Many math teachers are "wicked smart" but not many, in my experience, are good teachers. Prof Strang is not only "wicked smart" but he is funny--in a quirky way. Thanks for the lecture.
A word of warning: Like many lecture series at MIT, this starts out at a very basic level. There is a good reason for this. You simply must master these simple concepts or you will get lost when things get complicated. Professor Strang is teaching you to think in principles and he is a master at it... If you have any interest in calculus (or just want another shot at it), I urge you to continue to the next lecture. It just gets better and better...
That is totally true, if you do not learn to understand each topic you handle, you surely fail and become frustrated. The amount of topics you understand(and you know how to use) is inversely proportional to the time you will study in your career.
Fuck yeah! calculus the old fashion way. A really smart, qualified teacher and a dusty ass chalkboard with chalk. No overhead projector, no lecture notes, no iPad bullshit. Just straight into the work. Congrats Dr. Strang.
FINALLY!! Somebody gave a basic summary of how calculus works by showing the whole picture at once, instead of just nonsensical sections at a time!!! I've been trying to understand how it worked for decades!!! I only got through trig & pre-calc then life took over & I never had enough time to learn the rest, until now.... :-)
Hi Mr. Strang. Thank you and MIT very much for this video! I'm a mature student, out of school for quite some time. I was really bad with Math in grade school and high school. I'm now in college taking a Business program which involves taking a Microeconomics course. The course uses some fairly basic calculus, but was quite difficult for me. This video really helped me out giving me the "big picture" of it. I feel if I was taught in this manner at a younger age, I would of understood it a lot better. Excellent teaching.
If you're cramming, or in need of a quick crash course, I'd like to give you a small helpful hint: professor Strang's pace becomes quite nice if you speed the video up to 1.25-1.5x :)
I just finished Calculus I and needed a good reminder of the larger picture. This was a fantastic summary of the key topics. I'm very grateful for the kind professor's time. Thanks, Professor Strang.
Professor Strang is one of the many reasons why MIT is the best University in the world. Not just the best in leading technology research but because of teachers like this. I had some physics teachers like him. Professor Lewin comes to mind immediately,Dr. Barrett.... I apply what I learned in your classes to my plastic surgery work now. The simple stuff to be sure; vector calculus and Newtonian physics, yes. Its easy to break new ground in your chosen profession when you leave a place like this. Thank you, MIT, Professors Strang, Lewin , Barrett et al... I am forever indebted to you. Thank you.
I think Dr. Strang speaks more slowly than the average teacher, but I love it. A good teacher is patient and takes the time to explain the steps they're taking in a way that is unlikely to be misinterpreted. Dr. Strang has contributed much to mathematics education, and, like others on here, I am really grateful these videos are available to those of us who were never exposed to calculus prior to college.
I wish I could tell this guy how appreciative I am of him doing this. Considering he had no obligation to do it, and these are the kind of videos that I learn the most from. Not just learning formulas and solving 100's of problems, but understanding what they mean and why they are important. Great lecture series.
I love it.. This guy talks to me and presents the lecture and hand-holds like I am a total idiot in this area; which is exactly what I need, because that makes it easier to fundamentally digest and understand the information and concepts. He lays the foundations perfectly while also avoiding using any technical math jargon that someone may not yet be familiar with before learning calculus. This is one of the best intro lectures I've found and this guy is one of the few profs that actually knows how to TEACH properly and convey information.
I've been trying to self teach myself calculus for the past couple of days. I've been completely lost in the the jargon used in study the material i've use online. I found this video the "Boom!" my mind was blown. I actually understand everything now. What a difference a great teacher makes.
In less than 38 minutes, he gave me more understanding of Calculus than 3 years of Math class in high school did. You're a gift to mankind, professor Strang. I wish you health.
Well thank you SO MUCH for putting integration and derivatives into perspective. At the age of 50, I'm coming back to look at Calculus with a zero expectation angle. Integration and derivatives have always seemed a mystical topic - I cracked out an A in University but never really had it explained in a visual relationship between everyday concepts. Your having put the two concepts into relationship between two functions - distance with speed, height with growth, speed with acceleration -- has made ALL the difference as my first foray into revisiting the wonders of science ... I have three boys ... the oldest is 13 ... I want them to genuinely fall in love with science. Thanks to Professor Strang!
Note on the example about trip meters (at about 18:30): I don't know either, but an engineer's answer (or a mechanics answer) would be that trip meters ought to always go forwards regardless of which way you go, since I'm fairly sure the intent is to measure wear on the engine. Also, if you did make speedometers to measure velocity rather than speed (velocitydometers?), then they'd do it according to a general frame of reference (most likely the earth's surface) rather than which way the car was pointing, so trip meters would just be an approximation of the car's location relative to where you started driving it, not very useful in most circumstances.
This is pretty good. The professor seems to find it a little hard to get his ideas out in plain words, which makes it a little hard to follow the current point at certain times, but his use of many real world examples keeps everything going along pretty smoothly, and his short mental detours are kind of entertaining anyway and show a little human in the teacher without being much of a problem. Thank you for posting this information online for the world to watch for free.
These kinds of videos always have a bit of a bitter sweet taste. Sweet because here you have just a great teacher and MIT is sharing him for free.But how can you not feel bitter that not every teacher is as great as Professor Strang?
sir I am an Indian, right now studying in std 10th but the way u teach is really amazing. it made me realize n understand maths actually from your simple teaching techniques... I really appreciate your work sir...
after i watched this video, my insight is very open because the video Calculus is about change. One function tells how quickly another function is changing. Professor Strang shows how calculus applies to ordinary life situations is very good to give information
I like how you explain that calculus is the relationship between functions and you show how the function can be represented by other letters other than f and that the variable function can be represented by any letter inside the parentheses. Made a lot of sense. Everything you discuss in this video was helpful and enlightening. Thank you so much.
I know nothing of calculus except basic algebra courses and I understood most of his explanations. True talented teacher he is, shows that it can make or break a student, he makes is seem so common sense
You have a very nice way of abstraction. I never really understood the logic behind proof for many of calculus rules until I saw your videos. Thank you very much.
Regarding the trip meter, surely it's correct that it doesn't go backwards because it measures distance (a scalar quantity) not displacement (a vector quantity).
+Dominic London exactly what I was thinking. thanks for your comment, coz I was reconsidering my own understanding of the subject given that he is a MIT lecturer and I assumed he might not had got it wrong, especially because its online on MITcourseware. Doesn't anyone check and edit the material before posting online, or even the editor missed it!
+Michael Harris I would rather prefer authorities like MIT lecturers try not to get things wrong or messed up, coz people, quite reasonably I think, tend to take everything they say as facts..
+Romin Oli You have a point but I wonder if everything was corrected would the lecture become sterile and boring. I think it would. Using a car was an everyday object, but it’s meter didn't fit the bill exactly. He hesitated as the talked about it going backwards involving us in his thinking process. You see, he taught me through UA-cam and his style to understand calculus where others failed, so I would consider myself nitpicking if I criticized him.
In the movie Ferris Bueller's Day Off, the odometer did not register any change because the odometer measures from the wheels that aren't driven by the engine. That car was a rear-wheel drive car, and the odometer gets its measurements from the front wheels. The front wheels remained stationary, which is why the odometer didn't count anywhere. They'd have to spin the front wheels by hand, to roll back the miles. That trick could only work on a four wheel drive, that was built before 1960.
Sir, you are doing public service with these lectures and I am so grateful to you. Though I already knew it but still watching these lectures enriched my knowledge now I've learned something I will never forget. Thonk you.
Last night I was crying because I can't understand calculus,I watched many videos of teachers explains it,but They're explains the mathmatical side only,now is the first time I feel that I'm begaining to understand claculus:")💖 And so excited to do that! Thank you professor,thank you from all of my heart💜
I attended a course in the university, few years ago, using his book of linear algebra without to listen him like I can do now . He is an excellent teacher
correct equation is most definately f(t)=1/2 at^2. this is only under 1 dimensional motion with constant acceleration. function 2 is the derivative of function 1, and function 1 is the integral of function 2. you can even test this using the definition of an integral, ∫x^n dx=1/(n+1) x^(n+1), n≠-1
I really like how clear the English language pronounces this teacher: although I hardly know the English language, I understand practically everything he says thanks to the clear and perfect way he speaks English. He is also very good how he clarifyes that is the calculus : it is to calculate the rate or variation at each moment with which a dependent variable varies when it varies an independent variable. Thank you. from Spain. janay
I refer to the derivative with "rate or variation at each moment with which a dependent variable varies when it varies an independent variable", with a mathematical structure similar to that of the tangent (increment of Y divided by increment of X when increment X tends to zero)
For me It takes physics to truly understand calculus. When I took calculus I just memorized what I need to do. I did not know why. When I took physics I finally understood why I did what I did.
can you say what it was in calculus that is a benefit in physics?? ------ I wish both subjects - maths and physics.. had cross - pollinated .. they could have done the same example - from a use in physics ...add that example into teaching/showing calculus : here's how it can be applied
Hi Proffessor Strang I've seen this video by the interest of learning calculus,and i like doing maths very much. I'm only 11 and i want to learn calculus .in fact i like doing calculus. i just wanna say that you are a very good teacher of maths and teach calculus very confidently
good you should do that.. im 19 and a freshman in college and im just beginning to really learn it (i took it in high school though), and my sincere advise is to keep learning it will you help you so much more in college if you start younger if you can remember it till you get to college
I love you sooooo much Prof. Strang!!! This lecture is illuminating, fascinating, inspiring and amazing! I have finished Prof. Strang Linear Algebra courses, onward to Calculus! Can't thank you enough Prof. Strang, you are changing people's lives. What a great gift to humanity!
..see the other MIT videos; isn't it amazing that MIT still uses these traditional blackboards and chalk instead of the "more modern" white boards or - GASP! - the hated PowerPoint slide. Somehow reassuring.
Wabi Sabi using powerpoints is a serious crime and the person who does that is a criminal with power points there's no interaction no conversation no humanity It's a sin
I visited courses on an actually very well reputational university, but they never teach you the basics ... they always go right into the guts and details, and you wonder why you are even here, watching all those details. When watching videos like these i sometimes wonder if it is not intentional dumb keeping. Well, let's praise the internet, and foremost, let's praise MIT opencoursware and Gilbert Strang for these amazing things we are able to witness right now! I am truly blessed to live in these times, where information is so freely available.
Thank you for posting this to try to help people understand. I've been out of school for a while, so this is helpful. I always appreciate when people are generous with their knowledge.
Thank you Mr strang for this eye opener course on "what is calculus" that I finally and at once got it, at the age of 70+ 😁. Your lucid explanations drove it home to me that it is essentially about function of functions & their inter-relations. Thanks agn!
I enjoyed this lecture very much, but I believe the graph represents displacement rather that distance. As distance would increase when you were going forward and backward (17:25), but displacement would not.
at 34:30 he states that speed = acceleration multiplied by time; however acceleration = speed squared and the area under the line cannot be one half times speed squared times time squared. The area is one half times speed times time. Something doesn't add up here ...
What I am saying is that he appears to have put distance where speed should be and vice versa ... because distance = speed times time. Thus the right graph would be meters per second and the left graph would be acceleration with meters per second per second. He has the calculus right but, named his y axes wrong; he has them swapped.
Thank you, Dr. Strang, for your dedication to the sciences. I believe it is essential to have an educated populace, and for the cost of an internet connection and a laptop computer, we the people are able to do such a thing at an affordable cost. This would not be possible without dedicated professionals...for that, I bestow upon you the award of super-awesome professor of the year.
Hold on solving for at, d which he put in would have to equal 2...which is being multiplied by f/t. Got it now. it could also read 2(f/t)=at. or 2f/2t=at.
Great old school teaching from the Prof clear visual concepts helped me to grasp a deeper understanding and meaning behind what was just memorised gibberish glyphs back in school - thanks
Thanks Professor Strang, MIT and You Tube for this video. It isn't easy breaking laymen into the field of calculus, but at least he makes it interesting, with the sparkle of hope we can understand why calculus is so important in its applications, and more importantly, how to (eventually, as I am a newcomer to this field) use it.
If speed is a matter of the change in distance over the change in time, then even though we cannot have time changing as a negative (decreasing), we can still have distance changing as a negative, thereby making the speed negative.
I failed calculus the first time I took it because I got a bad teacher. When I got a good one it was so easy to learn. It just seems so easy once you really understand it. Every college student should learn it. If you put in the time anyone can learn it.
You are correct as long as you are defining speed as the absolute value of velocity. I think he is using the word "speed" loosely in this video because those being introduced to calculus are probably not as familiar with the concept of velocity.
In a car what’s important is the magnitude, or the absolute value, of the milagre |x| and not the direction or the sign; which in turn is the measure of how much a car has been used (be it in the forward or the reverse direction). In other words, if the wheels are turning, you’re putting mileage on the car, regardless of the direction. When it comes to a car, in fact, you can’t look at the algebraic sum of the mileage (in the forward or reverse directions) but the overall magnitude of the mileage that’s been put on the car. If you use calculus, in this particular example, you’re either fooling yourself, or else cheating a potential buyer, with regards to the total number of miles (the absolute value) that the car has being utilized.
Gilbert is amazing. I remember one course i took where my professor was so bad. He could write two boards full of math and end up with 2=1 haha. I had to stop going to his lectures. It just so happened that all the topics we read were in a course gilbert taught that was available on youtube. I passed the test even though english is a foreign language to me.
19:45 - This also becomes an interesting issue with utility meters. If you build an electrical meter without thinking about this issue, it is bidirectional and measures the net energy consumed, subtracting any energy during the time when power flows out of the facility. It doesn't end up counting lower than zero, but it does count down. However, people discovered that they could flip the device upside down, and rig the system. Then, the meter manufacturers got sophisticated. They built the conventional meters, so that they accumulate kW-hrs in the forward no matter which way power flows. If power flows either direction at any instant, it counts energy forward. For facilities that are given specific permission to backfeed the utility with distributed generation, an approved NET METER needs to be installed.
I remember taking single variable calculus in college. The way that I tried to understand calculus was by thinking rates and total sums. I watched this video, and finally I had been able to see the "Big Picture."
Thankyou for taking your time to do this. I watched this as a final study tool for my calc final and it really helped put all the pieces of calculus together for me.
Some people are discrediting this mans teaching ability. It is very displeasing knowing that public education is a complete joke and most are starving for a professor who can get a point across. This man is a marvelous instructor, and made the subject easily understandable for someone who has never taken a calculus course. P.S. If you cant do better or teach at M.I.T. Shut it!
So I have done David and Gilberts calculus and Linear algebra courses here and for some reason they explain much harder concepts than what I learned in college, in an easier way than my own professors explained it to me. Something about the quality here is different. That is teaching ability. Great videos.
I am your great fan of your lectures on Linear Algebra .It has helped me a lot in Image processing Course. And your book on calculus and Linear Algebra is really appreciable and makes image in the mind of the concerned subject. Thanks a lot for this contribution to mankind.
It`s been said a genius can make something complicated simple. It`s a fool that makes something simple complicated. I like this professor And wish there were lot more like him.
wile richards subjective opinion, but being able to explain things to the lamen is a good skill I must say. Still gives you no right to be an ignorant simpleton.
Teacher's like him should be in each part of world, thus will change the perception of every student that we should not fear the variable x the unknown in mathematics.
Many math teachers are "wicked smart" but not many, in my experience, are good teachers. Prof Strang is not only "wicked smart" but he is funny--in a quirky way. Thanks for the lecture.
Same goes for Walter Lewin's teaching of Physics!
Heck yeah!
Chris Jones That's unfortunate but at least he doesn't emphasize that in his lectures. Im not concerned with his personal ideals of mankind.
Chris Jones Who is racist?
"Wicked smart" was used in Good Will Hunting.
A word of warning: Like many lecture series at MIT, this starts out at a very basic level. There is a good reason for this. You simply must master these simple concepts or you will get lost when things get complicated. Professor Strang is teaching you to think in principles and he is a master at it... If you have any interest in calculus (or just want another shot at it), I urge you to continue to the next lecture. It just gets better and better...
thanks
That is totally true, if you do not learn to understand each topic you handle, you surely fail and become frustrated. The amount of topics you understand(and you know how to use) is inversely proportional to the time you will study in your career.
I've decided to donate MIT OCW, once everything starts to payoff(as i'm still a student), thank you MIT..these lectures solved my biggest mystery!❤
Fuck yeah! calculus the old fashion way. A really smart, qualified teacher and a dusty ass chalkboard with chalk. No overhead projector, no lecture notes, no iPad bullshit. Just straight into the work. Congrats Dr. Strang.
1Smoking Lizard I will share in a "fuck yeah!" with you.
Arlo I'd like to share a thumbs up with you too!!
+1Smoking Lizard fuck yea!!! i dont understand technology so i reject it and act superior fuck yea!!!
teachers like this are slowly dying off
+Richard Gluten Good one. You really showed all those elitists who don't understand how an overhead projector works.
haven't even taken this class yet
and i can actually understand what he's taken about. God bless this man
I ADORE Gilbert Strang. His lectures are an absolute delight.
FINALLY!! Somebody gave a basic summary of how calculus works by showing the whole picture at once, instead of just nonsensical sections at a time!!!
I've been trying to understand how it worked for decades!!!
I only got through trig & pre-calc then life took over & I never had enough time to learn the rest, until now....
:-)
Hi Mr. Strang. Thank you and MIT very much for this video! I'm a mature student, out of school for quite some time. I was really bad with Math in grade school and high school. I'm now in college taking a Business program which involves taking a Microeconomics course. The course uses some fairly basic calculus, but was quite difficult for me. This video really helped me out giving me the "big picture" of it. I feel if I was taught in this manner at a younger age, I would of understood it a lot better. Excellent teaching.
These kinds of videos are why I donate to MIT once in a while
If you're cramming, or in need of a quick crash course, I'd like to give you a small helpful hint: professor Strang's pace becomes quite nice if you speed the video up to 1.25-1.5x :)
I watch him at 4X speed and skip thru so it looks like he is "bampfing" around the screen at super speed lol.
Ish wright UA-cam has only 2x increasing
Is anyone sure this vid wasn't posted at the slower or wrong, speed?
Can you express that in an equation?
Fellow Traveler That's a great suggestion. Thanks. I never would have thought of it.
I just finished Calculus I and needed a good reminder of the larger picture. This was a fantastic summary of the key topics. I'm very grateful for the kind professor's time. Thanks, Professor Strang.
This guy is a great teacher. Thanks for what you're doing!!
Things like this show us what a beautiful thing the internet is.
damn fucking straight
thank you MIT and professor Strang for taking time and teaching such wonderful concepts of calculus.
Professor Strang is one of the many reasons why MIT is the best University in the world. Not just the best in leading technology research but because of teachers like this. I had some physics teachers like him. Professor Lewin comes to mind immediately,Dr. Barrett.... I apply what I learned in your classes to my plastic surgery work now. The simple stuff to be sure; vector calculus and Newtonian physics, yes. Its easy to break new ground in your chosen profession when you leave a place like this. Thank you, MIT, Professors Strang, Lewin , Barrett et al... I am forever indebted to you. Thank you.
I think Dr. Strang speaks more slowly than the average teacher, but I love it. A good teacher is patient and takes the time to explain the steps they're taking in a way that is unlikely to be misinterpreted. Dr. Strang has contributed much to mathematics education, and, like others on here, I am really grateful these videos are available to those of us who were never exposed to calculus prior to college.
I like his chalkboard setup when he raises the board you can still see the previous one on top
This is the weirdest professor I've ever seen. But his introduction is the most heart warming introduction I've ever seen.
I agree ..
@mohittiwari8934 why is he weird? His age makes perhaps a bit awkward but I wouldn't say weird
I wish I could tell this guy how appreciative I am of him doing this. Considering he had no obligation to do it, and these are the kind of videos that I learn the most from. Not just learning formulas and solving 100's of problems, but understanding what they mean and why they are important. Great lecture series.
The fundamental understanding this man posesses of his expert field is beautiful.
I love it.. This guy talks to me and presents the lecture and hand-holds like I am a total idiot in this area; which is exactly what I need, because that makes it easier to fundamentally digest and understand the information and concepts. He lays the foundations perfectly while also avoiding using any technical math jargon that someone may not yet be familiar with before learning calculus. This is one of the best intro lectures I've found and this guy is one of the few profs that actually knows how to TEACH properly and convey information.
You are the best Calculus Teacher i have ever had ! Thanks a lot .
I've been trying to self teach myself calculus for the past couple of days. I've been completely lost in the the jargon used in study the material i've use online. I found this video the "Boom!" my mind was blown. I actually understand everything now. What a difference a great teacher makes.
In less than 38 minutes, he gave me more understanding of Calculus than 3 years of Math class in high school did. You're a gift to mankind, professor Strang. I wish you health.
Little Black sheep has now become Tiger of the Jungle...
Well thank you SO MUCH for putting integration and derivatives into perspective. At the age of 50, I'm coming back to look at Calculus with a zero expectation angle. Integration and derivatives have always seemed a mystical topic - I cracked out an A in University but never really had it explained in a visual relationship between everyday concepts. Your having put the two concepts into relationship between two functions - distance with speed, height with growth, speed with acceleration -- has made ALL the difference as my first foray into revisiting the wonders of science ... I have three boys ... the oldest is 13 ... I want them to genuinely fall in love with science. Thanks to Professor Strang!
Note on the example about trip meters (at about 18:30): I don't know either, but an engineer's answer (or a mechanics answer) would be that trip meters ought to always go forwards regardless of which way you go, since I'm fairly sure the intent is to measure wear on the engine.
Also, if you did make speedometers to measure velocity rather than speed (velocitydometers?), then they'd do it according to a general frame of reference (most likely the earth's surface) rather than which way the car was pointing, so trip meters would just be an approximation of the car's location relative to where you started driving it, not very useful in most circumstances.
This is pretty good. The professor seems to find it a little hard to get his ideas out in plain words, which makes it a little hard to follow the current point at certain times, but his use of many real world examples keeps everything going along pretty smoothly, and his short mental detours are kind of entertaining anyway and show a little human in the teacher without being much of a problem. Thank you for posting this information online for the world to watch for free.
These kinds of videos always have a bit of a bitter sweet taste. Sweet because here you have just a great teacher and MIT is sharing him for free.But how can you not feel bitter that not every teacher is as great as Professor Strang?
sir I am an Indian, right now studying in std 10th but the way u teach is really amazing. it made me realize n understand maths actually from your simple teaching techniques... I really appreciate your work sir...
after i watched this video, my insight is very open because the video Calculus is about change. One function tells how quickly another function is changing. Professor Strang shows how calculus applies to ordinary life situations is very good to give information
Dr. Strang I was so happy to see and listen to you. I am a math enthusiast. you are my star. Thanks
I like how you explain that calculus is the relationship between functions and you show how the function can be represented by other letters other than f and that the variable function can be represented by any letter inside the parentheses. Made a lot of sense. Everything you discuss in this video was helpful and enlightening. Thank you so much.
I know nothing of calculus except basic algebra courses and I understood most of his explanations. True talented teacher he is, shows that it can make or break a student, he makes is seem so common sense
13:23 "You have to let me bring calculus into these lectures" Absolute legend.
This was one of the most lucidly explained calculus lectures I have experienced. Many thanks Prof. Strang!
You have a very nice way of abstraction. I never really understood the logic behind proof for many of calculus rules until I saw your videos.
Thank you very much.
From mannerisms alone, one can tell of the level of dedication to Mathematics this professor has, I think it's amazingly beautiful!!!!
Regarding the trip meter, surely it's correct that it doesn't go backwards because it measures distance (a scalar quantity) not displacement (a vector quantity).
Dominic London We'll forgive him. I think it's poetic licence to get where he wants to go.
+Dominic London and stop calling me Shirley.
+Dominic London
exactly what I was thinking. thanks for your comment, coz I was reconsidering my own understanding of the subject given that he is a MIT lecturer and I assumed he might not had got it wrong, especially because its online on MITcourseware. Doesn't anyone check and edit the material before posting online, or even the editor missed it!
+Michael Harris
I would rather prefer authorities like MIT lecturers try not to get things wrong or messed up, coz people, quite reasonably I think, tend to take everything they say as facts..
+Romin Oli You have a point but I wonder if everything was corrected would the lecture become sterile and boring. I think it would. Using a car was an everyday object, but it’s meter didn't fit the bill exactly. He hesitated as the talked about it going backwards involving us in his thinking process. You see, he taught me through UA-cam and his style to understand calculus where others failed, so I would consider myself nitpicking if I criticized him.
In the movie Ferris Bueller's Day Off, the odometer did not register any change because the odometer measures from the wheels that aren't driven by the engine. That car was a rear-wheel drive car, and the odometer gets its measurements from the front wheels. The front wheels remained stationary, which is why the odometer didn't count anywhere.
They'd have to spin the front wheels by hand, to roll back the miles. That trick could only work on a four wheel drive, that was built before 1960.
Sir, you are doing public service with these lectures and I am so grateful to you. Though I already knew it but still watching these lectures enriched my knowledge now I've learned something I will never forget.
Thonk you.
Last night I was crying because I can't understand calculus,I watched many videos of teachers explains it,but They're explains the mathmatical side only,now is the first time I feel that I'm begaining to understand claculus:")💖
And so excited to do that!
Thank you professor,thank you from all of my heart💜
I attended a course in the university, few years ago, using his book of linear algebra without to listen him like I can do now . He is an excellent teacher
NO ONE BETTER THAN Dr Gilbert Strang explaining this and Linear Algebra .....hes "THE GURU".
The Function is usually in the form of a formula. e.g S (speed) = a.t^2 where a is the acceleration and t is the time.
correct equation is most definately f(t)=1/2 at^2. this is only under 1 dimensional motion with constant acceleration. function 2 is the derivative of function 1, and function 1 is the integral of function 2. you can even test this using the definition of an integral, ∫x^n dx=1/(n+1) x^(n+1), n≠-1
I really like how clear the English language pronounces this teacher: although I hardly know the English language, I understand practically everything he says thanks to the clear and perfect way he speaks English. He is also very good how he clarifyes that is the calculus : it is to calculate the rate or variation at each moment with which a dependent variable varies when it varies an independent variable. Thank you. from Spain. janay
I refer to the derivative with "rate or variation at each moment with which a dependent variable varies when it varies an independent variable", with a mathematical structure similar to that of the tangent (increment of Y divided by increment of X when increment X tends to zero)
For me It takes physics to truly understand calculus. When I took calculus I just memorized what I need to do. I did not know why. When I took physics I finally understood why I did what I did.
same here bro. its like ohhh that's what slope is. ohh that's why we integrate. LOL
can you say what it was in calculus that is a benefit in physics?? ------ I wish both subjects - maths and physics.. had cross - pollinated .. they could have done the same example - from a use in physics ...add that example into teaching/showing calculus : here's how it can be applied
IMO Math is the language for measurements, physics tells the story of how those measurements relate in the wourld surrounding us
I would say the opposite. I understood physics (mechanics and kinematics) much better once I took calculus.
Issac Newton was first a physicist and then a mathematician ❤
Hi Proffessor Strang I've seen this video by the interest of learning calculus,and i like doing maths very much. I'm only 11 and i want to learn calculus .in fact i like doing calculus. i just wanna say that you are a very good teacher of maths and teach calculus very confidently
Shalini calculus at age 11 ? What are u doing currently now??
good you should do that.. im 19 and a freshman in college and im just beginning to really learn it (i took it in high school though), and my sincere advise is to keep learning it will you help you so much more in college if you start younger if you can remember it till you get to college
Consider myself so very fortunate to have free uni. lectures such as this on the internet. Thank you Prof. Strang.
I love you sooooo much Prof. Strang!!! This lecture is illuminating, fascinating, inspiring and amazing! I have finished Prof. Strang Linear Algebra courses, onward to Calculus!
Can't thank you enough Prof. Strang, you are changing people's lives. What a great gift to humanity!
Can I just say how perfect that chalk writes.
..see the other MIT videos; isn't it amazing that MIT still uses these traditional blackboards and chalk instead of the "more modern" white boards or - GASP! - the hated PowerPoint slide.
Somehow reassuring.
Wabi Sabi using powerpoints is a serious crime and the person who does that is a criminal with power points there's no interaction no conversation no humanity It's a sin
Ivy League chalk designed by MIT material science engineers!
70$ a stick!
Wabi Sabi. He is experienced person. And must be using chalk for many years 😊
Prof. Strang is the best math instructor I have ever seen. You should see him do matrices for computer science.
I visited courses on an actually very well reputational university, but they never teach you the basics ... they always go right into the guts and details, and you wonder why you are even here, watching all those details. When watching videos like these i sometimes wonder if it is not intentional dumb keeping. Well, let's praise the internet, and foremost, let's praise MIT opencoursware and Gilbert Strang for these amazing things we are able to witness right now! I am truly blessed to live in these times, where information is so freely available.
Let it be known that it was Gilbert Strang that dumbed down the concept of calculus enough for me to FINALLY understand. I love you man
Thank you for posting this to try to help people understand. I've been out of school for a while, so this is helpful. I always appreciate when people are generous with their knowledge.
I adore this man! Thank you so much for your generosity and thoughtfulness in putting this lecture series together, it's really a pleasure to see.
2:53 I've never heard anyone referring to f as how far LMFAO. I love this guy
I spent the last hour trying to learn calculus via youtube and they were all so broad and tedious. I thank you for this video, it was very cohesive.
Passionate teachers like this make all the difference in getting a quality education
Good God.. I love this guy. The second he started talking, I had just the best feelings from him =)
Thank you Mr strang for this eye opener course on "what is calculus" that I finally and at once got it, at the age of 70+ 😁. Your lucid explanations drove it home to me that it is essentially about function of functions & their inter-relations. Thanks agn!
I enjoyed this lecture very much, but I believe the graph represents displacement rather that distance. As distance would increase when you were going forward and backward (17:25), but displacement would not.
This is truly one of the best lectures I have ever listened to. I got the insight of calculus and laughed a lot.
at 34:30 he states that speed = acceleration multiplied by time; however acceleration = speed squared and the area under the line cannot be one half times speed squared times time squared. The area is one half times speed times time. Something doesn't add up here ...
What I am saying is that he appears to have put distance where speed should be and vice versa ... because distance = speed times time. Thus the right graph would be meters per second and the left graph would be acceleration with meters per second per second. He has the calculus right but, named his y axes wrong; he has them swapped.
i wish, i had a lecturer like him back then... he made it look easy to grasp calculus.
calculus is the science of determining or calculating change as much as possible
examples : exchange rate, weather forecasting, ....etc
Dear Mr. Gilbert!! you are a Magician to put it in simple terms. Glad to have these videos and Thanks a lot .
This lecture is the best lecture about calculus in my opinion. So clear and easy to understand, thanks
What a great lecture.
The kind of teacher everyone needs but no one deserves.
the readon a speedometer doesnt have negatives because if you have a moving object then there is speed
Thank you, Dr. Strang, for your dedication to the sciences. I believe it is essential to have an educated populace, and for the cost of an internet connection and a laptop computer, we the people are able to do such a thing at an affordable cost. This would not be possible without dedicated professionals...for that, I bestow upon you the award of super-awesome professor of the year.
hahaha "actually what do i know? you're long when you're born but as soon as you can stand up you're tall." hahah I love this guy
Hold on solving for at, d which he put in would have to equal 2...which is being multiplied by f/t. Got it now. it could also read 2(f/t)=at. or 2f/2t=at.
didnt get into mit...never mind ...guys like these are making it up for you....god bless mit....
Great old school teaching from the Prof clear visual concepts helped me to grasp a deeper understanding and meaning behind what was just memorised gibberish glyphs back in school - thanks
Thanks Professor Strang, MIT and You Tube for this video. It isn't easy breaking laymen into the field of calculus, but at least he makes it interesting, with the sparkle of hope we can understand why calculus is so important in its applications, and more importantly, how to (eventually, as I am a newcomer to this field) use it.
If speed is a matter of the change in distance over the change in time, then even though we cannot have time changing as a negative (decreasing), we can still have distance changing as a negative, thereby making the speed negative.
How can somebody dislike an excellent MIT Professor giving for FREE such a lesson?! This world is very wrong!
What a nice gentleman and good human being. I’m so grateful to have found this video!
I failed calculus the first time I took it because I got a bad teacher. When I got a good one it was so easy to learn. It just seems so easy once you really understand it. Every college student should learn it. If you put in the time anyone can learn it.
Study from Gavesh Bharadwaj sir. GOD of Maths but it's in Hindi
You are correct as long as you are defining speed as the absolute value of velocity. I think he is using the word "speed" loosely in this video because those being introduced to calculus are probably not as familiar with the concept of velocity.
That's my point. In the video(17:42 to 18:03) he says speed is negative. I am asking what he means by negative speed.
I'm watching this before learning any calculus, and it seems like it will be helpful to understand what I'll be getting into. Thanks
In a car what’s important is the magnitude, or the absolute value, of the milagre |x| and not the direction or the sign; which in turn is the measure of how much a car has been used (be it in the forward or the reverse direction). In other words, if the wheels are turning, you’re putting mileage on the car, regardless of the direction. When it comes to a car, in fact, you can’t look at the algebraic sum of the mileage (in the forward or reverse directions) but the overall magnitude of the mileage that’s been put on the car. If you use calculus, in this particular example, you’re either fooling yourself, or else cheating a potential buyer, with regards to the total number of miles (the absolute value) that the car has being utilized.
My idea regarding calculus enhanced dramatic. I am self learner who is fond of maths and physics and I have been learning a lot from professor Strang.
Gilbert is amazing. I remember one course i took where my professor was so bad. He could write two boards full of math and end up with 2=1 haha. I had to stop going to his lectures. It just so happened that all the topics we read were in a course gilbert taught that was available on youtube. I passed the test even though english is a foreign language to me.
This guy gave me a wonderful, fundamental explanation of calculus. He is also very hilarious, so it keeps you mentally focused.
Actual professor or not I absolutely loved listening to him. This was excellent.
19:45 - This also becomes an interesting issue with utility meters.
If you build an electrical meter without thinking about this issue, it is bidirectional and measures the net energy consumed, subtracting any energy during the time when power flows out of the facility. It doesn't end up counting lower than zero, but it does count down. However, people discovered that they could flip the device upside down, and rig the system.
Then, the meter manufacturers got sophisticated. They built the conventional meters, so that they accumulate kW-hrs in the forward no matter which way power flows. If power flows either direction at any instant, it counts energy forward.
For facilities that are given specific permission to backfeed the utility with distributed generation, an approved NET METER needs to be installed.
I remember taking single variable calculus in college. The way that I tried to understand calculus was by thinking rates and total sums. I watched this video, and finally I had been able to see the "Big Picture."
Thankyou for taking your time to do this. I watched this as a final study tool for my calc final and it really helped put all the pieces of calculus together for me.
Some people are discrediting this mans teaching ability. It is very displeasing knowing that public education is a complete joke and most are starving for a professor who can get a point across. This man is a marvelous instructor, and made the subject easily understandable for someone who has never taken a calculus course. P.S. If you cant do better or teach at M.I.T. Shut it!
Thank you so much for taking time out of your schedule to make this for curious minds everywhere.
So I have done David and Gilberts calculus and Linear algebra courses here and for some reason they explain much harder concepts than what I learned in college, in an easier way than my own professors explained it to me. Something about the quality here is different. That is teaching ability. Great videos.
I am your great fan of your lectures on Linear Algebra .It has helped me a lot in Image processing Course. And your book on calculus and Linear Algebra is really appreciable and makes image in the mind of the concerned subject.
Thanks a lot for this contribution to mankind.
Did you see the dedication at 7:22 to make a straight line as much as straight.. this needs we all :)
It`s been said a genius can make something complicated simple. It`s a fool that makes something simple complicated. I like this professor And wish there were lot more like him.
wile richards subjective opinion, but being able to explain things to the lamen is a good skill I must say. Still gives you no right to be an ignorant simpleton.
Great lecture, Dr. Strang!
34:36 it might be important to emphasize that L is 0 at t=0 when considering f as the area under s(t) curve.
Teacher's like him should be in each part of world, thus will change the perception of every student that we should not fear the variable x the unknown in mathematics.
i dont have the words to express the joy i had when i watched this video..thank you sir your lecture really helps me see the bigger picture.