Calculus 1 Lecture 4.2: Integration by Substitution

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  • เผยแพร่เมื่อ 3 ธ.ค. 2024

ความคิดเห็น • 356

  • @UrbanCommando63
    @UrbanCommando63 5 ปีที่แล้ว +690

    Missed a Calc class and my professor recommended we all watch this video. Insanely informative and my professor wasn't lying when he said "If you see a jacked dude with glasses, you're on the right video." Thank you for these videos.

    • @mussawarahmed8530
      @mussawarahmed8530 3 ปีที่แล้ว +28

      The comment of the Professor though. hhahaha

    • @aurumyt223
      @aurumyt223 3 ปีที่แล้ว +8

      @@mussawarahmed8530 agreed lmao

  • @rosskane-d8p
    @rosskane-d8p 9 หลายเดือนก่อน +27

    I should be paying my tuition fees to Professor Leonard, his style of teaching is vastly superior to the robot that teaches me. All my teacher does is equation after equation after equation, never explaining the concept of it. This channel is a serious help to me.

  • @darthboganis1356
    @darthboganis1356 4 ปีที่แล้ว +192

    Using Integration by Substitution Methodology w/examples 8:00
    Two Substitutions in One 1:08:30
    Difficulty finding u: Trial and Error (1:19:42) - Algebraic manipulation to get a dx = du/? which cancels out the remaining x terms in the function .. because we only want terms involving u.
    Substitution involving a trig function 1:25:00 recognise that this will not work the way it is currently written. Take advantage of known trig identities within each component of the major function. The focus is still getting rid of all the x terms.

    • @aria3326
      @aria3326 3 ปีที่แล้ว +10

      Bless you!

  • @anastasiaalexandersdottir1021
    @anastasiaalexandersdottir1021 9 ปีที่แล้ว +168

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  • @Maya-xs9xn
    @Maya-xs9xn ปีที่แล้ว +28

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    • @cate9541
      @cate9541 2 หลายเดือนก่อน

      The goat fr

  • @jacksonr260
    @jacksonr260 7 หลายเดือนก่อน +4

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  • @nickyraja3793
    @nickyraja3793 4 ปีที่แล้ว +87

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    • @yazeed370
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    • @a_smile55
      @a_smile55 3 ปีที่แล้ว

      Try one year

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      @adityaekbote8498 3 ปีที่แล้ว

      well this is exactly me

    • @manueldouglas5180
      @manueldouglas5180 2 ปีที่แล้ว

      Its been eight years from when I last took a calculus class and I only discovered this now (2022)

    • @Kevin-mm8go
      @Kevin-mm8go 8 หลายเดือนก่อน +1

      So very true

  • @TamImBlessed
    @TamImBlessed 8 ปีที่แล้ว +298

    I don't just know why online teachers are teaching more better than the ones that are being payed to teach in colleges. I always understand online lectures more than the classroom.

    • @dougetrillbe3174
      @dougetrillbe3174 8 ปีที่แล้ว +81

      Professor Leonard is teaching at a college, he just uploads videos of his lectures. The reason it is easier to find great online lectures is due to TH-cam being a meritocracy, and usually the better videos get more views, in tern making them easier to find.

    • @robertvanzandt4851
      @robertvanzandt4851 8 ปีที่แล้ว +128

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    • @greense65
      @greense65 8 ปีที่แล้ว +108

      I've listened to a lot of Prof. Leonard's videos, and here's what I've gathered.
      It seems he's had his fair share of bad teachers when he was coming up, and may even have had some classes that he really struggled with. But he persevered, finally learned the material in a way that made sense, and got a masters in math.
      He also seems to be a very empathetic guy who cares about his students. So he has devoted a lot of effort to figuring out how to explain what he eventually learned in a way that most people (with the sufficient prerequisite background) can understand. And even then, he realizes that we are sometimes rusty on those prerequisites, so part of his instructional approach is to patiently remind us of what we need to know to get the new stuff.

    • @akshaygiram
      @akshaygiram 7 ปีที่แล้ว

      @S Green And, you're a mentalist!

    • @yousefahmed8923
      @yousefahmed8923 7 ปีที่แล้ว +1

      well at least you are in college , i am taking this in school and it's so easy for us
      because i have two great teachers ,one online and one in my class
      .

  • @johnkiserliss123
    @johnkiserliss123 10 ปีที่แล้ว +47

    Professor Leonard
    Being a older person & having taught maths myself I find your teaching method very informative & easy to follow
    Thanks for the High School that you work at for the uploads.

    • @ravistman1254
      @ravistman1254 5 ปีที่แล้ว +13

      I think he works at UC Merced

    • @christianatanasov
      @christianatanasov ปีที่แล้ว +3

      bro tried to gaslight uni and collage students

    • @Dlowr7
      @Dlowr7 ปีที่แล้ว

      @@christianatanasov 😂😂

  • @nobody222ify
    @nobody222ify 8 ปีที่แล้ว +96

    literally cramming all his videos for finals.

    • @bballdaniel3
      @bballdaniel3 7 ปีที่แล้ว

      Me too

    • @Peter_1986
      @Peter_1986 6 ปีที่แล้ว +1

      +AliAA
      I have already finished Calculus 1-3 a few years ago, but I still re-watch these videos just to refresh my memory of various topics, lol.
      I crammed his Calculus 3 playlist a while ago as a preparation for Mathematical Physics, which at least here in Sweden is a lot about vector calculus, partial differential equations and Fourier/Laplace Transforms.

  • @cararacs
    @cararacs 10 ปีที่แล้ว +21

    Seriously, these lectures are saving my life. I am taking Calc II and it's been 7 years since Calc I, my currently professor is rushing through all the calc I review with little to now examples. Thank you SO much for posting these lectures.

    • @mail2nadapurayil
      @mail2nadapurayil 7 ปีที่แล้ว

      same boat now!

    • @Vipa567
      @Vipa567 6 ปีที่แล้ว

      @Wesley Richardson You still have notes from 7 years ago?

  • @xboxhater12345
    @xboxhater12345 5 ปีที่แล้ว +7

    I know I'm most likely the 200,000th person to really bring this up Professor Leonard, but thank you. I failed algebra 2 in high school three times, so math has never been my strong point. I have been struggling along my Calc 2 Class so far until I stumbled across the videos you have posted on the subject matters I have had issues on. I, and my fellow peers who have viewed your videos in the past, are viewing them now, and the ones who have yet stumbled across them on the internet are ALL thankful for your teaching style, and how you make the explanations so down to earth of such a complex math class. I truly believe that if math was taught like this from the basics of Pre algebra, all the way to D.E; across the nation there would never be such a thing as someone who doesn't understand math.

    • @cr7neymar908
      @cr7neymar908 ปีที่แล้ว +1

      Same here, barely passed algebra 1 with a D and failed every other math class. I now have an A+ in calc 1 with my eyes on calc 2,3 and physics 1,2

  • @ohbebe14
    @ohbebe14 4 ปีที่แล้ว +5

    I'm currently taking calc II. On the first day of class, we went straight into integrations. I took calc I a year ago so I was completely lost; seriously forgot everything I learned. I considered dropping the class. I'm currently reviewing with your videos and OH MY GOD the hope to succeed in Calc II has been restored.
    Seriously, thank you for sharing these videos. You're helping future STEM students around the world :)

  • @edwinhenrich8555
    @edwinhenrich8555 5 ปีที่แล้ว +15

    My uni lecturer: Today we're doing integration by substitution
    5min later: Here's the fundamental theorem of calculus. And one more equation origin story you need to know...
    Test: Just integ by substitution

  • @codeiscool5552
    @codeiscool5552 8 ปีที่แล้ว +16

    GOAT Math TH-cam teacher

  • @johnc4401
    @johnc4401 7 ปีที่แล้ว +1

    Professor L, you've helped me immensely by providing a second lecture to run parallel to my class to see what I miss. Thank you so very much for all the effort. You've helped me come from a low C at the start to scoring the top A on test 3. You're the man. You embody what it means to teach.
    A grateful student

  • @thomaswarren9693
    @thomaswarren9693 7 ปีที่แล้ว +12

    I wish I had found these videos sooner than 5 days before my final. Looks like I'll be using them when I take Calc 1 again next semester.

  • @jarellcomstock1004
    @jarellcomstock1004 ปีที่แล้ว +2

    You teach so much better than the professors I have. I can always rely on these videos to inform me when I'm lost.

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    @agadamichael3058 6 ปีที่แล้ว +2

    You are really a blessing to me here in Nigeria . The way your teaching sinks into my head is amazing...THANKS 4 THE GOOD JOB

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    @dorindaotoo3497 8 ปีที่แล้ว +6

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    @chadjohnson608 6 ปีที่แล้ว +2

    This man is single handedly getting me through calculus

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    @thanuriwarnakulage1127 3 หลายเดือนก่อน +2

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    @isademigod8073 3 ปีที่แล้ว +1

    These kids are so lucky to have such a charismatic and well-spoken professor to teach them calc.
    I am watching these videos because I am taking calc 2 online and my teacher gives us the textbook and just says "go nuts" like we can teach ourselves out of a textbook

  • @couragechaminuka3790
    @couragechaminuka3790 7 ปีที่แล้ว +3

    thumbs up to professor leonard, he is one of the mathematics legend lecturer

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    @ahmedabdalla1096 10 ปีที่แล้ว +5

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    @putriayumoedianto 9 ปีที่แล้ว +5

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  • @tshiovhekhuthadzo129
    @tshiovhekhuthadzo129 10 ปีที่แล้ว +21

    Thank you. your explanation really increases my passion for Maths. You make Maths enjoyable. Keep the good work up. :D

  • @sarahholloway7587
    @sarahholloway7587 2 ปีที่แล้ว +1

    Again, Professor Leonard to the rescue!!! This is way better than my online prof videos. Thank you for teaching so calmly and methodically!

  • @ninakruzo
    @ninakruzo 7 ปีที่แล้ว

    Best video for integration ever. It can be a bit time consuming to find a video on TH-cam that is easy for me to understand because some people will skip the steps and I'll be lost. Thank you so much for this.

  • @melaniewhite8827
    @melaniewhite8827 8 ปีที่แล้ว +2

    Thank you for posting all of these videos!!! You're saving my grade in calculus this summer! You do great job of explaining difficult concepts.

  • @nilamilo4348
    @nilamilo4348 11 หลายเดือนก่อน

    Thank you so much for uploading this. Substitution is one of the three concepts or applications I couldn't grasp for my calc one final coming up this week, and you showing all the steps in detail really helped me. My teacher and the book skip steps all the time and don't give any tips on assigning 'u'. You have restored my faith that I will pass the class. I can't thank you enough.

  • @junaidalam7697
    @junaidalam7697 8 ปีที่แล้ว +7

    Amazing and professional teaching Sir
    teachers like you should be in our university

  • @omniafawzy5119
    @omniafawzy5119 3 ปีที่แล้ว +1

    literately i wasn't understand the integ. substitution and now i understood it how to solve it . thank u very much really

  • @Sparroweatshawk
    @Sparroweatshawk 7 ปีที่แล้ว

    By far the best math teacher alive today. Thank you so much for making your lectures public!

  • @ryonwhyte
    @ryonwhyte 7 ปีที่แล้ว +1

    Thank you. After Getting 38% on a calculus test (I am usually an 'A' student) I have vowed to ace the course inspite of that. Your channel will make me do it.

  • @AliMohammed-ly8lx
    @AliMohammed-ly8lx 10 ปีที่แล้ว +4

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    @Peteork25 2 ปีที่แล้ว +2

    me and my boy chase use your video's for our study groups in calculus 2 and generally just to brush up on stuff through courses current and previous. Like now, where I need a refresh on integration as a whole.
    Thank you for doing what you do for without which we'd be screwed in our respective fields :)

  • @stephaniewang8807
    @stephaniewang8807 5 ปีที่แล้ว +1

    You are an amazing Professor! Thank you for sharing your videos.

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    @bosshaden2265 9 ปีที่แล้ว

    you are the best ever sir! Words cannot describe the joy, relief, and satisfaction i feel after watching these videos. Sure am not the only one who leaves my calculus class more confused than when i entered! thanks so much for what you do. God bless you

  • @rit4140
    @rit4140 8 ปีที่แล้ว +3

    Thanks Leonard, you are just the best

  • @Vipnailsbaytown2024
    @Vipnailsbaytown2024 3 ปีที่แล้ว

    you're really the best man. you saved me from the beginning of cal 2 because i didnt pay attention much in cal 1 so so spent the past 5 days watching all of your cal 1 videos and i'm rocking my cal 2 rn. tbh, i will eventually rather watch your lec to understand cal 2 than watching or listen to my teacher cus she does not know how to entertain their students like you do

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    @makhloufbannoud644 8 ปีที่แล้ว +4

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    THANK YOU SO MUCH FOR MAKING MY LIFE EASIER

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    @gagaaicee4367 7 ปีที่แล้ว +2

    You sir are amazing! Totally worth the time!

  • @BoOoMfull
    @BoOoMfull 7 ปีที่แล้ว +1

    يعطيك العافية ياشيخ ليونارد .. والله انك وحش يارجل ساعدتني وبقوة

    • @lordindex.
      @lordindex. หลายเดือนก่อน

      عاش

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    @paull2937 2 ปีที่แล้ว +4

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    @ins4rt_username18 3 ปีที่แล้ว +1

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    @cracked_cypher8761 9 ปีที่แล้ว

    This man is the real MVP, Thanks so much for helping me through Calculus!

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    @Gojover ปีที่แล้ว

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    @taekwondotime 4 ปีที่แล้ว +2

    *TIP:* By the time you finish his courses on Calc 1/2/3, if you're not already an "A+" student in Algebra, you WILL be. It's astonishing just how good you become at algebra when you're crunching derivatives and integrals every day and moving numbers around in the equations (something that used to give me problems). It becomes so easy that you won't even have to think about it any more. :)

  • @alekhaparida2914
    @alekhaparida2914 5 ปีที่แล้ว +1

    Thank you sir for your great help in making me understand about the substitution method

  • @JasonWard79
    @JasonWard79 6 ปีที่แล้ว

    In Calc 2 right now and am just now understanding u-subs. Thank you, Mr. Leonard!

  • @tenshikn
    @tenshikn 7 ปีที่แล้ว

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    @shaikhatifanees5431 7 ปีที่แล้ว +3

    live long man the way you taught was super great (Y)

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    @Sedonapass ปีที่แล้ว

    I remember watching this during my university days. Thank you for your assistance. 🐐

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    @rumpelforeskin8461 8 ปีที่แล้ว +7

    This man is an awesome teacher.

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    @eng-firas8178 6 ปีที่แล้ว

    You explained in few seconds and I get it. My teacher take 10 year to explain and all the students still lost....God bless you

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    @fethiocalan_1 11 หลายเดือนก่อน

    here is a real professor. thank your sir.

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    @bobhorton8662 7 ปีที่แล้ว

    Professor, you are literally saving my life.

  • @sl8094
    @sl8094 ปีที่แล้ว

    my favourite Proffessor in the whole world.🤗

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    @smeargloid 11 หลายเดือนก่อน

    HS student here THANK YOU SO MUCH FOR THIS my calc1/2 final is in three weeks and this was explained perfectly!!!

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    @chotachota3536 4 ปีที่แล้ว

    the length of the videos kills me........yet every time i leave feeling like a math pro.......THANK YOU!

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    @chucks2k 4 ปีที่แล้ว

    Looking for enhanced understanding of quantum mechanics via calculus. Your class and your style makes the process rewarding.!
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    @denivaletutto5092 9 ปีที่แล้ว

    Thank you!!!! You are the reason I'm not failing my business calculus course right now.

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    @KuldeepKumar-hl4jz 7 ปีที่แล้ว

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    @ashleyriot50 3 ปีที่แล้ว

    I'm really grateful for your videos.
    You break it down into simple terms that anyone could understand.
    I'm quite slow to connect the dots on how the operations works and the way my current professor taught it just went by me as she taught it too fast.
    (being taught online doesn't help either).

  • @lacklao8108
    @lacklao8108 8 ปีที่แล้ว

    got taught this and came across problems like the ones you teach after 1:08 and thank you so much for making me understand, honestly ur a great teacher , wishhhhh i had you u rlly know what ur doing and ur not boring XD

  • @AbdeenzRock
    @AbdeenzRock 3 ปีที่แล้ว +1

    AN ABSOLUTE LEGEND. MY CALC FINAL IS TOMORROW!

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    @jtwoms8119 ปีที่แล้ว

    haven't gone to class in weeks! THANK YOU SO MUCH

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    @sylvianamatsi2910 4 ปีที่แล้ว

    Wow...the lecture was well presented... I didn't catch up with my lec but thanks I now have the content on calculus

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    @TeamShadowmen 6 ปีที่แล้ว

    This man is the world's greatest math teacher. Not even joking.

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    @marythedelulu 3 ปีที่แล้ว +2

    King Leonard carrying me through uni

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    @Кротовыеноры 7 ปีที่แล้ว +1

    Big thanks from Russian student!!!

  • @xxdiegomx
    @xxdiegomx 9 ปีที่แล้ว

    Your video just saved me on my Calc test. Thank you

  • @follklor9976
    @follklor9976 8 ปีที่แล้ว +4

    amazing actually one of the best lecture ever i ve seen in integration
    and funny moment
    1:08:17 because i said so best answer :D

  • @carlosaguilera12
    @carlosaguilera12 9 ปีที่แล้ว +1

    Really appreciate the videos, man. Very in-depth. Thanks.

  • @Parameswar_Ghosal
    @Parameswar_Ghosal 9 ปีที่แล้ว +1

    very good sir , keep working on it ... God bless you.....

  • @malcombaretto8966
    @malcombaretto8966 9 ปีที่แล้ว

    leonard sir you rock .i wish i had a sir like u......

  • @Hype_Machine
    @Hype_Machine 5 หลายเดือนก่อน +1

    my parents always slam the doors so hard so the constant background of a door being slammed in these videos kind of keep be on alert of my surroundings IRL.

  • @aisu7876
    @aisu7876 6 หลายเดือนก่อน

    The best lecturer ever👍

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    @sbget 7 ปีที่แล้ว +1

    great song, vocals are very powerful!

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    @rikchild7518 5 ปีที่แล้ว

    Great teaching and interesting relationship advice!

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    @bencater7158 2 ปีที่แล้ว +1

    I can't believe this is free

  • @oneofyk
    @oneofyk 6 ปีที่แล้ว

    thank you professor leonard. you dont know me, but youve made a positive impact on my life

  • @cwengaz
    @cwengaz 3 ปีที่แล้ว

    Thank you Professor Leonard this help alot

  • @warrenfranklin6173
    @warrenfranklin6173 8 ปีที่แล้ว

    This was an amazing explanation of this topic.

  • @missdee212
    @missdee212 10 ปีที่แล้ว

    Thanks it made integration clear like water instead of mud.

  • @robertflores5520
    @robertflores5520 7 ปีที่แล้ว +40

    broke up with my girl before her birthday and then got back with her a week later. Thanks for all the money I saved

  • @shadabzahra6274
    @shadabzahra6274 3 ปีที่แล้ว +1

    The universities should not hire teachers and take money from us who can't make us learn a single thing. Just take a test from us and give us our degree we have got far better teachers on internet who actually knows how to teach although we can't interact with him but still all my concepts are now vivid clear. Professor Leonard is the the best calculus teacher I ever had.

    • @elainemachado5063
      @elainemachado5063 3 ปีที่แล้ว +1

      100% absolutely agree. My professor has a doctorate in mathematics but doesn't know how to lay things out in a way students can understand. Learning instead through this channel now

  • @ayahussain2070
    @ayahussain2070 9 ปีที่แล้ว

    thank you sir , your videos are so useful for me. I'm a college student and i really needed to understand the lesson for my quiz

  • @JawadAli-tj3ec
    @JawadAli-tj3ec 7 ปีที่แล้ว

    sir I have no words ...to apreciate u .....u r a really great teacher ,,fantastic ....I wish to take ur classess

  • @Ной-п2ц
    @Ной-п2ц 8 หลายเดือนก่อน

    Thank you very much, Professor big love from Iraq ❤

  • @5starradiant339
    @5starradiant339 2 ปีที่แล้ว

    This is saving my life right now. Could never get u-sub down in Calc I, and it came back to bite me in the ass in Calc II. But this is really helpful and well explained

  • @Moisi547
    @Moisi547 8 ปีที่แล้ว +55

    Who hits the dislike button for such a great class 🤔

    • @viviang37
      @viviang37 7 ปีที่แล้ว +29

      probably all of our resentful teachers who are jealous of him, hahaha

    • @isademigod8073
      @isademigod8073 3 ปีที่แล้ว

      They don't dislike the video, they dislike the subject :)

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      @zeeshan7372 2 ปีที่แล้ว

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  • @abdullahmohammad5613
    @abdullahmohammad5613 7 ปีที่แล้ว +1

    🌟 Simply A Legend 🔥

  • @FlexcuteFlexcute
    @FlexcuteFlexcute ปีที่แล้ว

    u r life saver
    the best of the best

  • @miguelbahena9245
    @miguelbahena9245 4 ปีที่แล้ว

    This guy is AMAZING, thank your mr buff sir

  • @socal4348
    @socal4348 9 ปีที่แล้ว +14

    I would be screwed without your videos! I wish my school would take a cue from you and simply post a teacher giving a lecture, instead they choose to focus on production value and flashy images when making videos with very little useful content.

    • @Peter_1986
      @Peter_1986 6 ปีที่แล้ว

      +Chance Hope
      One thing that I have always disliked about certain math teachers is that they spend way too much time deriving theorems and proofs.
      It would've been much better if they gave the students an intuition for what in the world was happening and gave examples on how to solve simple problems instead of talking forever about abstract proofs which don't mean anything to complete beginners anyway, especially when those proofs are always derived in detail in the course literature.
      Professor Leonard instead focuses a lot on intuition and example problems, which is awesome.

  • @math1932
    @math1932 10 ปีที่แล้ว +3

    amazing prof.

  • @felsefikproblem
    @felsefikproblem 9 หลายเดือนก่อน +1

    he's better than my own calculus instructor 😩

    • @cate9541
      @cate9541 2 หลายเดือนก่อน

      Many such cases