Khan Academy Video 1 (Gradient vs. Directional Derivative)

Ғылым және технология

Пікірлер: 342

  • @joereadman4390
    @joereadman43905 жыл бұрын

    can we all just take a moment to appreciate that she managed to write the word 'gradient' whilst spelling the word 'tail' out loud? this is a talent!

  • @user-wr8yg8ix6r

    @user-wr8yg8ix6r

    4 жыл бұрын

    meanwhile, me who can't even spell her own name while spelling her father's name out loud

  • @nuklearboysymbiote

    @nuklearboysymbiote

    4 жыл бұрын

    tale* she literally spelled it out loud too

  • @ehinspections
    @ehinspections2 жыл бұрын

    This video has to be the best explanation of the Gradient in KZread, well done!

  • @rhondahughes9648

    @rhondahughes9648

    2 жыл бұрын

    Thank you so much!

  • @wwmheat
    @wwmheat2 жыл бұрын

    Wow, it's a standing ovation!! Having watched all the great content available now in 2022 on this topic (3b1b, Grant's explanation in Khan academy and others), I still couldn't get why directional derivative can be expressed by gradient and dot product.. I mean, it certainly makes sense as a vague statement, it has an intuitive support, but I couldn't get it rigorously, including how it can be derived purely in terms of definition of derivative. And now finally it's crystal-clear!

  • @rhondahughes9648

    @rhondahughes9648

    2 жыл бұрын

    Thank you for those kind words!

  • @scottkelly3062
    @scottkelly30628 жыл бұрын

    I see you just made this video a few months ago. I hope you make some more videos. This was the best youtube video on any topic on Calculus I have watched. I find that most videos rush into an example or start off a concept slow and when it gets to the abstract part speed it up. This one stays consistent throughout and maybe even slows down to help the viewer. This was just great.

  • @rhondahughes9648

    @rhondahughes9648

    8 жыл бұрын

    +Scott Kelly Thank you, I appreciate that!

  • @alexramirez5104
    @alexramirez51047 жыл бұрын

    Haha! The "Is that middle earth? I don't know" remark had me cracking up! Thanks so much!

  • @rhondahughes9648

    @rhondahughes9648

    7 жыл бұрын

    Thank YOU, Alex!

  • @ozzyfromspace
    @ozzyfromspace4 жыл бұрын

    2:57 When she said "at any rate..." I immediately thought of professor Herbert Gross (an extraordinary MIT math educator from the 1960's). I like Rhonda's style and pace of teaching, it's almost like a conversation. Best wishes!

  • @rhondahughes9648

    @rhondahughes9648

    4 жыл бұрын

    Thank you!

  • @johnholme783
    @johnholme7835 жыл бұрын

    Beautiful! So simple, yet so useful.

  • @muralidhar40
    @muralidhar406 жыл бұрын

    I was hopping from one video after the other on youtube to find the difference between DD and Gradient, My journey has come to an end. Thank you madam/miss.

  • @rhondahughes9648

    @rhondahughes9648

    6 жыл бұрын

    I'm happy to hear that!

  • @justwatchingmathvideos130
    @justwatchingmathvideos130 Жыл бұрын

    thanks, now i see that the vector can be used in a parmetric equation. that helped a lot.

  • @PhilV205
    @PhilV2058 жыл бұрын

    I hope to see many more videos from you. I had a hard time seeing the difference between the two but those days are long gone. Thanks again

  • @Raynover
    @Raynover3 жыл бұрын

    Enlightening from start till end. Unbelievable! Great graph too.

  • @rhondahughes9648

    @rhondahughes9648

    3 жыл бұрын

    Thank you so much for your kind words!

  • @yj6439
    @yj64392 жыл бұрын

    Thank you very much for your video, Rhonda! It’s been a very long time ever since I first studied it, and I can tell you this. Despite all fashionable, computational stuff of our days, there’s nothing like the old school way to learn calculus! You covered the whole package in 14 minutes. Thank you again!

  • @rhondahughes9648

    @rhondahughes9648

    2 жыл бұрын

    You are welcome!

  • @robjows
    @robjows4 жыл бұрын

    Amzing Video. In my Calculus 1 class we've jumped from Integration techniques to the gradient vector and multi-variable chain rule - simply being taught the equations with no background on what we're actually doing. This video answered the majority of my questions.

  • @LearnPhysics-xz3mf
    @LearnPhysics-xz3mfАй бұрын

    I just can't think you enough ma'am, it's amazing, the relationship between directional derivative and gradient is just amazing, I'm just overwhelmed by the beauty of mathematics and teaching 💕💕💕

  • @rhondahughes9648

    @rhondahughes9648

    Ай бұрын

    Thank you so much!

  • @EvaPev
    @EvaPev8 жыл бұрын

    Wow! I'm impressed! Great intuitive explanation! Thank you very much for your effort!

  • @rhondahughes9648

    @rhondahughes9648

    8 жыл бұрын

    Thank you, Evelina.

  • @mateennaser5347

    @mateennaser5347

    7 жыл бұрын

    Please Miss Rhonda could you help me?I need your help, please if I could contact with your e-mail. My e-mail is (matalaubidy@gmail.com). Thanks.

  • @depresso18163
    @depresso181636 жыл бұрын

    This is amazing. I wish this channel had more videos on multivariable calculus.

  • @rhondahughes9648

    @rhondahughes9648

    6 жыл бұрын

    Thank you!! I've been working on other videos, but will try.

  • @solomonv4184
    @solomonv41847 жыл бұрын

    Awesome explanation!

  • @lythien390
    @lythien3904 жыл бұрын

    Wowww!! It's so fascinating. Thank you for being my savior in Calculus!

  • @rhondahughes9648

    @rhondahughes9648

    4 жыл бұрын

    Thank you!

  • @dangargiullo9634
    @dangargiullo96345 жыл бұрын

    Not even halfway through the video and I already feel like it all makes sense. By far the most helpful video I've watched on any multivar topic. Thank you SO MUCH!!!!

  • @rhondahughes9648

    @rhondahughes9648

    5 жыл бұрын

    Thank you!!

  • @Japzastronomy
    @Japzastronomy8 жыл бұрын

    Thank you so much, Rhonda! Finally a wonderful explanation to the concept. Good job! :)

  • @rhondahughes9648

    @rhondahughes9648

    8 жыл бұрын

    +Japjee Kaur Thank YOU, Japjee! I appreciate that.

  • @adnansakeeb739
    @adnansakeeb7392 ай бұрын

    OMG you are so good at what you do ! it instantly made sense. TYYY.

  • @rhondahughes9648

    @rhondahughes9648

    2 ай бұрын

    Thank you SO much!

  • @ting-yuhsu4229
    @ting-yuhsu42295 жыл бұрын

    Vielen lieben Dank! Sie haben echt gut gemacht! :D

  • @yavuzanyavuz
    @yavuzanyavuz7 жыл бұрын

    clearly one of the best video( maybe the best) about these topic. Appreciated!

  • @rhondahughes9648

    @rhondahughes9648

    7 жыл бұрын

    Thank you very much!

  • @student6830
    @student68304 жыл бұрын

    I solved an entire problem set of directional derivatives but didn't really know what they were about. This video helped me understand. Thank you.

  • @tifawine9113
    @tifawine91137 жыл бұрын

    It's Very helpful. Thank you 😀

  • @nichkvn
    @nichkvn8 жыл бұрын

    You did a wonderful job! Great clarity!

  • @rhondahughes9648

    @rhondahughes9648

    8 жыл бұрын

    +Nicholas Van Nest Thanks so much!

  • @salehahmed4139
    @salehahmed41394 жыл бұрын

    Best explanation of directional derivative, now I actually understand what the directional derivative" means.Thank you

  • @rhondahughes9648

    @rhondahughes9648

    4 жыл бұрын

    Thank you!

  • @abylkaiyromar4149
    @abylkaiyromar41496 жыл бұрын

    very informative lesson, thanks

  • @josegadelha8271
    @josegadelha82714 жыл бұрын

    Beautiful!!

  • @rhondahughes9648

    @rhondahughes9648

    4 жыл бұрын

    Thank you so much!

  • @epilepsyawareness
    @epilepsyawareness4 жыл бұрын

    very well done. concise. thanks.

  • @RepeatingData69
    @RepeatingData696 жыл бұрын

    Great approach to deriving it!!! I hadn’t seen it done this way. Very easy to remember.

  • @rhondahughes9648

    @rhondahughes9648

    6 жыл бұрын

    Thank you very much!

  • @garrettnicolay6310
    @garrettnicolay63104 жыл бұрын

    This was amazing. Eyes officially opened

  • @rhondahughes9648

    @rhondahughes9648

    4 жыл бұрын

    Thank you!

  • @shockban6725
    @shockban67255 жыл бұрын

    Incredible explanation!

  • @rhondahughes9648

    @rhondahughes9648

    5 жыл бұрын

    Thank you so much!

  • @mkalysto
    @mkalysto4 жыл бұрын

    Briliant! Clear and informative! Thank you

  • @rhondahughes9648

    @rhondahughes9648

    4 жыл бұрын

    Thank you!

  • @thinkanddo2352
    @thinkanddo23526 жыл бұрын

    Thank you so much Ms Rhonda!That was extremely helpful!

  • @rhondahughes9648

    @rhondahughes9648

    6 жыл бұрын

    You are very welcome.

  • @TeotoniodeCarvalho
    @TeotoniodeCarvalho7 жыл бұрын

    Very kind of you to share that! Thanks a lot!

  • @rhondahughes9648

    @rhondahughes9648

    7 жыл бұрын

    You're welcome!

  • @jessewilliams1276
    @jessewilliams12764 жыл бұрын

    This was much better than the video that they had on Khan Academy. At first i was upset that she named it the way she did, but after watching, i was glad that i was “click-baited” into watching this video 😅

  • @rhondahughes9648

    @rhondahughes9648

    4 жыл бұрын

    Not "click bait." This was an entry to the Khan Academy Talent Search several years ago.

  • @haroonj4298
    @haroonj42984 жыл бұрын

    They way you expressed the concept is the way we wanted, it is the way which fulfill our thirst and remove headache, diabetes and pregnancy.

  • @rhondahughes9648

    @rhondahughes9648

    4 жыл бұрын

    Thank you! That is quite a compliment.

  • @MrAshok34
    @MrAshok348 жыл бұрын

    The Perfect Explanation!!!!! :)

  • @rhondahughes9648

    @rhondahughes9648

    8 жыл бұрын

    +Harsha Vardhan Wow, thank you!!

  • @xavier.antony
    @xavier.antony Жыл бұрын

    Wonderful explanation just using marker and board.. Teaching Mathematics is an unique talent, not everyone can do that. Thank you..

  • @rhondahughes9648

    @rhondahughes9648

    Жыл бұрын

    Thank you so much!

  • @eduardopaiva4846
    @eduardopaiva48465 жыл бұрын

    Such an amazing explanation! Thank you!

  • @rhondahughes9648

    @rhondahughes9648

    5 жыл бұрын

    You are welcome!

  • 6 жыл бұрын

    Just the best!

  • @rhondahughes9648

    @rhondahughes9648

    6 жыл бұрын

    Thank you so much, Marcio!

  • @Jax-ke6jf
    @Jax-ke6jf3 жыл бұрын

    I was so confused on this until this video, thank you so much!

  • @rhondahughes9648

    @rhondahughes9648

    3 жыл бұрын

    Thank you!

  • @santoshijyothi7661
    @santoshijyothi76616 жыл бұрын

    Awesome.... impressive..... to the point.....I can't even imagine to find so much explanation anywhere

  • @rhondahughes9648

    @rhondahughes9648

    6 жыл бұрын

    Thank you!

  • @Jalpow
    @Jalpow8 жыл бұрын

    Great video, very helpful!

  • @rhondahughes9648

    @rhondahughes9648

    8 жыл бұрын

    +Aaron Cheong Thank you!

  • @chainesanbuenaventura2874
    @chainesanbuenaventura28747 жыл бұрын

    I'm amazed! Thank you!

  • @rhondahughes9648

    @rhondahughes9648

    7 жыл бұрын

    You're welcome:)

  • @CR_07770

    @CR_07770

    3 жыл бұрын

    @@rhondahughes9648 why you stop making videos.

  • @Harsh-mw3vd
    @Harsh-mw3vd7 жыл бұрын

    Great video!! You really bind the concepts together well!

  • @rhondahughes9648

    @rhondahughes9648

    7 жыл бұрын

    Thank you!

  • @johnholme783
    @johnholme783 Жыл бұрын

    Such an simple equation, yet so useful! Excellent derivation, thank you!

  • @rhondahughes9648

    @rhondahughes9648

    Жыл бұрын

    Thank you!

  • @johnholme783

    @johnholme783

    Жыл бұрын

    @@rhondahughes9648 Your welcome! Hi Rhonda; I’m currently studying physics at degree level and I was wondering if you could recommend a maths textbook, preferably an illustrated one for physics at this level. Regards John.

  • @marshallking6478
    @marshallking64782 жыл бұрын

    Thanks so much for your teaching, it really helps me a lot! Salute! And hope for your future classes in KZread~

  • @rhondahughes9648

    @rhondahughes9648

    2 жыл бұрын

    Thank you so much!

  • @CDinkle
    @CDinkle5 жыл бұрын

    Very helpful, and the drawing explaining the two partial derivatives was also very clear. Thank you.

  • @rhondahughes9648

    @rhondahughes9648

    5 жыл бұрын

    You're very welcome.

  • @yusong1141
    @yusong11413 жыл бұрын

    Beautifully proven, took my breath away!

  • @rhondahughes9648

    @rhondahughes9648

    3 жыл бұрын

    Thank you so much!

  • @rajarshichatterjee3281
    @rajarshichatterjee32815 жыл бұрын

    this somewhat also gives an intuition about directional derivatives being generalisation of partial derivatives .

  • @SamirKhan-os2pr
    @SamirKhan-os2pr5 жыл бұрын

    This was very useful. My understanding on calculating the Jacobian matrix over multidimensional planes has improved ;)

  • @rhondahughes9648

    @rhondahughes9648

    5 жыл бұрын

    Thanks so much!

  • @salehahmed4139
    @salehahmed41393 жыл бұрын

    Best explanation of directional derivative. Thank you. Please post more videos on multi variable calculus.

  • @rhondahughes9648

    @rhondahughes9648

    3 жыл бұрын

    Thank you!

  • @gloryths
    @gloryths5 жыл бұрын

    One of the best explanations out there. Thanks

  • @rhondahughes9648

    @rhondahughes9648

    5 жыл бұрын

    Thank you so much!

  • @dr.rajnandkeolyar4482
    @dr.rajnandkeolyar44828 жыл бұрын

    Excellent video...Very helful

  • @rhondahughes9648

    @rhondahughes9648

    8 жыл бұрын

    +Dr. Raj Nandkeolyar Thank you!

  • @guitarttimman
    @guitarttimman4 жыл бұрын

    Thank you. I love your videos.

  • @akhileshroopan7793
    @akhileshroopan77934 жыл бұрын

    actually we need two kinds of tutors, the one who teaches us tricks and hacks for solving problems and the other who explains the shit out of it to make it absolutely clear. you madam is the latter one😂👍..

  • @rhondahughes9648

    @rhondahughes9648

    4 жыл бұрын

    Those are kind words. Thank you very much!

  • @CardiganBear
    @CardiganBear7 жыл бұрын

    Thanks for this very nice explanation of the directional derivative. I really like the way you start with this concept and then (in the following video) move on to show that the directional derivative has a maximum value when it is parallel to the gradient.

  • @rhondahughes9648

    @rhondahughes9648

    7 жыл бұрын

    Thank you, CardiganBear!

  • @benjaminhobson2085
    @benjaminhobson20855 жыл бұрын

    You are better than my professor. Thanks!

  • @seswaran4834
    @seswaran48342 жыл бұрын

    freaking genius!

  • @rhondahughes9648

    @rhondahughes9648

    2 жыл бұрын

    Thank you so much!

  • @yadpreetcheema4806
    @yadpreetcheema48066 жыл бұрын

    by far the best video I've found on this topic.

  • @rhondahughes9648

    @rhondahughes9648

    6 жыл бұрын

    Thank you so much!

  • @kittycat1768
    @kittycat17687 жыл бұрын

    I CANNOT THANK YOU ENOUGH.

  • @rhondahughes9648

    @rhondahughes9648

    5 жыл бұрын

    You're welcome!

  • @MichaelZibulevsky
    @MichaelZibulevsky7 жыл бұрын

    Simple and intuitive explanation. Thanks!

  • @rhondahughes9648

    @rhondahughes9648

    7 жыл бұрын

    You are welcome!

  • @isaiahvalencia5954
    @isaiahvalencia59546 жыл бұрын

    Ms. Hughes! fantastic video! you give concise, intuitive, and rigorous explanations! we'd all like to see more from you! thank you!

  • @rhondahughes9648

    @rhondahughes9648

    6 жыл бұрын

    Thank you very much, Isaiah!

  • @9888565407
    @98885654073 жыл бұрын

    Thanks Rhonda, you are a life saver

  • @rhondahughes9648

    @rhondahughes9648

    3 жыл бұрын

    You are very welcome.

  • @aaryanbudhirajamusic6874
    @aaryanbudhirajamusic68746 жыл бұрын

    This was extremely helpful

  • @rhondahughes9648

    @rhondahughes9648

    6 жыл бұрын

    Thank you!

  • @soyeonkim5228
    @soyeonkim52287 жыл бұрын

    Awesome. ❤️❤️❤️

  • @rhondahughes9648

    @rhondahughes9648

    7 жыл бұрын

    Thank you very much!

  • @rashmisingh6361
    @rashmisingh63618 жыл бұрын

    Mam please upload some more videos on calculus. Finally I understood their geometrical meaning.. Mam thanks a lot, you are doing a great work!!

  • @rhondahughes9648

    @rhondahughes9648

    8 жыл бұрын

    +Rashmi singh Thank you!

  • @spaceman392001
    @spaceman3920012 жыл бұрын

    Happy Birthday!

  • @jacobvandijk6525
    @jacobvandijk65254 жыл бұрын

    In short, the well-known partial derivate (in some point P) is just a special case of the directional derivate, using the standard-basisvectors as unit-vectors.

  • @rhondahughes9648

    @rhondahughes9648

    4 жыл бұрын

    Precisely!

  • @hesokaheso855
    @hesokaheso8556 жыл бұрын

    Man i Spent hours on youtube, trying to understand this, Finaly i can see where this was coming from, thank you very very much.

  • @rhondahughes9648

    @rhondahughes9648

    6 жыл бұрын

    Thank you, Hesoka!

  • @VikasSharma-tv4hn
    @VikasSharma-tv4hn8 жыл бұрын

    Thank you Rhonda! This will help me in understanding the concept much better 😊.

  • @rhondahughes9648

    @rhondahughes9648

    8 жыл бұрын

    +Vikas Sharma You're welcome, Vikas.

  • @RamkumarNatarajan93
    @RamkumarNatarajan937 жыл бұрын

    You are amazing!

  • @rhondahughes9648

    @rhondahughes9648

    7 жыл бұрын

    Thank you so much.

  • @doxo9597
    @doxo95972 жыл бұрын

    When someone asks me “why?” I always respond with “y_0”.

  • @adeelakhtar3540
    @adeelakhtar35404 жыл бұрын

    I want to say big thanks for explaining this concept in a super clear and intuitive way! Could you please make a video, or explain, on covariant derivative, connections, and the relation of these two concepts with gradient and direction (Lie) derivative? Thanks 😀

  • @jahansaid6382
    @jahansaid63826 жыл бұрын

    You opened my mind, now I can understand very profound this topic!! Thank you Rhonda :)

  • @rhondahughes9648

    @rhondahughes9648

    6 жыл бұрын

    Thank you for your kind words, Jahan!

  • @rhondahughes9648

    @rhondahughes9648

    6 жыл бұрын

    Thank you so much, Jahan! I appreciate your comment.

  • @lordrothschild4627
    @lordrothschild462710 ай бұрын

    Loved the middle earth reference.

  • @rhondahughes9648

    @rhondahughes9648

    10 ай бұрын

    Thank you!

  • @sadiaahmed3921
    @sadiaahmed39218 жыл бұрын

    Thanks 💕💕💕

  • @richardli745
    @richardli7458 жыл бұрын

    This is yet the best video I've seen on KZread explaining Directional and Gradient derivatives. Please make more future posts.

  • @rhondahughes9648

    @rhondahughes9648

    8 жыл бұрын

    +Richard Li Thank you! Working on it:)

  • @fariazislam4077
    @fariazislam40773 жыл бұрын

    Finally found a tutorial which rocks

  • @rhondahughes9648

    @rhondahughes9648

    3 жыл бұрын

    Thank you so much!

  • @vikramsinha3642
    @vikramsinha36425 жыл бұрын

    You're a great teacher

  • @rhondahughes9648

    @rhondahughes9648

    5 жыл бұрын

    Thank you, Vikram.

  • @safaali1330
    @safaali13306 жыл бұрын

    The best video I have seen What a beauty

  • @rhondahughes9648

    @rhondahughes9648

    6 жыл бұрын

    Thank you very much!!

  • @martincoourage7557
    @martincoourage75578 жыл бұрын

    Amazing video thank you!

  • @rhondahughes9648

    @rhondahughes9648

    8 жыл бұрын

    +Martin Coourage Thank you!

  • @user-ei9nl5ce4e
    @user-ei9nl5ce4e3 жыл бұрын

    The best explanation I found on the net

  • @rhondahughes9648

    @rhondahughes9648

    3 жыл бұрын

    Thank you so much!

  • @johnbatchler8551
    @johnbatchler85515 жыл бұрын

    Great job

  • @gurleenkaur9601
    @gurleenkaur96016 жыл бұрын

    Great explanation ma'am. I wish my economics teacher taught as wonderfully as you do. Lots of admiration!!!

  • @rhondahughes9648

    @rhondahughes9648

    6 жыл бұрын

    Thank you very much!

  • @tszkinwong6170
    @tszkinwong61702 жыл бұрын

    you are such a lifesaver

  • @rhondahughes9648

    @rhondahughes9648

    2 жыл бұрын

    Thank you!

  • @leeszefoo9492
    @leeszefoo94928 жыл бұрын

    Wow, such a clean and interesting presentation of the topic. Helped me clear a lot of confusion. Thank you so much!

  • @rhondahughes9648

    @rhondahughes9648

    8 жыл бұрын

    +Lee Sze Foo Merci!

  • @Justmetmt24
    @Justmetmt248 жыл бұрын

    Who doesn't like stories?! Very well put. I now see how everything is linked together. Especially the gradient for vectors in physics =0

  • @rhondahughes9648

    @rhondahughes9648

    8 жыл бұрын

    +Justmetmt24 Thank you very much!

  • @warrenfernandes2460
    @warrenfernandes24607 жыл бұрын

    Thx so much. Awesome explanation!

  • @rhondahughes9648

    @rhondahughes9648

    7 жыл бұрын

    You are very welcome!

  • @pulpettedilmare9597
    @pulpettedilmare95974 жыл бұрын

    You are amazing!!! thx so much! gracias

  • @rhondahughes9648

    @rhondahughes9648

    4 жыл бұрын

    De nada.

  • @TaahirBhaiyat
    @TaahirBhaiyat9 жыл бұрын

    Hi Ronda. I really appreciate this video, as my engineering maths lecturer admitted that she could not explain the concept of directional derivatives, however, she did just show us the method of computing it. I now properly understand what's going on, and once again, I'm loving calculus! Thank you so much.

  • @rhondahughes9648

    @rhondahughes9648

    8 жыл бұрын

    +Taahir Bhaiyat Thank you so much, Taahir! Good luck with the rest of your math!

  • @mr6462
    @mr64626 жыл бұрын

    this is very intuitive!!! thank you very much!!!

  • @rhondahughes9648

    @rhondahughes9648

    6 жыл бұрын

    You are very welcome!

  • @siddharthtyagi9133
    @siddharthtyagi91333 жыл бұрын

    Thanks for this video. Was finding bit difficulty in this topic but this video gave gave me that Epiphany and then I was satisfied ❤️❤️😭😭😭thank you

  • @rhondahughes9648

    @rhondahughes9648

    3 жыл бұрын

    Thank you so much!

  • @TheLegend34e32
    @TheLegend34e327 жыл бұрын

    Thank you for your help, you really helped me visualize this!

  • @rhondahughes9648

    @rhondahughes9648

    7 жыл бұрын

    I'm glad this helped.

  • @andeslam7370
    @andeslam73705 жыл бұрын

    Nice video, somehow I could get my intuition only after watching this video. thanks a lot rhonda

  • @rhondahughes9648

    @rhondahughes9648

    5 жыл бұрын

    You're very welcome!

  • @Majd-Al-Din-Alaraby
    @Majd-Al-Din-Alaraby7 жыл бұрын

    thanks a lot ! .. very simple and descriptive ..

  • @rhondahughes9648

    @rhondahughes9648

    7 жыл бұрын

    You are welcome!

  • @solomonv4184
    @solomonv41847 жыл бұрын

    It would be great if you make a playlist for Multivariable Calculus :)

  • @svr1578
    @svr15786 жыл бұрын

    this is what I've been looking for. thanks :)

  • @rhondahughes9648

    @rhondahughes9648

    6 жыл бұрын

    I'm happy it was helpful!

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