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@@mustafanaser9789 My videos will always remain free for everyone. But, if people want to donate, they can do so through my Patreon page at www.patreon.com/EugeneK Thanks.
Your methodology for teaching is very conducive to learning concepts that aren't really all that intrinsically difficult to understand, but that are commonly hard to learn because of the way the information is commonly presented. Good job and thank you!
Beautiful! Every video is a gem. This is what's been missing from the higher education system. I hope you get to a level where you can higher animators (or take volunteers) and blow this thing up to Khan Academy status. I can absolutely see this happening, please keep it up!
+Musa Yusuf By "Khan Academy status" I was referring to popularity and success. Eugene's videos are clearly of superior quality but also fundamentally very different from Khan Academy videos.
+Physics Videos by Eugene Khutoryansky Absolutely. It also makes you more able to apply it to real problems because you know what's being the equations.
@@EugeneKhutoryansky ; wow. what a great philosophy. I really hope that this will be the future. Teaching and learning would then be full of fun for everyone :)
I started with studying about Neural Networks, which led me to a Multilayer Perceptron, which led me to the Backpropogation algorithm, which led me to the calculus of gradient descent and it's intuitive meaning, which led me to a doubt, which led me to searching about the meaning of partial derivatives and gradients and that led me to this video and I have finally clarified my doubt. Thank you Dr. Eugene, your videos are amazing.
The only things that I really dislike about these videos are the Fundamental Missing Pieces in the explanations, which I notice at almost every video. For example, here the it does not explain why gradient indicates the direction for which the function increases by the largest amount. Missing explanations like that diminish the value of this channel by the largest amount. If you fill the "explanation gaps" a little further, I believe your channel would be one of the very best.
Thank you Eugene. You are a true visionary in terms of how using visualization one can give ' real life' and better understanding to the complex math and statistical concepts. Wish I had this available in my college times.
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I can't believe I didn't even know the basics what use was my education from 10th grade to uni I didn't even know the basics thanks for explaining everything so clearly
This really helped me understand the concept of the gradient. I finally understand how the gradient relates to the partial derivatives and why the it points in the direction of greatest increase in z. Thanks for putting it together! What would be super cool would be an animation of the gradient changing along with the x and y components as the dot traversed the surface.
Very powerful how you keep it all in the same shot this time. I often find that your "whoosh" and make things confusing, I hope you'll keep some of this style in the future.
Excellent stuff. By far the best channel on RU-vid for an introduction to this sort of advanced mathematics. I can't overstate how much I've learned from just a handful of these videos. Please keep doing this.
I hope you do more videos like this. I always try to imagine a landscape to understand multivariable related maths, but sometimes it's too difficult and I fail. I'd very much like you to explain the implicit derivation theorem in your own way.
Eugene's videos just keep getting better and better! I love the math topics discussed recently. I could never quite understand them as a student, and I am pretty sure some of the teachers couldn't either. Explaining in this way is a revelation!
I have been a subscriber of your channel for more than a year now. I have seen your channel progress from the puppy picture, to the amazing quality of animation. I would like to thank you once again for continuing to make videos, and for being an awesome science RU-vid channel. You, along with many other RU-vid channels, have inspired me to be a science student. You're the best, Eugene! Sincerely, Ahnaf Abdullah
+Ahnaf Abdullah, thanks for the compliments. I am glad that you liked my videos, and I am glad to hear that I have helped inspire your pursuit of science.
Every time I go through a simple lively and very intuitive explanation of Math, I well with a lot of joy. I am very happy I came across this video. Earned yourself a subscriber, and much much love
Your videos are simply fabulous! What major channels couldn't explain to me in 2 whole videos consuming almost 20 mins, yours did it in 5!! Again, amazing videos. Do keep up the good work.
استمر يا صاحب القناة فأنت تقوم بعمل رائع !!!!! فبمساعدتك فهمت معنى غراديان متجهة ما ..... تعميم في 3 أبعاد أو أكثر للاشتقاق في بعد واحد ... الشكر موصول للمترجم محمد مصطفى موسى....
Pretty nice, quite difficult to digest the conclusion when adding the X,Y vectors to get the Z as gradient. Not sure how the gradient is built by the sum of those since you get their divisions but then add them up for a vector (what I wonder is how they translate in the gradient for visualization and not into a certain color at that point in the grafic for X, Y coordinates).
+Alexandru Gheorghe at every point there is a vector that points in the direction of greatest increase (with the length denoting how much that increase is). So instead of the colors, you could imagine all of the arrows everywhere but sometimes that might be more difficult to do/read from. Try googling 'gradient field' and looking through the images. You can find some examples of what I'm talking about. I hope this helps!
You turn the magnitude of each partial derivatives of z with respect to x or y into vectors, then add the vectors. The magnitude is the slope (the derivative), and the direction is negative or positive depending on the slope. I got confused thinking about how you would add negative or positive vectors if the slopes were different signs, but in smooth functions, there is a gradual change, and if the function is all in the quadrant were x and y are positive, then only the change in z will be positive or negative. So this is easy to visualize. The gradient is just the vector sum of the partial derivatives, and this gradient vector points in the direction the combined maximum amount of change. The hypotenuse of the triangle. The colors in the video graphs only represent if the change in z is positive or negative with respect to x or y.
Partial derivatives indicate the slope ( of z w.r.t y ) with x kept as a constant at some particular point . Now , how are we sure that the slope is maximum at that point ? Because , to construct the direction of the del operator, we need maximum change of z w.r.t y and not just any change... So , if dz/dy (x contstant) indicates the slope w.r.t y at some point and similarly dz/dx (y con) indicates the slope w.r.t x at the same point , then , does the gradient indicate the maximum change of z still , or should we choose that point at which the slope (of z w.r.t x and y ) are maximum ?
@@abhishekkj3662 I too have this confusion and I thought someone would have answered you in these years. Miller told almost the answer usually written in books but with a caution that one can conceive a function for which gradient may not point in the direction of maximum rate of change (and poor me, I cannot either conceive such function 🤣), but I am still searching these videos and comments for the same answer. One guy above who proved mathematically seems quite good and hope he answer from intuitive point of view.
I did examples on partial derivative s 7 yrs ago and also scored good marks. But i understood what exactly it is today. Thank you, Hope more people try to understand what exactly it is rather than just solving numericals.
This video did an absolutely amazing job getting me to understand gradients. I was trying to learn gradients/partial derivatives to understand the math behind optimization functions in machine learning. Thank you!
After two weeks of staring vacantly at clumsy and confusing analogies, FINALLY I get the intuition behind the gradient. The computation and the analytical representations were never difficult for me but it nagged me that I couldnt visualize it. Thank you!
For the first time I'm seeing this type of explanation now I am able to understand what the partial derivatives and the concept of keeping x or y constant.x. very great teaching.
A very good legendary work for physics. These such awesome creators make me realise that knowledge does not require long hours of hardwork and stuffs like that but the dedication and the ability to feel the beauty of the subject matters a lot . I would like to encourage the team to expand it's beautiful pedagogy of explaining concepts in every subjects and disciplines that exist around us.
Your videos are so essential for understanding and strengthening basic concepts that they should be included in the syllabus of courses of all science colleges across the world!
I think there should be more people teaching mathematics and physics the way you do it! You do a great job in making abstract concepts more graphical and choose really interesting topics, you really show the beauty behind those subjects. Thank you very much for using media like youtube to motivate people and to show that such technologies have also the power to enhance thinking. Thanks again for posting such great videos : )
Thank you so much for video! Event in big universities there is little effort to provide resources for students to help them visualize concepts in linear algebra. Using videos like these in the curriculum would make a huge difference.
I thank you from the bottom of my heart for making such beautiful videos and helping humanity understand all monotonous things that they dont even care about. U r simply awesome.
I have a really great intuition of this in machine learning topics (gradient descent & optimizing), this is really helpful and makes learning about not only ML but the maths behind it clear!
the part of about treating the partials as vectors is really the money shot. i was always confused what the partial values actually did in the equation but now i understand it contributes to the height of z, both variables do. thus the net height contributions of both partials makes the gradient, you are the man
the most satisfying video about partial derivatives is yours. seeing mathematics this way is lot more helpful than to study it from books. thanks for the video.
Thanks for such a nice and simple explanation! I love how you use physics visualization examples to teaches math and concepts that’s difficult to understand.
Your videos are absolutely awesome! You have really inspired a love of physics and math in me! I really appreciate your channel and I hope you continue to make many more videos:)
these videos will make u immortal....it might not viewed much ..but when world will come to senses...they will appriciate u...please more videos ..multivariable calulas
I should be honest here.... I am fan of 3b1b, Dave sir, Bazett and Sir Ghrist and I watched videos of all of them regarding gradient, but this one cleared the deepest essence of Calculus right at this interval. 3:54 - 5:24 Thank You very much!! Many Respect
This video should be shown to all students learning integrals honestly. It is such a useful visualization, which really captures the reality of what the math is meant to model.
It is not just India. This is a problem with education systems in all countries. I discuss this in my video at ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-k6QhhocnZ-M.html
