Change of Variables & The Jacobian | Multi-variable Integration

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  • Опубліковано 28 лис 2024

КОМЕНТАРІ • 292

  • @imanabu5862
    @imanabu5862 4 роки тому +360

    Quarantine isn't that bad when we have people like you helping us out, thanks sooooooo much 🌸🌸🌸

    • @beoptimistic5853
      @beoptimistic5853 3 роки тому +1

      ua-cam.com/video/vFDMaHQ4kW8/v-deo.html 💐

    • @pattiknuth4822
      @pattiknuth4822 3 роки тому +2

      quarantine is ALWAYS bad

    • @anonymous9217w2
      @anonymous9217w2 Рік тому +1

      @@pattiknuth4822 not that bad he said

    • @boctama6626
      @boctama6626 7 місяців тому +2

      Can’t believe quarantine was four years ago now…

    • @thisukainol
      @thisukainol 7 місяців тому +1

      @@boctama6626 true :(

  • @pbillings808
    @pbillings808 4 роки тому +96

    Greatly appreciated the second half as to WHY the Jacobian comes into play!

  • @Chomusuke71
    @Chomusuke71 3 роки тому +62

    The Jacobian part in the end is pure gold

    • @treynoe4934
      @treynoe4934 3 роки тому +2

      Hey can someone explain how to find the individual parts of the jacobian? I’m using this vid as a study guide for a test and I’m struggling to find the multiplicative factor

    • @treynoe4934
      @treynoe4934 3 роки тому +1

      help please someone

    • @Chomusuke71
      @Chomusuke71 3 роки тому

      @@treynoe4934 what do you exactly mean by the individual parts, elaborate a bit ill try to help

    • @Chomusuke71
      @Chomusuke71 3 роки тому

      do u mean the functions inside the determinant?

  • @mockingbird5919
    @mockingbird5919 3 роки тому +141

    When you're a visual learner, videos like this are an absolute godsend

    • @DrTrefor
      @DrTrefor  3 роки тому +15

      Thank you!

    • @aashsyed1277
      @aashsyed1277 Рік тому +3

      Watch veritasium's video .
      There is no such thing as visual learners

    • @ShanBojack
      @ShanBojack Рік тому +1

      ​@@aashsyed1277exactly

    • @herobrine1847
      @herobrine1847 Рік тому +2

      When you are any* learner

    • @ShanBojack
      @ShanBojack Рік тому

      @@herobrine1847 real

  • @aadi.p4159
    @aadi.p4159 4 роки тому +323

    Can I report this video for too eye opening

    • @benjiusofficial
      @benjiusofficial Рік тому +5

      tfw your 3rd eye is so open you become a 4 eyes

    • @Saujas
      @Saujas 18 годин тому

      @@benjiusofficial as a person with glasses i am offended

  • @SuperDeadparrot
    @SuperDeadparrot Рік тому +1

    This guy is doing exactly what I used to do and get wrong all the time! I eventually learned that you don’t define u= f( x, y ), v= g(x, y ) but you imagine the BACKWARD transformation, x = F( u, v ), y = G( u, v ).

  • @abhinavhampiholi54
    @abhinavhampiholi54 4 роки тому +95

    I had taken multivariable calculus a couple of years ago and needed a refresher. This was great!

  • @lancelovecraft5913
    @lancelovecraft5913 4 роки тому +34

    Excellent vid my friend. I took multivariable calc years ago and never really understood the jacobian or its purpose. Your explanation made it so simple and obvious. Thank u

  • @TANHA-xh6ok
    @TANHA-xh6ok Місяць тому +1

    Just watched the multivariable calculus playlist in one go as I have my viva exam coming up. I had learnt it all before but forgot most of the things due to few months of gap. I'm so glad that this playlist exists. Thank you so so so much!! This worked as a great revision material for me.

  • @kabascoolr
    @kabascoolr 3 роки тому +2

    I am actually shook. Whenever I watch videos like these, I expect to be disappointed. But when you started discussing the cross product, everything suddenly clicked.

  • @GoutamDAS-ls1wb
    @GoutamDAS-ls1wb 2 роки тому +3

    Thank you Professor Bazett for an excellent video on the Jacobian. I am taking Multivariable Calculus (II) right now on edX offered by MIT but I always return to your videos because of your clear and lively teaching style. I look forward to many more. You make the videos entertaining as well!

  • @Harry-ub2fv
    @Harry-ub2fv 4 роки тому +5

    That one dislike is given by a man who didn't even know the single variable calculus. Awesome explanation Sir!❤

  • @menoima9501
    @menoima9501 3 роки тому +2

    underrated,underrated,underrated,underrated,underrated,underrated,underrated,underrated,underrated

  • @99chartered
    @99chartered 2 роки тому +1

    I was about to google to find out the reason why we needed the Jacobian, your video presented is so beautifully it can't be beaten!!. Thank you so much !!

  • @unsaturated8482
    @unsaturated8482 4 роки тому +40

    no one can dislike this video

  • @sdsa007
    @sdsa007 Рік тому

    I’m a visual learner too… but being a stupid visual learner i had to watch this twice, because the first time i was watching it in small screen mode… small screen mode confused me because the dark red font used for J was no J enough, so i thought it was a close bracket… and this distracted me to no end looking for an open bracket in small screen mode. Jeeeez… I was so relieved after switching to a larger screen to make up for the idiosyncratic font style for depicting J… But i am definitely reaching my end goal of getting better intuition on cross product, curl, determinants and Jacobian! Thank You!

  • @Harry-ub2fv
    @Harry-ub2fv 4 роки тому +7

    This channel doesn't make me feel that I'm quarantined at home.:)

  • @fidelazuara5352
    @fidelazuara5352 4 роки тому +2

    This is the absolute best explanation on the topic I've watched so far!

  • @ProCelestialEmpire
    @ProCelestialEmpire Рік тому +1

    Thanks a lot Dr. Bazett! I searched many materials and so far to me you are the only one that made the vectors transform part clear. Subscribed.

  • @briandwi2504
    @briandwi2504 2 роки тому +2

    That was the last one of the whole series on Calculus 3. I watched every one and they were brilliant. Thanks for all the insights.

  • @tomatrix7525
    @tomatrix7525 4 роки тому +5

    This was absolutely top class as far as an explanation on an advanced topic can be. Great

  • @reinliu5090
    @reinliu5090 3 роки тому +1

    This is the best tutorial on change of variables I've watched!

  • @maxpercer7119
    @maxpercer7119 4 роки тому +13

    Jacobians tie together powerful ideas from linear algebra and calculus.

  • @proxy8918
    @proxy8918 3 роки тому +2

    You are so good at explaining the intuition of things. You are a great teacher, thank you.

  • @PinakCborty
    @PinakCborty 4 роки тому +1

    This is one of the most beautiful explanations on the intuition behind Jacobian I have come across on youtube. Thank you.

  • @maulaahmad2542
    @maulaahmad2542 6 місяців тому +1

    I was banging my head trying to understand the jacobian cuz it was introduced with the chain rule topic in my school. This video just made it very easy to undertand now. Thank you very much

  • @emc2884
    @emc2884 2 роки тому +2

    Thanks sir after exploring whole day in youtube to understand the jacobian your single lecture gave me a tremendous touch of the concept of jacobian
    Really sir you are genius and also have very good experience as compared to other professionals 🥰🥰🥰🥰

  • @mnada72
    @mnada72 3 роки тому +7

    This channel is awesome 👌 You bridged the gap of the required imagination to understand the concepts by the brilliant use of animation. Explaining something that can be seen brings the beauty of Math. I am following all your playlist just to learn and see again this beauty which I missed before . Thank you 😊 Moving on to Calculus IV 👋

    • @DrTrefor
      @DrTrefor  3 роки тому +1

      Thank you! Have fun in calc4:)

  • @walac
    @walac 4 роки тому +5

    Man, I was struggling to understanding the reasoning behind the Jacobian, but your video provided me the insight thanks a lot!

  • @AmitKumar-ud7yq
    @AmitKumar-ud7yq 3 роки тому +4

    Never found mathematics this much interesting.. Thank you for all the efforts you have made for us sir.# respect

  • @secretaryfig5364
    @secretaryfig5364 Рік тому

    AS SOON AS I SAW PARALLELOGRAM AND HEARD CROSS PRODUCT IT ALL CLICKED; THANKS MAN

  • @jonasfarbo2661
    @jonasfarbo2661 4 роки тому +2

    The motivation for the Jacobian explained with the u-substitution method from calculus 2 was very helpful for my intuition behind this topic. Thank you.

  • @ayush9psycho
    @ayush9psycho 2 роки тому +1

    simply amazing...! this is such a wonderful explanation..!! I am really sick of the way they have been teaching this stuff at university..!!

  • @SAVO-hp4yq
    @SAVO-hp4yq 2 роки тому +1

    I love your attitude! You make Calculus so much more enjoyable to learn :)

  • @drewmariani2964
    @drewmariani2964 3 роки тому +1

    That explanation about the origin of the Jacobian factor is very helpful!!! Thank you!!!!!

  • @Franko1411
    @Franko1411 2 роки тому +1

    Thank you so much for this video. I wish my Calculus 2 classes were this straightforward.

  • @foivossourlas
    @foivossourlas 2 роки тому +1

    What an absolute legend, thank you so much for this.

  • @continnum_radhe-radhe
    @continnum_radhe-radhe 2 роки тому

    I never think that i understand this concept in such an easy manner 🙏🙏🙏

  • @bird9
    @bird9 3 роки тому +1

    Thanks !
    you truly deserve more subscribers !

  • @sheetalmadi336
    @sheetalmadi336 3 роки тому +1

    I always feel you are underrated.

  • @samwhite4284
    @samwhite4284 2 роки тому

    at no point in my maths undergrad did any of notes/proffs explain the (actually simple) motivation for transforming with the Jacobian as well as this video - it was v enlightening... Thanks a lot!

  • @nomachinesinthisroom
    @nomachinesinthisroom 7 місяців тому

    Your explanations have helped me a lot, I am very grateful!
    Thank you very much for creating context at the beginning of each of your videos and for making such clear points!

  • @thisisntdana5222
    @thisisntdana5222 2 роки тому +2

    Have my calc 3 final today and this is such an amazing review!! Thank you!

  • @AJ-et3vf
    @AJ-et3vf 2 роки тому +2

    Awesome video! Thank you! Interesting how the Jacobian features into integration when I first learned it for using newton's method for vector functions and vector root-finding, needing to get the partial derivatives of the vector function F.

  • @CalculationStation
    @CalculationStation Рік тому

    Wow... Simple and best explanation 👌

  • @Rogue_Art
    @Rogue_Art 3 роки тому +1

    That part at the end was mindblowing. That literally tied everything together and I can't believe they never showed that between my professor's lectures and two textbooks!

    • @DrTrefor
      @DrTrefor  3 роки тому +5

      isn't that part cool!?

  • @menoima9501
    @menoima9501 3 роки тому +8

    this literally saved me from failing in my exams

  • @TN6625
    @TN6625 4 роки тому +3

    A really informative explanation and presentation!

  • @dekkeroid2962
    @dekkeroid2962 2 місяці тому

    i finally understand why i kept hearing about this dawg so much

  • @sayannitdgp8957
    @sayannitdgp8957 2 роки тому +1

    finally this topic got crystal clear.....thanks a lot 😊😊

  • @SanjiZoroAnime
    @SanjiZoroAnime 3 роки тому +2

    Wow, I can't believe, you made this look so easy now ✨🌺, you are best 🙏

  • @redone9553
    @redone9553 3 роки тому +1

    Thank you finally a rigorous explanation

    • @DrTrefor
      @DrTrefor  3 роки тому +1

      Glad it was helpful!

  • @shirsenduroy19-7
    @shirsenduroy19-7 6 місяців тому +1

    Ohh , i was looking for the video ans now i have found it
    Nice explanation sir for the basic

  • @propoop6991
    @propoop6991 Рік тому +1

    this is such a good intuitive explanation, my textbook just derived it without any intuition lol

  • @anguszou3477
    @anguszou3477 2 роки тому +2

    Feels like Obi-Wan Kenobi's Brother is teaching me math QAQ.

  • @TheMrMEEEEE
    @TheMrMEEEEE 2 роки тому +1

    SOOOOOOO helpful. Thank you for taking the time to make this!

  • @mayanksinha1883
    @mayanksinha1883 2 роки тому +1

    dudee explained so well sire!!! thanksss a ton

  • @olehborys1462
    @olehborys1462 Рік тому

    That was amazing, visualisation hits different from a table at university. Thanks!

  • @ImJustSoOriginal
    @ImJustSoOriginal 3 роки тому +1

    Thank youuuuu! Got my 3rd year finals coming up and this really helped me get my head around it. :)

  • @lucasfrykman5889
    @lucasfrykman5889 2 роки тому +2

    9:10 that explaination was excellent. It seems stupidly obvious now why we scale with the jacobian that I'm kind of dissapointed I didn't try to heuristically derive it myself. Damn.

  • @junyili-dh8be
    @junyili-dh8be Рік тому

    Love it, it makes a clear picture to me

  • @hienhoangminh1370
    @hienhoangminh1370 3 роки тому +1

    it's just too great and your voice is amazing

  • @mdyasir25
    @mdyasir25 3 роки тому

    Completed the multivariable calculus for the first time with intuition and visualisations. Thanks Professor. Looking forward for Ode series.

    • @DrTrefor
      @DrTrefor  3 роки тому +1

      Congrats on making it to the end!

    • @mdyasir25
      @mdyasir25 3 роки тому

      @@DrTrefor Thanks ❤️❤️❤️

  • @profarvind
    @profarvind Рік тому

    Sir, you are brilliant. Thanks a zillion.

  • @georgebayliss6177
    @georgebayliss6177 4 роки тому +1

    Watching this at 2am studying for tomorrow’s final. Thank You!

  • @kevinjavanmardi6165
    @kevinjavanmardi6165 Рік тому +1

    Hi there! Thank you so much for this video!! I was wondering if there is an explanation on how to invert the Jacobian matrix if solving for y and x becomes messy.

  • @sakshambhatnagar7386
    @sakshambhatnagar7386 26 днів тому

    sir ur videos are magical !!😌

  • @meredilkibaat7467
    @meredilkibaat7467 3 роки тому +1

    very very helpful and I love the way you explain!!

  • @christoskettenis880
    @christoskettenis880 3 роки тому +1

    Very nice explanation!

  • @scientist1905
    @scientist1905 Рік тому

    best explanation + nice visualization

  • @TheVigyanPodcast
    @TheVigyanPodcast 4 роки тому +1

    Finally i understand this J. Great video sir😊

  • @BadAss_691
    @BadAss_691 11 місяців тому

    Jacobian also takes you from moving frame from rest frame via Lorentz Jacobian in Minkowski space which is just a hyperbolic rotation

  • @MrBurstfire99
    @MrBurstfire99 2 роки тому

    Excellently explained

  • @PunmasterSTP
    @PunmasterSTP 15 днів тому

    Jacobian? More like "Just awesome; you're the man!" 👍

  • @anikethdesai
    @anikethdesai 4 місяці тому

    I wish I could like this video more than once

  • @dtgiabao9915
    @dtgiabao9915 2 роки тому +1

    Thanks you Dr Trefor! Absolutely amazing explaination :))

  • @hubenbu
    @hubenbu 2 роки тому

    It takes time to finally figure out why Jacobian determinant works in variable change of double integral. I traced back the dependency and find a resource that is as great as this one, the jacobian matrix section from Khan academy.

  • @continnum_radhe-radhe
    @continnum_radhe-radhe 2 роки тому +2

    Thank you so much sir 🔥🙏🔥

  • @lucanicoletti4133
    @lucanicoletti4133 11 місяців тому

    You make amazing videos, bless you!

  • @desaisandeep2070
    @desaisandeep2070 3 роки тому +2

    your videos are very helpful !!

  • @the_fundamental_theor3m
    @the_fundamental_theor3m 3 роки тому +1

    This blew my mind 🤯

  • @chevycecil233
    @chevycecil233 3 роки тому

    I was really stuck on this concept for my class, but after this i now understand what i was doing wrong

  • @youw6876
    @youw6876 3 роки тому +1

    This is just soooo beautiful and mind-blowing! Thank you so much for the great explanation :)

  • @obitwokenobi69
    @obitwokenobi69 7 місяців тому +1

    At 9:10, the cross product is the same as the determinant of the two vectors as far as I understand. Then how the heck is du and dv OUTSIDE of the determinant, arent they a part of the vectors that should go in to the determinant? Thanks

  • @Manoj_b
    @Manoj_b Рік тому

    This channel is so.... Good

  • @kylevebar3909
    @kylevebar3909 3 роки тому +1

    Just finished playlist very good introduction to the material

    • @DrTrefor
      @DrTrefor  3 роки тому +2

      Congrats on making it to the end!

  • @liviumircea6905
    @liviumircea6905 4 роки тому +1

    Brilliant explanation sir ! I got stuck on the subject trying to understand 3blue1brown's ideas..anyway these last minutes from this video made me to understand Grant's

  • @GeekyGothJussi
    @GeekyGothJussi 2 роки тому +1

    Always love your videos. Thank you!

  • @walidkerchouche1727
    @walidkerchouche1727 3 роки тому +1

    Very good video thanks for your help.

  • @jaydipvasani
    @jaydipvasani Рік тому +2

    like video because of content and explaination .
    create series on tensor.
    👍👍👍👍👍👍👍
    👍👍👍👍👍

  • @oraz.
    @oraz. 6 місяців тому

    Could you find the scaling factor in 1d U sub, instead of treating du/dx as a fraction and solving, by using the Jacobian in some single variable way and get the same scaling value?

  • @user-or7ji5hv8y
    @user-or7ji5hv8y 3 роки тому +1

    great content. excellent that you made the connection with change of variable and help see that connection. thanks

    • @DrTrefor
      @DrTrefor  3 роки тому +2

      Glad it was helpful!

  • @sukranochani5764
    @sukranochani5764 3 роки тому +1

    very nice sir, you solved my dought which was prevailing from years in mimd.

  • @sudeshdas9998
    @sudeshdas9998 3 роки тому +1

    Awesome explanation...
    Thank you sir...💜

  • @HowToTechChannel
    @HowToTechChannel Рік тому +1

    Thank you for the amazing content!

  • @tim-701cca
    @tim-701cca Рік тому

    Thank you very much, this helps a lot. I still have a question why the Jacobian is defined in the matrix of these orders, not define as it’s transpose?

  • @soumapriyamondal3808
    @soumapriyamondal3808 4 роки тому +1

    very nicely explained...

  • @SerdceDikarya199
    @SerdceDikarya199 3 роки тому +3

    I owe my first trimester of college to you !!😂

  • @nosms6581
    @nosms6581 Рік тому

    Hi Dr.Trefor I really love the way you teach math. But I have a question. Should we take the absolute value of the Jacobian in the substitution? Thanks in advance

  • @Bl1tzkr13g
    @Bl1tzkr13g 4 роки тому

    Thank you so much Trefor, your series of videos really helped me clarify some questions I had from Calculus Adam's textbook.. Keep up the great work and thanks for teaching! :)