Directional Derivatives | What's the slope in any direction?

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  • Опубліковано 16 лис 2019
  • A directional derivative gives the slope in any particular direction, similar to partial derivatives which give the slope just in the x or y directions. We formally define directional derivatives by modifying the familiar limit definition of the derivative for when you move along some vector in the input space. Then we see a very nice feature that we can use the gradient vector grad(f) to make computing directional derivatives easy. If you have the gradient, you can get the directional derivative in the u direction with one easy dot product.
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КОМЕНТАРІ • 350

  • @subse5371
    @subse5371 3 роки тому +153

    I'm an undergrad and believe me this is the first time i understood anything about calculus hats off man👍

    • @kafuu1
      @kafuu1 9 місяців тому +1

      thats the power of Internet

    • @mikzin630
      @mikzin630 8 місяців тому +8

      you made it to calc 3 without ever understanding anything about calculus?

    • @shivangsingh5834
      @shivangsingh5834 5 місяців тому +1

      ​@@mikzin630😂😂

  • @broqentoys
    @broqentoys 4 роки тому +131

    self-studying this over the summer.... wish u were my teacher!! thank you

  • @jaydean5243
    @jaydean5243 3 роки тому +59

    Dr Bazett, your videos are incredible , concise , animated, and to the point, VERY well done.
    I'm a retired pharmacist , in my spare time i try to keep learning advanced math. were I left off with
    adv calculus , and ODE (1974) . I appreciate all your time and effort THANK YOU....Jay

  • @chetanraina5649
    @chetanraina5649 4 роки тому +6

    This is the best explanation of directional derivatives. Please never delete these videos.

  • @v-doc5230
    @v-doc5230 3 роки тому +45

    I am a very experienced engineer, studied mathematics in five different lectures, not including mathematic heavy lectures like aerodynamics, gas dynamics, etc. Yet, I never saw it that way. Very well done and informative! Thanks!

  • @samyakgupta4301
    @samyakgupta4301 3 роки тому +13

    Didn't knew that PewDiePie was such a great teacher.
    Okay sorry. You are awesome Dr. Bazett.

  • @dushyantsengar9381
    @dushyantsengar9381 4 роки тому +71

    Amazing animation at start to show directional derivatives. I have really got a better understanding to how to visualize the directional derivative now. Amazing video..keep up the good work :)

  • @pultural
    @pultural 3 роки тому +4

    This video was like the last brick in the wall of understanding gradient and partial derivative, that's insane..I get my 'ahaaaa' moment so fast! Thank you so much, also for explaining how we came from limit to composition function and after applying the chain rule to dot product of gradient vector in the point and unit vector!

  • @muhammadharoonlatif5154
    @muhammadharoonlatif5154 3 роки тому +5

    Some of the videos I just watched them because they were so engaging, despite not being part of my syllabus.

  • @effizienzlizenz
    @effizienzlizenz 4 роки тому +18

    I love your enthusiasm. Calculus is beautiful once one has grasped the logic behind algebraic framing of questions.

  • @AndyOrtiz93
    @AndyOrtiz93 7 днів тому +1

    This video is INSANE. Learned more from this than a 2-hour lecture from my professor 😭

    • @user-jc2uv4re8h
      @user-jc2uv4re8h 6 днів тому

      I don't know why school doesn't teach this way. They only give a bundle of complex formulas without comprehensive explanations and then assign a ton of tedious homework. Thanks to this 12-minute video and a bit of imagination, I can handle all of it.

  • @Hinchey613
    @Hinchey613 16 днів тому +1

    The visual explanation up to 2:40 really helped me understand the main concept better.

    • @DrTrefor
      @DrTrefor  14 днів тому +1

      Glad it helped!

  • @donlansdonlans3363
    @donlansdonlans3363 4 роки тому +23

    Omg finally I understand this

  • @tuncerakilli
    @tuncerakilli 30 хвилин тому

    Gradient vector is such an awesome property when dotted with u unit vector evaluated at a point on a x-y plane in 3D space! Thanks a lot and much appreciated!

  • @MinhLe-se6bs
    @MinhLe-se6bs 3 місяці тому

    Thanks for your explanation. Please never delete this video. You inspire students who want to see the beauty of math. Thanks again.

  • @rockyjoe3817
    @rockyjoe3817 Рік тому +1

    I am so happy to see your channel getting the recognition it deserves . You really saved me during university period.

  • @darkphoenix_007
    @darkphoenix_007 Рік тому +6

    Amazing Dr.Trefor.. Never imagined the concepts in this way. Please continue making videos. Big fan

  • @arthurbaz2
    @arthurbaz2 2 роки тому +1

    I've studied this in Calculus about four years ago, but never actually learned it. This helped a lot, thank you!

  • @vahegizhlaryan5052
    @vahegizhlaryan5052 3 роки тому +3

    Certainly the best explanation of DD I've seen so far) I had several "wow" moments during this video)

  • @yashmohangupta5379
    @yashmohangupta5379 3 роки тому +2

    Holy smokes!!! . how can a student not fall in love with you sir ? . Just struck in awe.

  • @Alexanderkermani
    @Alexanderkermani 3 роки тому +2

    This was a stellar video on a topic that I could not wrap my head around. Thank you.

  • @squidsword0
    @squidsword0 2 роки тому +9

    Thank you! Everything feels so complicated looking at the notation from far away, but somehow it becomes so intuitive the way you present it. I feel so empowered right now.

  • @sashamuller9743
    @sashamuller9743 4 роки тому +1

    the visuals and your teaching really make it!

  • @altaccproxy9890
    @altaccproxy9890 3 роки тому +2

    Incredible explanation! So detailed and easily understandable!

  • @derickblacido2267
    @derickblacido2267 3 роки тому +1

    Thanks so much Dr Trefor. I was stumbling on this topic for about a month withouth getting the gist of the formula IN GEOMETRICAL terms. Now I can see ligth in my seemingly enduring night. Greetings from Peru.

  • @___SSS___
    @___SSS___ 3 роки тому +1

    Maths is more fun if we can visualise it rather than mugging up formulae . We need teachers like you . 😍😍😍😍😍👏

  • @fraserpye9667
    @fraserpye9667 9 місяців тому

    This man is a genius at geometric intuition for calculus. Help me alot, thank you.

  • @user-wu8yq1rb9t
    @user-wu8yq1rb9t 2 роки тому +2

    When I watched your videos, my feeling is changing, and I know why!
    It's because of harmony! There is a beautiful harmony on your Math and your teaching.
    I take an oath, Everytime I'm watching your Math at first I enjoyed and then I'm learned.
    You can change my mood! (It means a lot for me)
    Thank You SoOoOo Much Teacher ❤️
    ((I'm sorry, I forget to say hello !!!
    Hello teacher))

  • @iskur_
    @iskur_ 3 місяці тому

    I'm and engineering undergrad and I had no idea how to solve these questions without overcomplicating it until I saw your videos.
    Really appreciate the videos and how you also talk about the theory behind the equations.

  • @jadkhalil9263
    @jadkhalil9263 2 роки тому +2

    You make calculus easy to understand and fun, keep up the good work!

  • @mirandagonzalez5586
    @mirandagonzalez5586 4 роки тому +1

    Great video.
    I am watching this during my attempt to stay accountable in my semester during COVID-19 and you are really helping me not only to understand better but also to stay interested in this subject
    Thanks!

  • @guitarttimman
    @guitarttimman 4 роки тому +3

    This is a great demonstration. Thank you.

  • @blankspace1959
    @blankspace1959 2 роки тому +1

    amazing content, I always appreciate a skilled mathematician.

  • @leadtoexemplify
    @leadtoexemplify 3 роки тому +2

    Dr Trefor, many will remember you for life time. God bless you.

  • @levimungai1846
    @levimungai1846 Рік тому

    The normal partial derivative is a special case of directional derivatives where you dot the gradient of F
    with the common unit vectors(i,j,k) or(1,1,1). Your explanation is very insightful.Great video

  • @LudusYT
    @LudusYT 4 роки тому +8

    Hey man, I love your videos! Quick question, how do you make those graphs & animations? Python I assume?

    • @LudusYT
      @LudusYT 4 роки тому +2

      Trefor Bazett - Sweet thanks!

  • @danamvenkata
    @danamvenkata 3 роки тому

    i have been searching for simple detailed explanation since very long before i found this.... Thank you very much

  • @a.b.6677
    @a.b.6677 6 місяців тому

    Wow, brilliant & beautiful, I watched the video 2 or 3 years ago, & I still enjoy going back to it, kudos Professor

  • @jacobvandijk6525
    @jacobvandijk6525 4 роки тому +2

    Nice combination of graphs and equations. Good stuff!

  • @madhavkawagucci8539
    @madhavkawagucci8539 3 роки тому +12

    why do good teachers and professors exist only online :(. Amazing video

    • @carultch
      @carultch Рік тому +1

      Trefor teaches in person as well.

  • @praveenbethini7126
    @praveenbethini7126 3 роки тому +1

    I wish I had a maths teacher like you
    THANK YOU VERY MUCH 🙏

  • @siwasoontreerat6125
    @siwasoontreerat6125 2 роки тому +6

    Best directional derivative explanation. I once learn this when I was in engineering school but I have no idea what does it mean. Now I clearly understand it. Thank you. ^ ^

  • @tanayasharma7776
    @tanayasharma7776 3 роки тому +1

    the visual explanation helped me a lot ,I'm extremely happy for some reason after watching this video, thanks a lot.

  • @arnavbhavsar8567
    @arnavbhavsar8567 3 роки тому

    Earlier I didn't understand this but now I appreciate how beautiful calculus is

  • @SUMITKUMAR-ox5gg
    @SUMITKUMAR-ox5gg Рік тому +1

    Very well explained with proper intuition with real graphs
    There was a lot of help while understanding with graph
    Things get more real and understandable when done with actual graphs

  • @abdulghanialmasri5550
    @abdulghanialmasri5550 2 роки тому +1

    You are really one of the best teachers.

  • @shanmukh3174
    @shanmukh3174 10 місяців тому

    I have never seen this kind of detailed and articulate explanation
    Thanks a lot sir 🙏

  • @bitbyte8177
    @bitbyte8177 3 роки тому +5

    4:57 That's what she said.

  • @ycc_j
    @ycc_j Місяць тому +1

    Such clear explanation. I couldn’t understand anything my professor said in class but you made it so easy to learn. Thank you so much!

  • @anshikatyagi6533
    @anshikatyagi6533 3 роки тому

    The animation was amazing and the way u explained was really nice, we are today complaining abt this online education whereas mentors like had been acing this skill since forever, just WOW

  • @dianafarhat9479
    @dianafarhat9479 4 місяці тому

    All channels explain the concepts, but never solve p-sets and think out loud. Your explanation is amazing, would really love to have such videos.

  • @sarvanray3971
    @sarvanray3971 3 роки тому +1

    Have never seen such a logical explanation.

  • @irfanelahi1384
    @irfanelahi1384 Рік тому +1

    Maza Agiya Bahi sahb❤👍

  • @aldoperez8551
    @aldoperez8551 4 роки тому +1

    Beautiful Explanation. Thank u so much

  • @leadtoexemplify
    @leadtoexemplify 3 роки тому +2

    I am surprised that only 1.8k thumbs up when 38k people watched it. This video deserves 38k thumbs ups.

  • @waqasmuneer7951
    @waqasmuneer7951 2 роки тому

    Amazing Dr Trefor. The combo of 3blue 1 brown + Dr Trefor= Mastery of the subject.... No need to go anywhere.

  • @walac
    @walac 3 роки тому +3

    Best explanation of directional derivatives I’ve ever seen!

  • @edgbaston149
    @edgbaston149 3 роки тому +1

    I am so happy UA-cam recommended me your videos.😊
    Lots of love from India 🇮🇳❤

  • @SathanaST
    @SathanaST 3 роки тому +1

    Wish others that are struggling find this video, Thank you for making the video.

  • @alicebobson2868
    @alicebobson2868 Рік тому

    i always come to your channel whenever im stuck on a topic, you have the best explanations ever!!! thanks!

  • @asme212
    @asme212 2 місяці тому

    Very illustrative and visual. Thank you.

  • @ayushthada9544
    @ayushthada9544 3 роки тому +10

    I had some confusion over differential surface traversal and I ended up on your video. It is a great help. Thank you for posting these amazing videos.

  • @henriquenunes7196
    @henriquenunes7196 2 роки тому +1

    Thank you. Important stuff made simple by your expert video. Outstanding.

  • @temesgentesfaye9584
    @temesgentesfaye9584 5 місяців тому

    Clear & concise. 👏

  • @yashodabhattarai4206
    @yashodabhattarai4206 2 роки тому +2

    Wow, this is extraordinary explanation 👏👏👏

  • @yuheonjoh1336
    @yuheonjoh1336 4 роки тому

    Just AMAZING! Thank you!!!

  • @xiu8548
    @xiu8548 4 роки тому +3

    Cool animation!!!!!! I understand it right away! !

  • @reubenjames8836
    @reubenjames8836 4 роки тому

    great stuff dude! deserves more attention

  • @codedoc1046
    @codedoc1046 4 роки тому +2

    Thanks this cleared things up for me.

  • @abhayranjith
    @abhayranjith 3 роки тому +1

    I wasn't able to understand anything from class for the topic of partial derivatives, but I'm starting to understand now, thanks to your videos

  • @Inkidinkichi
    @Inkidinkichi 3 роки тому +1

    I really wished if you were my tutor! Until now I was just memorizing those formulas! Thank-you sir! Love from india!

  • @ssoomi
    @ssoomi 3 місяці тому

    dude you just saved my life. thank you so much 🙏🙏

  • @bobbysokhi7296
    @bobbysokhi7296 Рік тому

    Amazing Video ! Supplementing this with my lecture notes ! Thank you professor.

  • @cherylzhang1189
    @cherylzhang1189 Рік тому

    Your diagram was so helpful!! I have been struggling to understand the idea of directional derivatives and this video helped so much!

  • @solmaths
    @solmaths 2 роки тому

    Simply fantastic !

  • @blymark83
    @blymark83 3 роки тому +4

    This is a wonderful video! The visuals are just about perfect, and your using the chain rule to inspire the dot product formula is quite lovely!
    As a fellow university educator, I've stumbled upon a number of your videos previously and this is among my favorites!
    You're providing a significant service to the undergraduate mathematical community! Your efforts are appreciated.

    • @DrTrefor
      @DrTrefor  3 роки тому +3

      Thank you so much for your kind words:)

  • @marlorizkalla5889
    @marlorizkalla5889 Рік тому +1

    So great way explaining this lesson , Very well done prof .

  • @doeunkwon4607
    @doeunkwon4607 3 роки тому +1

    Thank you so much, Dr. Bazett

  • @sudarshanv9797
    @sudarshanv9797 2 роки тому +1

    This one video cleared all my questions on multivariate calculus

  • @subhamadhikari
    @subhamadhikari 7 місяців тому +1

    The explanation was concise and very clear.

  • @joaomattos9271
    @joaomattos9271 Рік тому

    Fantastic way of teaching!!! I recommend the classes here in Brazil!

  • @nuthakantirohan4685
    @nuthakantirohan4685 2 роки тому +1

    incredible i was strugling to understand this by reading and visiualizing thank u so much nice explanation along with the killer graphics

  • @curiousman1812
    @curiousman1812 3 роки тому

    You Nailed It !

  • @julioreyram
    @julioreyram 3 роки тому

    Brilliant explanation, thank you very much

  • @Junker_1
    @Junker_1 3 роки тому +1

    Thanks for all this wonderful explanation.

  • @alijoueizadeh2896
    @alijoueizadeh2896 6 місяців тому

    Thank you for your time and effort.

  • @shuvohasan8223
    @shuvohasan8223 2 роки тому +1

    You're the greatest teacher I never had... ❤❤❤

  • @codyr9951
    @codyr9951 2 роки тому +1

    Great explanation!

  • @mirmos
    @mirmos Рік тому

    Thank you for this beautiful advanced explanation. Both animations and expressions were excellent :)

  • @curiousman1812
    @curiousman1812 3 роки тому

    Mind blowing !

  • @youssefdirani
    @youssefdirani 2 роки тому +1

    Thanks a lot Dr.

  • @xxyhop
    @xxyhop 3 роки тому +1

    Very nice explanation, thank you!

  • @jeankayembe5775
    @jeankayembe5775 4 роки тому

    You’re the best!!!!! Thank you so much for your help 🙂

  • @psiandschrody4160
    @psiandschrody4160 8 місяців тому

    Thank you! This video was very helpful!

  • @saralewis99
    @saralewis99 3 роки тому +1

    Love your passion!

  • @norapatharjanurak1212
    @norapatharjanurak1212 2 роки тому +1

    Thank you 😀. This video helps me alot.

  • @alizerg
    @alizerg Рік тому

    Thanks Doc, this was really helpful.

  • @sumitkumarsahoo7601
    @sumitkumarsahoo7601 3 роки тому +2

    thanks, great intuition great teacher, well done sir

  • @mostafakooti7729
    @mostafakooti7729 2 роки тому +1

    Very nice
    Easy to understand

  • @rutika17
    @rutika17 3 роки тому +1

    Wow🤩 best explanation