Calculus 3 Lecture 14.6: How to Solve TRIPLE INTEGRALS (Along with Center of Mass and Volume)

Calculus 3 Lecture 14.6: How to Solve TRIPLE INTEGRALS (Along with Center of Mass and Volume): What Triple Integrals mean and methods of solving them. Also discussed is the idea of a triple integral representing mass and volume of a 3-D region. Center of Mass is also covered, but more examples in 14.7)

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  • @realslimshady1100
    @realslimshady11003 жыл бұрын

    That moment when you realized that you'd rather watch a free video thats 3x longer than your college class to which you've paid a shit ton of money for.

  • @siddheshss12345
    @siddheshss123455 жыл бұрын

    I was looking at my phone when he said "look at the board, stop what you're doing and look at the board" so I put my phone down and did what he said.

  • @JML1987
    @JML19874 жыл бұрын

    "Yo dawg, we heard you like integrals. So we put integrals inside integrals inside integrals so you can integrate the integration while you integrate." - Leibniz

  • @theshoulderofgiants

    @theshoulderofgiants

    3 жыл бұрын

    Newton**

  • @anthroporraistes_

    @anthroporraistes_

    3 жыл бұрын

    @@theshoulderofgiants Leibniz***

  • @nebaashibruce8793

    @nebaashibruce8793

    3 жыл бұрын

    dis sound like a yaad man mek dis comment.

  • @gregtroll

    @gregtroll

    2 жыл бұрын

    Turducken…

  • @canman5060

    @canman5060

    2 жыл бұрын

    I integrate 1500 times in my Phd Maths Thesis !

  • @junior5146
    @junior51463 жыл бұрын

    30:00 Z-simple 40:30 Ex 1 47:00 Ex 2 58:00 Ex 3 1:19:16 Ex 4 Finding mass with p(x,y,z) 1:36:00 Ex 5 Using Y-simple. Example when you are not sure which order the upper/lower bounds are 2:02:55 Ex 6 2:36:22 Ex 7 3:02:00 Ex 8

  • @invincible2914

    @invincible2914

    2 жыл бұрын

    3:15:00 center of mass 3:22:52 Example 9

  • @receperdogan9285

    @receperdogan9285

    2 жыл бұрын

    thx for helping

  • @deemgr7

    @deemgr7

    Жыл бұрын

    Thanks

  • @purewaterruler
    @purewaterruler8 жыл бұрын

    Damn it, why couldn't the video be 2 seconds longer.

  • @Nicoder6884

    @Nicoder6884

    8 жыл бұрын

    You mean one second?

  • @gwaites6329

    @gwaites6329

    7 жыл бұрын

    hha yea either 2 seconds longer or 1 sec shorter, or even 5 seconds longer so we get 3+33=36

  • @gwaites6329

    @gwaites6329

    7 жыл бұрын

    X D go to about 1:15:42 and put at .5x speed X D sounds like a high californian surfer

  • @gwaites6329

    @gwaites6329

    7 жыл бұрын

    1:15:39 *

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    @tlhomotsemoteme2423

    4 жыл бұрын

    G Waites lmfao

  • @adamt6024
    @adamt60243 жыл бұрын

    I owe my A’s in calc 1, calc 2, and now calc 3 to professor Leonard. Professor you are a fantastic teacher and have set the bar for all professors across the globe. Thank you for being an amazing human being and being their for me in my upper division math. I honestly don’t know where I would be with out your videos.

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    @hassanaftab6219

    3 жыл бұрын

    Which book Professor is using!

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    @irenewilliams5145

    2 жыл бұрын

    That's cool

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    @evanjones9602

    11 ай бұрын

    @@hassanaftab6219 Early Trancedentals, James Stewart

  • @cfraijo4898
    @cfraijo48988 жыл бұрын

    THE LEONARD!! Simply awesome. Math isn't so bad when you've got the Leonard in your corner. It's actually kinda fun! Thanks Professor. Not too many people can do what you do.

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    @masoomaibrahim3893

    2 жыл бұрын

    8th

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    2 жыл бұрын

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    @RakeshYadav-tj5os

    Жыл бұрын

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    @ILikeWeatherGuy7 жыл бұрын

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    @Anigmus_

    2 жыл бұрын

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    2 жыл бұрын

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  • @bawol-official

    @bawol-official

    2 жыл бұрын

    Same here, its par the course though for most places that arent prestigous or private schools. Thats not to say you cant find them. The best math teacher ive had in my life was taking a College Algebra course at my community college, flunked math all throughout highschool and passed with an A. Changed my major to Computer Science just so i could learn more math while staying true to my experience in tech. Theres Prof. Leonards out there its just a matter of chance.

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    2 жыл бұрын

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  • @dagkouta986
    @dagkouta9865 жыл бұрын

    the fact that we use the same textbook is sooo helpful. For anyone wondering, it's Calculus Late Transcendentals 10th edition by H.Anton, I.Bevens and S.Davis.

  • @sterlingmillhollon2520

    @sterlingmillhollon2520

    Жыл бұрын

    It is also following closely the "Calculus" 10th edition by Ron Larson and Bruce Edwards

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    @evanjones9602

    11 ай бұрын

    Early Transcendentals 8th edition too

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    @Je663844 жыл бұрын

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    @keylanoslokj1806

    2 жыл бұрын

    Yeah cause colleges try to give you overly compact knowledge in just 4 months

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    @mewos838

    2 жыл бұрын

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    @miguel1502009

    3 жыл бұрын

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    3 жыл бұрын

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    @sergeirachmaninoff6397

    2 жыл бұрын

    Walter Lewin is as good or even better with his demonstrations! Regarding explanations they are on the same level.

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    @Lena-zn4re

    2 жыл бұрын

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    @ritesha8050

    2 жыл бұрын

    sir Walter Lewin is a physics god. There is no way you cant understand.

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    @adriannavarro134511 ай бұрын

    Love this man, can’t believe I didn’t watch him until now. Would’ve been great for calc I and II

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    @mahmoudm4515 жыл бұрын

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    @guitarttimman

    4 жыл бұрын

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    2 жыл бұрын

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    2 жыл бұрын

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    Жыл бұрын

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    @nataliemendez91537 жыл бұрын

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    @cc-gg6cd2 жыл бұрын

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    @mzboop34835 жыл бұрын

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    @NoanahMalati-mg4db7 ай бұрын

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  • @deepaksree6
    @deepaksree67 жыл бұрын

    you are the best calculus teacher ever!!!!Thank you prof. Leonard

  • @franciscodonoso1654
    @franciscodonoso16546 жыл бұрын

    Damn I have been using integrals for years and never really understood the concept behind triple integrals. The way you explained how single, double and triple integrals are used at the very beginning was perfect.

  • @chrisrabe655
    @chrisrabe6552 жыл бұрын

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    @SuperZ3917 жыл бұрын

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  • @kd.lovesyellow
    @kd.lovesyellow5 жыл бұрын

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  • @justjoannak
    @justjoannak4 жыл бұрын

    Wasn't fully understanding triple integrals for my test in 2 hrs and I *NEED* to pass Calc 3 to transfer. This helped a lot, since it's a lecture

  • @arkinidnani1665
    @arkinidnani1665 Жыл бұрын

    I spent hours trying to understand double and triple integrals. Literally an hour into his videos, it all makes sense... Thank you so much!!

  • @debendragurung3033
    @debendragurung30336 жыл бұрын

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  • @Macbethinspace
    @Macbethinspace7 жыл бұрын

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    @chrispinbgwoni86425 жыл бұрын

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    @sami_keyd6 жыл бұрын

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  • @KoruGo
    @KoruGo2 жыл бұрын

    Thank you so much for these videos! I'm a high school student taking multivariable calculus, but because our periods are so short the class is being rushed and is nowhere near comprehensive enough for the tests. Thanks to these videos I am getting such a better understanding of the concepts we're learning in class!

  • @diegol4452
    @diegol44525 жыл бұрын

    video 33:33 long (almost 33 secs), 333K subscribers, 3 integrals, 3D regions, Calculus 3, I'm scared!

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    @crunchyleif23685 жыл бұрын

    Would you ever consider putting up some kind of mock up of your exams with their answers? I feel like your tests would be much more challenging in the right way than our teachers.

  • @elijahbarnet
    @elijahbarnet6 ай бұрын

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  • @SachaTholl
    @SachaTholl6 жыл бұрын

    Awesome course, that's now 12 years i'm off the university and with your explanations, everything came back in. In only 3 hours! That's so cool. You're the coolest math prof. i never had......in fact, there were all super-boring without any exception. Two thumbs up!

  • @newjsdavid1
    @newjsdavid17 ай бұрын

    Thank you for reiterating everything you’re saying, no monotony, everything said with purpose. It took me watching the 1st 19 minutes like 3x before it all finally clicked but once i got it we’re good 👍🏼

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    @tommychong3269 Жыл бұрын

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    @shadanjaved88275 жыл бұрын

    you are really good!!! way more good than my professor!! loved your teaching style... lots of love & keep it up!!

  • @boraerdemkaratay7243
    @boraerdemkaratay7243 Жыл бұрын

    Dear Professor Leonard, Thank you for your explanations. greetings from Slovenia and Turkey!

  • @niquemo18
    @niquemo184 жыл бұрын

    I want to say, thank you for this. During this time it is extremely hard to find help. This help me to the core. Z-simple. I have a great insight on integrals. I wish my professor was like you. You're amazing and handsome too.

  • @TeamShadowmen
    @TeamShadowmen4 жыл бұрын

    This guy is the world's greatest math teacher. Without a single doubt.

  • @Pete-Logos
    @Pete-Logos4 жыл бұрын

    .....and also THANK YOU FOR NOT SKIPPING STEPS!!!! You rock, bruh!!

  • @georgesadler7830
    @georgesadler78302 жыл бұрын

    Professor Leonard, thank you for another fantastic and lengthy video/lecture on How to Solve Triple Integrals(Along with Center of Mass and Volume) in Calculus.This is another tremendous amount of material to absorb, however the way each example is explained is incredible. In Mathematics, the Center of Mass is explained really well in comparison to other courses in Science and Engineering.

  • @tauceti8341
    @tauceti83418 жыл бұрын

    Single integral - area under f(x) (2-d, x,y) *OR* mass of a straight line (1-d) (??? investigate/review) "Distance along x-axis" 14:38 Double Integral - VOLUME under f(x,y) (3-D) *OR* mass of a thin plate (plane region) -thin- flat (xy-plane) Trippe Integral - Some measurement of region under f(x,y,z) (4-D concept) *OR* Mass of plate *with* thickness (cube, or surface) 14:58 ... Tripple integrals create a region just like double and single integrals. However it is defined in 3D so it a surface of x,y,z (cone/spike). Now take the mass density of EVERY point on this surface, and it tells you the mass. 18:00 Tripple integral defined S as between two Surfaces. 24:20

  • @hwp842
    @hwp8428 ай бұрын

    professor leonard, you are an amazing teacher. my current calc 3 class sucks, and i understand everything so clearly thanks to you. thank you so so much!!

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    @hasithrathnayake75695 жыл бұрын

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    @giei45158 жыл бұрын

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    @chandranichaki9580

    2 жыл бұрын

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  • @ethan22ethan
    @ethan22ethan2 жыл бұрын

    Amazing professor this guy. I passed Calc 3 a few years ago and it is so neat to go back through this stuff. Great work

  • @f.b.i1068

    @f.b.i1068

    Жыл бұрын

    Why do you have to go back through it again?

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    @marylynn55843 жыл бұрын

    I LOVE EVERYTHING ABOUT THIS!! Thank youuu!!!!!

  • @craponAsPTULA
    @craponAsPTULA5 ай бұрын

    Literally better than any math professor has explained anything in my whole time at university, I'm so bugged I found this channel in my last semester before I graduate. If I had to give any stem majors advice it would be to watch these videos.

  • @esau101
    @esau1016 жыл бұрын

    professor Leonard is our Math Superman.... awesome!

  • @sergioandres8041
    @sergioandres80418 жыл бұрын

    Happy birthday Leo :D Thanks a lot lot for this videos

  • @guitarttimman
    @guitarttimman4 жыл бұрын

    It's all about identifying what's bounded and what's simple. Good video.

  • @pedrolotti45
    @pedrolotti452 жыл бұрын

    i spent the day studing this video, easy to understand. Thanks professor Leonard, obrigado!

  • @umairiqbal4719
    @umairiqbal47196 жыл бұрын

    You are possibly best Cal 3 Prof!!!

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    @aymanadel34703 жыл бұрын

    Such an amazing instructor. Thanks

  • @ILikeWeatherGuy
    @ILikeWeatherGuy7 жыл бұрын

    professor leonard is a 4d function of mass density of education. my brain gets smarter as this video goes on.

  • @ILikeWeatherGuy

    @ILikeWeatherGuy

    7 жыл бұрын

    i.e the mass density of the correct electrons in place in my neurons get denser :D

  • @Pete-Logos
    @Pete-Logos4 жыл бұрын

    Thank you!!!!!! I've been yelling at my book for 3days and asking it "how many dimensions am I in???!!!!!" (3 or 4????) this helped a lot!!

  • @cattoowhtsp
    @cattoowhtsp2 ай бұрын

    this video really helps me a lot in understanding what triple integrals represent and mean, thanks a lot !!! ❤

  • @johnsnow3444
    @johnsnow34442 ай бұрын

    more i watch professor leonard the more i absolutely love his teaching style. so many amazing examples with clearly outlined definitions.. also he sometimes smiles just like homelander after cracking a joke lmao Cant wait for his linear algebra series! I need it

  • @jesse_sukh1785
    @jesse_sukh17856 жыл бұрын

    You are Mr. master mind sir......Luv the way u explaining concept.

  • @BillyOGrady
    @BillyOGrady3 жыл бұрын

    This was amazingly helpful. Thank you!

  • @rizalevans483
    @rizalevans4835 жыл бұрын

    hi Professor Leonard, thanks so much for your videos. I use to love math, i even competed in the mathematic olympiads and managed to get second place. But when i started engineering I hate math and barely managed to pass calc 1 and failed calc 2. But after stumbling across your videos im starting to enjoy math again and am kinda sad that i have finished all of my math courses for my degreee. Thank you so much

  • @zhanghowie7713
    @zhanghowie77134 жыл бұрын

    crushing my calculus tests easily after watching this far.

  • @brianwashingtonmusungwa7567
    @brianwashingtonmusungwa75674 жыл бұрын

    Give you credit sir ... You explained what many professors doesn't do ... They just teach for exams not for beneficial use and right applications

  • @oneofyk
    @oneofyk4 жыл бұрын

    this was a great lesson. learned so much. thank you

  • @muaadhahmed5419
    @muaadhahmed54194 жыл бұрын

    ابداااااع ... ليت بعض الدكاتتره يتعلموا منك ..

  • @Gabriela-zf1jy
    @Gabriela-zf1jy7 жыл бұрын

    I wish my calc professor explained like this and was good looking as well. I would never miss class ever lol

  • @tripp3468

    @tripp3468

    7 жыл бұрын

    racist

  • @user-lc6jq1hi1r

    @user-lc6jq1hi1r

    3 жыл бұрын

    "good looking"?? what? are you going to college to marry your teacher or to study?

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    @vaiterius

    3 жыл бұрын

    @@tripp3468 how tf

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    @astrar7

    3 ай бұрын

    ?????????????/@@tripp3468

  • @liantiu8185
    @liantiu81852 ай бұрын

    Z-simple - 30:00 Ex 1 - 40:30 Ex 2 - 47:00 Ex 3 - 58:00 Ex 4 Finding mass with p(x,y,z) - 1:19:16 Y-simple. Example when you are not sure which order the upper/lower bounds are - 1:36:00 Ex 6 - 2:02:55 Ex 7 - 2:36:22 Ex 8 - 3:02:00

  • @loganphillips1674
    @loganphillips16746 жыл бұрын

    Professor Leonard, what book does your class use? Thank you for this great video also!

  • @nigistgebremeskelll5314
    @nigistgebremeskelll53146 жыл бұрын

    i love u professor leonardo toooooooooooooo muchhhhhhhhhhhhh.thanks alot am a first in calculus in our class .from ethiopia

  • @afzolkarim6001
    @afzolkarim60015 жыл бұрын

    You are amazing sir,.. you helped me alot, simply more than enough...

  • @SmathH
    @SmathH6 жыл бұрын

    U r awesome!!!!! Thank u mr. Leonard.Its really helpful to me.

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    @mariabacanurschi37953 ай бұрын

    give this man a raise

  • @RAJSINGH-of9iy
    @RAJSINGH-of9iy6 жыл бұрын

    What a wonderful lecture !!! Ty sir

  • @solinsaadi2473
    @solinsaadi24735 жыл бұрын

    thank yoy so so so much ❤ l'm watching your videos from the first second till the final second l can't tell you how much you helped me l really appreciated ❤ much love for you professor ❤

  • @deanharris7149
    @deanharris7149 Жыл бұрын

    Man! This guy is great at what he does. Makes me wish I could go back to school.

  • @communikater
    @communikater8 жыл бұрын

    +Professor Leonard - I am so thankful for all of your time and incredible teaching methods! I have been using your videos for a couple years now, and they have been the most valuable resource for me. Whatever we are learning in class, I always understand conceptually and how to solve the problems 100% more effectively after watching your videos. Thank you, thank you, thank you! Side question- We are wrapping up the semester with Line Integrals, Parametric Surfaces, Curl/Divergence, etc. - Will you be covering this in your class soon? I want to watch your lectures so I can study for my final!

  • @jenslonn6046
    @jenslonn6046 Жыл бұрын

    I wish I had a professor like this when I was at the University. This was very interesting. I graduated (msc engineering physics) 17years ago and by chance stumbled upon this and I just had to watch the whole thing. Awesome example of a great teacher, focussing on understanding so it is much easier to understand what is happening instead of just learning integration techniques. Thanks for sharing!!

  • @John-iy1xi
    @John-iy1xi3 жыл бұрын

    You know what I love about Professor Leonard's teaching, he squeezes a reminder of past vital concepts and ideas from previous topics. So if you learned, but didn't fully understand something entirely in i.e. double integration, you wouldn't need to go back to his double integration videos; he catches you up on the go. Like the level of in-depth teaching is far beyond what any of my past/current lecturers do, so coming from any other lecturer to videos literally fills those knowledge gaps.

  • @Festus2022
    @Festus20222 жыл бұрын

    Dr. Leonard, Thanks so much for the great videos. What happened to lecture 14.5. Apparently, this a key video for understanding 15.6, but I can't find it in the playlist. PLEASE ADVISE.

  • @abdelmajid3409
    @abdelmajid3409Ай бұрын

    Thanks a lot, you are a very good teacher

  • @knightace742
    @knightace7422 жыл бұрын

    Bro first video and with In The first five minutes I can tell I wish I had you as my math teacher. So helpful.

  • @user-rg1nt9lf4s
    @user-rg1nt9lf4s6 жыл бұрын

    you are great sir you are very fundamental ...love you and thank you

  • @mariambobat3227
    @mariambobat32275 жыл бұрын

    Thank you. Thank you. Thank you. I am yet to see your teaching style matched. Much appreciated from Zambia.

  • @CluckYou21
    @CluckYou214 жыл бұрын

    I laughed when he said "Y, no I mean por qué". Hahaha.

  • @jfresh2054
    @jfresh20548 жыл бұрын

    in calc 2 now. I can't even express how much I'm looking forward to calc 3.

  • @Peter_1986
    @Peter_19864 жыл бұрын

    I just use Geogebra when I graph this stuff, haha. Perfect program for 3D graphs, and you can graph curves as well if you plot them as parametric equations.

  • @charlesfkessler
    @charlesfkessler3 жыл бұрын

    At the beginning of the video (around the 6:50 mark) , he's talking about the ambiguity of a 4-d equivalent of volume. I wonder if you could express it as the change in displacement experienced by free space over a given time period. Maybe that's way out in left field, but it kinda works in my head.

  • @shakilahmed5636
    @shakilahmed56364 жыл бұрын

    I wish you were math teacher..............before I come here...........calc 3 was like nightmare for me.......thanks a lot sir...........I looooove the way you teach.....

  • @User-ci3su
    @User-ci3su Жыл бұрын

    Thank you so much. You are a hero!!!!!!!

  • @anthonydeleon4104
    @anthonydeleon41048 жыл бұрын

    Yesss thank you so much for this video!

  • @SamuelLee-gw6wr
    @SamuelLee-gw6wr2 жыл бұрын

    There are two versions of calc 3 in my uni and I am taking the easier version suited for engineering and most business students. But these vids are for the harder version, so I am going above and beyond on such vids. I only need an average of 1.52 attempts to solve a calc 3 webwork problem correctly, but for calc 2 without Leonard it was above 3.00. And now I have calc 3 as the course to pull my grades up. So many of my friends are struggling but I am breezing through.

  • @rachellee9998
    @rachellee99986 жыл бұрын

    "I'm 83, I age really well. Strick diet of quinoa and steroids. I'm joking don't take steroids they do weird things. Ask my uncle he was Mr. America." --Professor Leonard what a golden quote...No way is your uncle Gary Leonard!!! LOLOL

  • @ProfessorLeonard

    @ProfessorLeonard

    6 жыл бұрын

    Hahaha, love to have fun!! But yes, Gary Leonard really is my uncle

  • @claricea5353
    @claricea53533 жыл бұрын

    Super helpful - thanks!

  • @jeffreygalle
    @jeffreygalle5 жыл бұрын

    He wasn't lying about Gary Leonard. That is awesome.

  • @nabeelali6721
    @nabeelali6721 Жыл бұрын

    I wish there was a professor like you for linear algebra as well

  • @Peter_1986

    @Peter_1986

    Жыл бұрын

    He will start Linear Algebra in the near future; he said that in his most recent video on this channel.

  • @RiseNurtureThrive
    @RiseNurtureThrive2 жыл бұрын

    Estou gostando muito dos seus vídeos, dando like em todos.