Big Picture of Calculus

[@dr.reidsheftalltruthinscie2007]

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...

[@johnnycockatoo1003]

thanks

[@gaussiano]

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.

[@SantoshvasaTB]

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!❤

[@mikesimone1]

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.

[@aasthabanerjee9899]

Same goes for Walter Lewin's teaching of Physics!

[@rancegarrett3696]

Heck yeah!

[@rancegarrett3696]

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.

[@gaurav.raj.mishra]

Chris Jones Who is racist?

[@chessandmathguy]

"Wicked smart" was used in Good Will Hunting.

[@blaby4ever]

haven't even taken this class yet and i can actually understand what he's taken about. God bless this man

[@1SmokingLizard]

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.

[@SilverArro]

1Smoking Lizard I will share in a "fuck yeah!" with you.

[@1SmokingLizard]

Arlo I'd like to share a thumbs up with you too!!

[@787310]

+1Smoking Lizard fuck yea!!! i dont understand technology so i reject it and act superior fuck yea!!!

[@stocks4bt]

teachers like this are slowly dying off

[@darrenringer9811]

+Richard Gluten Good one. You really showed all those elitists who don't understand how an overhead projector works.

[@soadtoxicity12]

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.

[@RetinnaBell1]

I ADORE Gilbert Strang. His lectures are an absolute delight.

[@upmperthay]

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.... :-)

[@JohnStrikwerda]

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.

[@k7iq]

These kinds of videos are why I donate to MIT once in a while

[@LouisHong97]

This is the weirdest professor I've ever seen. But his introduction is the most heart warming introduction I've ever seen.

[@mohittiwari8934]

I agree ..

[@7yep4336dfgvvh]

​@mohittiwari8934 why is he weird? His age makes perhaps a bit awkward but I wouldn't say weird

[@sandeepgrover395]

thank you MIT and professor Strang for taking time and teaching such wonderful concepts of calculus.

[@Endisupertramp]

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 :)

[@fluxpistol3608]

I watch him at 4X speed and skip thru so it looks like he is "bampfing" around the screen at super speed lol.

[@JoffreyB]

Ish wright KZbin has only 2x increasing

[@TheBman13298]

Is anyone sure this vid wasn't posted at the slower or wrong, speed?

[@i.p.knightly149]

Can you express that in an equation?

[@baruchben-david4196]

Fellow Traveler That's a great suggestion. Thanks. I never would have thought of it.

[@jeffreygong6678]

This guy is a great teacher. Thanks for what you're doing!!

[@dr.reidsheftalltruthinscie2007]

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.

[@BlindPacemaker]

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.

[@theultimatenewplayer9341]

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.

[@speedgaming8131]

The fundamental understanding this man posesses of his expert field is beautiful.

[@mattgriffiths59]

Things like this show us what a beautiful thing the internet is.

damn fucking straight

[@Dlsspfldyt]

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.

[@enzymatic1]

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.

[@selim8611]

I like his chalkboard setup when he raises the board you can still see the previous one on top

[@LittleBlacksheep1995]

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.

[@Fjfcjcfjfjccjcjjkf]

Little Black sheep has now become Tiger of the Jungle...

[@mtdeezy]

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.

[@chelleweatherspoon2226]

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.

[@jeffchapman8992]

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!

[@2009worstyearever]

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?

[@kazifarzin5037]

You are the best Calculus Teacher i have ever had ! Thanks a lot .

[@ebrahimalfardan8823]

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.

[@flow2004]

Dr. Strang I was so happy to see and listen to you. I am a math enthusiast. you are my star. Thanks

[@masterduff]

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

[@paradigmshift03]

This was one of the most lucidly explained calculus lectures I have experienced. Many thanks Prof. Strang!

[@LateNightViddys]

What a great lecture. The kind of teacher everyone needs but no one deserves.

[@mohammadalkousa2856]

Great! Connected to the integral calculus, recently it was published a book about MIT integration bee, under the title " MIT Integration Bee, Solutions of Qualifying Tests from 2010 to 2023" You can simply find it!

[@WRATH9636]

Consider myself so very fortunate to have free uni. lectures such as this on the internet. Thank you Prof. Strang.

[@supersnowva6717]

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!

[@Bobxchen333]

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.

[@jayluvlogs9154]

same here bro. its like ohhh that's what slope is. ohh that's why we integrate. LOL

[@johnnycockatoo1003]

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

[@nicolasortiz2638]

IMO Math is the language for measurements, physics tells the story of how those measurements relate in the wourld surrounding us

[@sanjaygandhi7962]

I would say the opposite. I understood physics (mechanics and kinematics) much better once I took calculus.

[@Fjfcjcfjfjccjcjjkf]

Issac Newton was first a physicist and then a mathematician ❤

[@shalinisharma1977]

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

[@Fjfcjcfjfjccjcjjkf]

Shalini calculus at age 11 ? What are u doing currently now??

[@raghu45]

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!

[@rsplenum]

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.

[@toqa002]

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💜

[@nehasingh8179]

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...

[@kemalunal4776]

This is truly one of the best lectures I have ever listened to. I got the insight of calculus and laughed a lot.

[@marcousosewelle5501]

13:23 "You have to let me bring calculus into these lectures" Absolute legend.

[@mariepi]

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

[@mariepi]

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)

[@artc8281]

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.

[@524megan]

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.

[@jamespotts8197]

From mannerisms alone, one can tell of the level of dedication to Mathematics this professor has, I think it's amazingly beautiful!!!!

[@ndipagbor7280]

You learn at least two things from this lecture, Calculus and patience.

[@Fjfcjcfjfjccjcjjkf]

You will learn calculus and patience when u complete the whole series

[@Matthew-zc8qt]

What a nice gentleman and good human being. I’m so grateful to have found this video!

[@cyanide4u539]

Dear Mr. Gilbert!! you are a Magician to put it in simple terms. Glad to have these videos and Thanks a lot .

[@imegatrone]

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

[@wabisabi9427]

Can I just say how perfect that chalk writes.

[@warplanner8852]

..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.

[@zuesr3277]

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

[@stardaggerrihannsu2363]

Ivy League chalk designed by MIT material science engineers! 70$ a stick!

[@JayTheMachine]

Wabi Sabi. He is experienced person. And must be using chalk for many years 😊

[@foreverxundefined]

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.

[@raymie17]

i wish, i had a lecturer like him back then... he made it look easy to grasp calculus.

[@mssr1965]

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

[@soupisready619]

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.

[@brucewayne3141]

2:53 I've never heard anyone referring to f as how far LMFAO. I love this guy

[@denverfan141191]

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.

[@bluddysoul]

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

[@carultch]

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.

[@DominicLondon]

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).

[@MichaelHarrisIreland]

Dominic London We'll forgive him. I think it's poetic licence to get where he wants to go.

[@richsmith4884]

+Dominic London and stop calling me Shirley.

[@rominoli3909]

+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!

[@rominoli3909]

+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..

[@MichaelHarrisIreland]

+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 KZbin and his style to understand calculus where others failed, so I would consider myself nitpicking if I criticized him.

[@AlexanderRM1000]

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.

[@arianawaller3454]

This guy gave me a wonderful, fundamental explanation of calculus. He is also very hilarious, so it keeps you mentally focused.

[@16yearoldwhiteboy]

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

[@Phillyfast]

Really happy I came across these videos. I'm a college student majoring in computer science that has yet to ever take a calculus course. The last math course I took was the precalculus algebra and trigonometry sequence. These videos that Professor Strang and MIT OCW put up really makes me less nervous about the calculus I'm going to have to take in the future. Cheers!

[@nekojindes]

+Brian Fassbender You're very lucky! I managed to go through my whole Computer Science degree a decade ago with only a superficial understanding of calculus without understanding the context of it all.

[@esepecesito]

How can somebody dislike an excellent MIT Professor giving for FREE such a lesson?! This world is very wrong!

[@MisterBinx]

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.

[@Fjfcjcfjfjccjcjjkf]

Study from Gavesh Bharadwaj sir. GOD of Maths but it's in Hindi

[@novigreg]

I got C score on Calculus about 17 years ago. And just understood the fundamental of Calculus by watching this. Lol. Its never too late to fix the failure. 💪 Thank you so much.

[@Fjfcjcfjfjccjcjjkf]

Return of calculus. Hats off to ur perseverance for 12 years wait🎉

[@larseriksson1184]

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.

[@THEQuantumPolkaDots]

Actual professor or not I absolutely loved listening to him. This was excellent.

[@rh-uv5gu]

Thank you kind sir. I'm a busy single mom with a very good overall GPA, but I'm struggling in my online calculus class and am worried at how behind I feel. Thank you for making calculus feel less overwhelming.

[@Fjfcjcfjfjccjcjjkf]

Why a single mom would study Calculus?? Logic??

[@joeimbesi99]

NO ONE BETTER THAN Dr Gilbert Strang explaining this and Linear Algebra .....hes "THE GURU".

[@thomasjurgy]

Thank you so much for taking time out of your schedule to make this for curious minds everywhere.

[@lyminhtien7526]

This lecture is the best lecture about calculus in my opinion. So clear and easy to understand, thanks

[@AbrahamMaliktauseef]

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.

[@anthonyegboh8825]

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

[@TheRealMake-Make]

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.

[@wesdouglas6061]

I love this guy! I just learned in fifteen minutes what would have probably taken in a classroom a month at an hour a day, including time to class, and time in traveling..

[@Fjfcjcfjfjccjcjjkf]

Bro why you didn't complete the video. Why only 15 mins??

[@remembertedcruz7213]

Passionate teachers like this make all the difference in getting a quality education

[@jvicinip]

Thank you very much Professor Strang for so generously sharing your knowledge. I wish I had been taught calculus years ago just like you have done.

[@MelgMike53]

Good God.. I love this guy. The second he started talking, I had just the best feelings from him =)

[@NikhilSharma-pc3ot]

didnt get into mit...never mind ...guys like these are making it up for you....god bless mit....

[@mattgrossmann8599]

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

[@urbansilhouettemedia]

Prof. Strang is the best math instructor I have ever seen. You should see him do matrices for computer science.

[@deepakbellur9676]

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.

[@fernandogallardo3477]

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."

[@bohubrihiuk2]

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.

[@kururugisuzaku9199]

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.

[@givenlukwesa2688]

Wow great teacher you are Prof. Strang....I have really learnt a lot from this video...Thumbs up MIT for making this video public...Am gonna watch all of them....

[@medomedomed3609]

calculus is the science of determining or calculating change as much as possible examples : exchange rate, weather forecasting, ....etc

[@gregorybattis9588]

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.

[@dwiprasetyaputra221]

I was chuckling at "I don't mean slowing down with the chalk". Thank you Mr. Strang

[@MrIgor20011]

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.

[@Ztingjammer]

Thank you so much Professor Gilbert Strang and MIT. This was explained beautifully so I now understand the concepts better. Will watch more videos with him here. The open courseware here and Khan Academy is really lovely. Liking mathematics more and more as time goes on thanks to videos like this.

[@aussieaddict122]

This guy really loves his job. Great video. I'm a really big math nerd. I'm only in AP Calc 1, but I just love math. It's art. And I really enjoyed listening to this guy. Great vid.

[@andrewrufo2421]

Thanks for sorting out the important things. And for clarifying the language.

[@xtimrs]

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

[@encellon]

I'm a geezer, though also a 2nd-yr grad student in geology who took math classes so long ago that I may as well never have taken calculus. I actually remember algebra, but calculus was never really there to lose. Considering how geophysics is mostly equations, I'm feeling better as Dr Strang explains the basics. Many thanks for this video series!

[@philipmartensson4299]

Superb lecture. Altough I have to point out that we cannot have a negative speed since it only have magnitude and not direction. Velocity, on the other hand, is a vector quantity which means that it has both a magnitude and a direction.

[@trumanhw]

Meh, a negative correlates to our common sense of a vantage point, preference or special case. When cars brake we know they're accelerating backwards, but it's a different pedal which to our worlds deserves conditional notation.

[@rushikesh8132]

Understood Concepts of Physics and Calculus with this session ! WOW !