product that wasn't mentioned but I feel is just as significant is that it doesn't just check for orthogonality whether two vectors are perpendicular or not, but that it also tests if two vectors either coincide or are parallel! They are parallel or coincide when the dot product yields (-1). This is simply because theta will equal either +/- 180 degrees or +/- PI radians where cos(+/- 180) or cos(+/- PI) yields (-1) because the cosine is an even function.
lmao stfu
c=a-b because it leads from where b is to a. numerically: b+c=b+a-b=a
To anyone watching: This first video is introductions to vectors including rules and applications.
37:40 Wrong assumption, one of the lengths of the vectors can be 0, in which case angle isn't defined and even though it's perpendicular(by definition of euclidean spaces if I remember correctly) you can't deduce cos theta is 0 from that.
Thank you very much MIT for these free lectures.
7:50
17:00
35:00 example
Don't act confused guy, i'm not saying anything about the teaching capabilities if the lecturers or the work they cover at MIT. All i'm saying is that the title of being one of the greatest engineering schools in the world is due to talented students every now and then and a wide range of resources available to them.
2,3,8,9,10,11,12,13,15,16,25 - chapters needed for economists
Excellent Lecture by an Excellent Teacher.
I am absolutely in love with that accent
This guy's accent is seriously the best.
Integrate from 0 to (1/2) x^3 arctan(x) dx to 4 decimal places.
Watching this to make me feel better about college algebra. lol
What do you mean?
because knowledge is more important for them than their appearance
same content as my non ivy league university. in fact because the professor is so good here and i had to teach my self everything i would say it was harder.
Is sad for me to see how much i could learn some years ago if i have acces to his class.
@xo20202004 i also forgot to mention that you can also type in the name of the college eg. harvard, cambridge, StanfordUniversity, UCBerkeley, nptelhrd, calcommunitycontent etc
these lectures are great! thank you, MIT!