Big Picture: Integrals

แชร์
ฝัง
  • เผยแพร่เมื่อ 23 ธ.ค. 2024

ความคิดเห็น • 180

  • @thegreencascade
    @thegreencascade 12 ปีที่แล้ว +17

    This series has been great for reteaching myself the Calculus I have forgotten before the next college term starts. In my past classes, the professor could never explain what dy/dx meant, or why dx was found after the function behind the integration symbol. I finally fully understand the notation. Thank you.

  • @gregorybattis9588
    @gregorybattis9588 3 ปีที่แล้ว +15

    This guy teaches difficult topics like no other. No wonder MIT has the greatest. The difference between him and my high school math teachers is astonishing. Thank you MIT and Dr Strang.

  • @Antrikxh
    @Antrikxh 8 ปีที่แล้ว +98

    I knew the formulas and how to solve questions in Calculus. But for the first time I am able to visualize it and truly understand it. Thank you, Prof. Strang.

    • @forthrightgambitia1032
      @forthrightgambitia1032 4 ปีที่แล้ว +2

      And it's a shame few know it intuitively like this. Calculus is one of the most beautiful discoveries in human history, and it's not even that hard to understand and yet gives so much explanatory power to things you see around you.

  • @jamescotton9710
    @jamescotton9710 7 ปีที่แล้ว +4

    Decided to watch these as a "refresher" since it has been years since I used any calculus...He does a great job explaining it, and he has an enthusiastic personality, which made it seem a lot less dry. I wish I had instructors like this when I was an undergrad...

  • @Ana-wq6nv
    @Ana-wq6nv 6 ปีที่แล้ว +17

    i can't express with words how grateful I am about this class! Thanks from Brazil!

  • @sophiestrang6737
    @sophiestrang6737 9 ปีที่แล้ว +277

    I love you, grandpa

    • @yusifsadiqov5004
      @yusifsadiqov5004 9 ปีที่แล้ว +3

      +sophie strang :D

    • @ch.ajaysingh
      @ch.ajaysingh 8 ปีที่แล้ว +5

      +sophie strang :) same here

    • @alfonshomac
      @alfonshomac 8 ปีที่แล้ว +9

      Such a rockstar.

    • @EliotMcLellan
      @EliotMcLellan 6 ปีที่แล้ว +2

      LOL STOP LYING ;0

    • @EUMmusic
      @EUMmusic 4 ปีที่แล้ว +1

      Awww this is so lovely

  • @BrianFoster-ji9fp
    @BrianFoster-ji9fp หลายเดือนก่อน

    Absolutely love everything this teacher has to offer. My abiding gratitude to all who made this possible for me to learn.

  • @tonycmac
    @tonycmac 8 ปีที่แล้ว +4

    I've taken calc courses at UMD, even gotten good grades. This explanation sheds light on the ONE thing I never got - WHY calc works. Wonderful lecture!

  • @chriscollins4047
    @chriscollins4047 10 ปีที่แล้ว +7

    I actually understand why integrals work now thanks to this guy! if you want to understand why integration finds the area under a curve, watch this video.

  • @FordBurden
    @FordBurden 12 ปีที่แล้ว +2

    Thank you Professor Strang. I hope you read these comments. You are very much appreciated.

  • @anonymous.youtuber
    @anonymous.youtuber 3 ปีที่แล้ว +5

    Just magnificent ! It takes a true genius to explain something like that in a way you gain deeper insight.

  • @rounaksodhi8399
    @rounaksodhi8399 3 ปีที่แล้ว +1

    Prof. Strang u are just amazing .....Me a student of class 12th could for the first time visualize all of this so well .... I can't thank u enough....This was truly very interesting lecture and because of u it seemed so easy.....

  • @moseshall9428
    @moseshall9428 9 ปีที่แล้ว +8

    IF ONLY I had seen this video in 1988, I might have gotten > a C in Calculus 101! Beautiful. The whole connection with area has always mystified me.

  • @wistfulthinker8801
    @wistfulthinker8801 5 หลายเดือนก่อน

    this man is a wonderful teacher. I love watching him on things I thought I already new. I wish there was an algebra 1 he did so I could show my son.

  • @sarojpandeya9762
    @sarojpandeya9762 5 ปีที่แล้ว +1

    Thank you very much to our old math guru. We are very much fortunate to get your ideas.

  • @TXSTIGG
    @TXSTIGG 8 ปีที่แล้ว +38

    I got A's in both calculus 1 and calc 2 and yet I did not know the basic concepts behind the math until now. Public Texas Universities for you....

    • @TadasG258
      @TadasG258 5 ปีที่แล้ว +1

      Don't you have theory exams?

    • @Sol-gl3nl
      @Sol-gl3nl 4 ปีที่แล้ว +1

      @@TadasG258 understanding why the rules exist is different from just memmorizing the rules

    • @axlrose5082
      @axlrose5082 4 ปีที่แล้ว

      @@Sol-gl3nl But you can't pass a theory exam if you just memorize the content...

    • @freeeagle6074
      @freeeagle6074 4 ปีที่แล้ว

      Sol the

  • @georgesadler7830
    @georgesadler7830 3 ปีที่แล้ว +2

    DR. Strang thank you for another solid lecture on integrals.

  • @longdragon3
    @longdragon3 12 ปีที่แล้ว

    exposition is outstanding! this is how math ought to be taught. Thank you to all who played part in the production of educational such as this one.

  • @matinhewing1
    @matinhewing1 6 ปีที่แล้ว +14

    Prof strang is a god amongst men...

  • @mohamedradwan388
    @mohamedradwan388 9 ปีที่แล้ว +11

    I think I would have saved a lot of time and effort in my research, if Dr Strang was my lecturer in university.

  • @Mike-ks6qu
    @Mike-ks6qu 10 ปีที่แล้ว +7

    Love his lectures, just read that he was a Rhodes scholar, very impressive. I hope to be 1/2 as good as whatever it is I do as he is with teaching and mathematics.

  • @srinathtk86
    @srinathtk86 4 ปีที่แล้ว +1

    Prof. Strang ... awesome 👏 will be indebted to you forever

  • @nirajabcd
    @nirajabcd 5 ปีที่แล้ว

    Thank you internet! This is the best time to live if you are yearning for knowledge. Thank you Professor Strang and MIT.

  • @GabrielaaCOLOMBIANA
    @GabrielaaCOLOMBIANA 11 ปีที่แล้ว +1

    Thank you very much Professor!
    We are all sheerly grateful for your work!

  • @warnexus
    @warnexus 12 ปีที่แล้ว +1

    I love your explanation on derivatives. It was a good refresher and a nice mind exercise. Thanks for your time and energy.

  • @maximliu
    @maximliu 14 ปีที่แล้ว +1

    Good lecture and terrific idea on giving a big picture on the topic. We are sometimes sink too deep in the bolts and nuts of the areas and lost the overview and forget why we are there...
    Hope there will be more lectures...

  • @hassanouanir6107
    @hassanouanir6107 10 ปีที่แล้ว +1

    Very good explanation professor! I have studied this integral part of calculus in a different way... Now I got a good picture of where this all came from. Thanks professor and all MIT people

  • @avivon100
    @avivon100 12 ปีที่แล้ว +1

    i love this kind of teaching suddenly things are crystal claer and make sense from the beginning.... great math
    this is how the real father of math , thought about math.
    other make it too complex and in the end it doesnt make sense so the student have to memorize and not really understand.

  • @feynmanaruda8063
    @feynmanaruda8063 2 ปีที่แล้ว

    This explanation is a piece of art.

  • @justinwu3574
    @justinwu3574 4 ปีที่แล้ว +4

    One day I will get into MIT and tell him how thankful I am in person. He is just amazing.

  • @RafaelMANJI
    @RafaelMANJI 14 ปีที่แล้ว

    here in Brazil, we learn it in college.
    high school stops at derivades, and, most part of schools dont reach neither limits.

  • @eleonoraformatoneeszczepan8807
    @eleonoraformatoneeszczepan8807 3 ปีที่แล้ว

    Big thank you Professor Strang and MIT OpenCourseWare, from Australia.

  • @lucas_vasconcelos
    @lucas_vasconcelos 10 ปีที่แล้ว +5

    the best video about integral

  • @fierydino9402
    @fierydino9402 2 ปีที่แล้ว +1

    This lecture is soooo precious😀 Thank you professor and OCW!

  • @inquisitive871
    @inquisitive871 8 ปีที่แล้ว +4

    Holy shit. So basically, delta X is the base, and the height is the slope. The sum of these areas gives you the area in the aggregate.

    • @MarkMcDaniel
      @MarkMcDaniel 6 ปีที่แล้ว

      inquisitive871 -- delta y is the height and delta x is the run of the slope, which is the ratio that comprises the derivative. The definite integral is the area of the function between two points.

  • @30secondstolive
    @30secondstolive 14 ปีที่แล้ว

    @MasterDemon25 the audience is high school students, so yeah, it should be for 16 year olds... check the description of the course

  • @carlosalbertocuadros5469
    @carlosalbertocuadros5469 2 ปีที่แล้ว +1

    Good Job Professor

  • @YorangeJuice
    @YorangeJuice 2 ปีที่แล้ว

    i liked seeing where ylast-yfirst comes from that was really insightful

  • @hemm2333
    @hemm2333 2 ปีที่แล้ว

    This is why MIT is different. You focus on understanding the idea rather than memorise and solve

  • @Amine-gz7gq
    @Amine-gz7gq 2 ปีที่แล้ว

    I wish I had a teacher like him. Education in my country is not expensive like in the US but the quality is poor, we have to learn by heart without understanding and it is a torture for me (I'm not a sheep). Using the differences between the numbers in a series is key to better understanding Calculus, if you want to understand Taylor series, think about the differences of the differences of the differences and how they can help you find the next number in a series.

  • @NothingMaster
    @NothingMaster 4 ปีที่แล้ว

    This is all so incredibly easy. Then again, not many schools have a Strang-caliber faculty member on hand to predigest the subject and turn it into a child’s game.

    • @ankeunruh7364
      @ankeunruh7364 3 ปีที่แล้ว +1

      Is it really easy? You need to know something about coordinate systems, the zero, geometry basics; adding, multiplying, powers, brackets; using characters of different alfabets, their meanings in math, and basics of algebra (equations without numbers)...

    • @semicolumnn
      @semicolumnn 3 ปีที่แล้ว

      @@ankeunruh7364 Yea?? most singlevariable calculus deals with the cartesian plane. it is so basic that a 5th grader could come up with it if they wanted a coordinate system. using characters of different alphabets? by singlevariable calculus, the only greek letters I used was pi and theta.. basics of algebra arent hard, and no they're not "equations without numbers" they just represent a certain function to numbers (in the case of an integral)

  • @kenbob1071
    @kenbob1071 3 ปีที่แล้ว

    Dividing up the area under the curve with rectangles is the conventional teaching method, but judging from the comments, you'd think it was some miracle insight that no other teachers had thought of explaining...lol.

  • @edsonmacedo7188
    @edsonmacedo7188 11 ปีที่แล้ว

    great job professor we in Brzil apreciate your hard work.

  • @cocosn79
    @cocosn79 4 ปีที่แล้ว

    Great presentation, never been better explain!

  • @DYoung2112
    @DYoung2112 11 ปีที่แล้ว

    Thx to MIT and the Proffessor for posting this.

  • @user-ny1vt3ek4i
    @user-ny1vt3ek4i 7 ปีที่แล้ว +1

    Thank you MIT!!! Thank you Lord Foundation!!

    • @Hi-6969
      @Hi-6969 3 ปีที่แล้ว

      you forgot to thank the prof., Gilbert Strang

  • @Captnmolywop
    @Captnmolywop 10 ปีที่แล้ว

    Thank you Professor Strang and MIT. My summer college calculus taecher is giving us definitions, equations, and then practice problems. I had difficulty seeing the entirety of the integral idea.

  • @nocomment2477
    @nocomment2477 3 ปีที่แล้ว

    You're absolutely brilliant.

  • @musa78692
    @musa78692 14 ปีที่แล้ว

    @HamiAlDiar
    What he is saying in arabic is that we wish to benefit from these amaizing lectures in the Arab world especially

  • @sulfrum
    @sulfrum 14 ปีที่แล้ว

    Thanks for your really good work. We all need more...

  • @gianpieromattei9357
    @gianpieromattei9357 4 ปีที่แล้ว +1

    Many thanks.... a genius, an artist of math...

  • @lunardust201
    @lunardust201 7 ปีที่แล้ว +2

    Bah...get to 33:32 and I still don't see how to actually *perform* the limit. We jump right to guessing the derivative..

    • @chehboubimededdine6746
      @chehboubimededdine6746 7 ปีที่แล้ว

      that's what really fucked my mind , 1 hour and in the end we are back at guessing the fucking derivative.

    • @chehboubimededdine6746
      @chehboubimededdine6746 7 ปีที่แล้ว

      I have to say , i get it now.

    • @gdaaps
      @gdaaps 6 ปีที่แล้ว

      Yes, you kind of guess and you show you're right by doing the derivative back to get the integral argument

  • @angminhnguyen8221
    @angminhnguyen8221 7 ปีที่แล้ว

    even i have learnt all of these things that prof delivers in this lecture, it's still an interesting lecture :) thanks sir

  • @saketkumar5167
    @saketkumar5167 4 ปีที่แล้ว

    Beautiful courses

  • @30secondstolive
    @30secondstolive 14 ปีที่แล้ว

    @aramian21 indeed... the applications to social sciences are remarkable too...

  • @l1mmg0t
    @l1mmg0t 11 ปีที่แล้ว

    good professor. I wish there were TH-cam 40 years ago when I took differential eq. course

  • @berenjervin
    @berenjervin 6 ปีที่แล้ว

    A much better approach is to show the ideas behind derivatives and integrals as separate concepts, THEN prove they are inverses of each other. Faster, and most straightforward, AND lays the ground work for other things like numerical methods.

  • @jurisicdjina
    @jurisicdjina 8 ปีที่แล้ว

    Very clear presentation, realy great!

  • @PotatoMan1491
    @PotatoMan1491 7 ปีที่แล้ว

    I really like this professor.

  • @hemungkapoor2000
    @hemungkapoor2000 4 ปีที่แล้ว

    Thank you so much MIT❤️

  • @Waranle
    @Waranle 14 ปีที่แล้ว +1

    @gerardrbain1972 gerardrbain the question is which high school did you go to lol, this is high school math, this is basic calculus!

  • @BMGBOX
    @BMGBOX ปีที่แล้ว

    Dr. Strang is a Wonder of Nature and the best teacher ever ! He simplifies the complex as no other person can.

  • @datpham31415
    @datpham31415 6 ปีที่แล้ว +1

    Great lecture. 👍🏼

  • @kaoseda1886
    @kaoseda1886 4 ปีที่แล้ว

    I do love MIT.

  • @gizemozkabak6519
    @gizemozkabak6519 ปีที่แล้ว

    He is so good to be true!

  • @Springleriffy
    @Springleriffy 12 ปีที่แล้ว

    EXACTLY how it should be, the method is a million times more important than the result, and some results such as simple equations and basic math become memory recall anyway

  • @ekhliousful
    @ekhliousful 7 ปีที่แล้ว

    if i have a problem set of two functions & i have to determine one from the other how do i know which is function 1 & which is function 2 which will be the derivative & which is the integral is there kind of rule to know that?

  • @adityaear
    @adityaear 12 ปีที่แล้ว

    instrumen apa yang bapak mainkan? What's musical instrument did you played yesterday, Sir?

  • @gerardrbain1972
    @gerardrbain1972 14 ปีที่แล้ว

    @MasterDemon25 you learned intergral calculus in high school? Which country did you go to high school?

  • @lisinka3
    @lisinka3 14 ปีที่แล้ว

    I wish MIT had video lectures on more math topics.

  • @dataskin
    @dataskin 9 ปีที่แล้ว

    Brilliant lecture.

  • @shreyasaxena6653
    @shreyasaxena6653 6 ปีที่แล้ว

    Amazing Explanation

  • @LaRoJita
    @LaRoJita 10 ปีที่แล้ว

    Thank You Professor! Last time I saw this was in 2003!

  • @Aa11qq
    @Aa11qq 7 ปีที่แล้ว +5

    I wish my teacher taught like this... My teacher uses power points and it's horrible. I have to see how the problem is solved without steps being skipped.

    • @fragyfraginston9430
      @fragyfraginston9430 7 ปีที่แล้ว

      Edi IKR?!,Like good god i wanna see you solve the Eq and go step by step

  • @spatalay
    @spatalay 14 ปีที่แล้ว

    Thanks for the effort Sir!

  • @dreee9700
    @dreee9700 5 ปีที่แล้ว

    this guy is genius af

  • @gerardrbain1972
    @gerardrbain1972 14 ปีที่แล้ว

    @themanisheab180237ce I went to a catholic high school in the W.I. When I took my G.C.E's I only did o-level math. I guess I should have taken a-level math instead: since the first time I encountered intergral calculus was at college.

  • @saifrehman7699
    @saifrehman7699 6 ปีที่แล้ว

    Sir what is use of calculus in real life

    • @Hoodratliker
      @Hoodratliker 5 ปีที่แล้ว

      For a million things. Look up optimization problems. For example if you wanted to manufacture a can for selling soda and wanted to find out the cheapest way to make it while it can still hold 12 ounces...you use calculus for that. To see how to maximize square area if you have a certain amount of fencing....i can go on forever.

  • @savemybrain2036
    @savemybrain2036 5 ปีที่แล้ว

    nee kaa güzel anlatmışınız hocam .

  • @utube201052
    @utube201052 14 ปีที่แล้ว

    Very wonderful sir

  • @simonwallis1787
    @simonwallis1787 7 ปีที่แล้ว

    lol. In the UK some years ago we did this when we were 15 years old !

    • @fragyfraginston9430
      @fragyfraginston9430 7 ปีที่แล้ว +1

      Simon Wallis so what? i learned this when i was 15 as well,no need to be a showoff.I bet that if you learned it when you was 15 you learned it in a lower level of understanding.

  • @intellectracoon
    @intellectracoon 12 ปีที่แล้ว +2

    thank you professor Gilbert :)

  • @abd.alharbi
    @abd.alharbi 8 ปีที่แล้ว +4

    He said infinitesimal!

  • @joepup8348
    @joepup8348 3 หลายเดือนก่อน

    If Archimedes had found out the connection between the first and second functions, he would have yelled, "EUREKA!"

  • @alarabi101
    @alarabi101 12 ปีที่แล้ว

    Thank you so much professor!!!! great review

  • @AlexzandrSpringvale
    @AlexzandrSpringvale 11 ปีที่แล้ว

    2:42 4:20

  • @sarthaktewari1192
    @sarthaktewari1192 3 ปีที่แล้ว

    He is a magician..

  • @30secondstolive
    @30secondstolive 14 ปีที่แล้ว

    @aramian21 algebra? :)

  • @mohammedshifan1537
    @mohammedshifan1537 6 ปีที่แล้ว

    Thanks from Sri Lanka

  • @SydiusVideo
    @SydiusVideo 11 หลายเดือนก่อน

    Thank you

  • @Gimipork
    @Gimipork 11 ปีที่แล้ว

    Brilliant! Thank you, professor =)

  • @taimoor722
    @taimoor722 12 ปีที่แล้ว

    change is called slope change value is called slope value

  • @KDonovanEdu
    @KDonovanEdu 14 ปีที่แล้ว

    Great job!

  • @TheRealJackfrog
    @TheRealJackfrog 7 ปีที่แล้ว

    29:22 Someone actually applauded..

  • @hondajr1
    @hondajr1 9 ปีที่แล้ว

    Very good! Thank you!

  • @kenichimori8533
    @kenichimori8533 7 ปีที่แล้ว

    Some check space pictureing area detopic defind communiative space minus integrate equal Big Picture.
    Try comment.

  • @Starfire777
    @Starfire777 8 ปีที่แล้ว

    I envy Mr Strang, I wish I could understand what he is saying!!!

  • @awesomewinter3103
    @awesomewinter3103 7 ปีที่แล้ว

    Sir Strang, you are a legend!

  • @skoolwal3874
    @skoolwal3874 9 ปีที่แล้ว +1

    Beautiful mind!!

  • @samsnapx
    @samsnapx 12 ปีที่แล้ว

    thanks you sir! this discussion is very helpful. :D