I was very confused when people said the gradient was "normal" to the curve. I thought they meant the function itself, not the "level curve". Now it makes complete sense! Thanks!
@@sumittete2804 rate of change of the function is minimum in the direction of the tangent vector i.e. in you move perpendicular to the gradient vector
@@Suyogya77 But if i move opposite to gradient vector i.e 180° I'm getting rate of change of function as negative which is less than 0. Moving along tangent vector the rate of change of function is zero. So how ??
Man if my college calculus profs. were as articulate as Dr. Bazett..I would have gotten better grades in those classes. I'm now a retired software "geek" and really love watching these presentations. Very few folks who understand advanced math (and EE-Comp Sci) are good at teaching it to "undergrads". Of course I love the animations also.
Couldn't agree more, lot of lectures I have i can barely understand what they are trying to present. It's pretty funny that a you tuber can present ideas in a much more clear and straight forward matter.
Thank you so much. I read my textbook and understood about half of this material and watched this video a couple of times and now understand the gradient vector much better. You really helped me.
Thank you for this video. You are a very clear example of the fact that you don't need 3Blue1Brown levels of visual editing in order to explain something intuitively and clearly.
I am a civil engineer , now a days I am pursuing master's in structural engineering ,in structural engineering we use these concepts to find maximum stresses/strains , Before this video I tried a lot but couldn't get into the depth of concept but after watching this video ,I got the concept of it ,animations are very helpful .thankyou and keep up the good work.
I usually don't comment on videos but that's the best explanation i've ever watched to understand... i had this confusing for a long time and this lecture cleared that up! you deserve more subs!
I found myself really “down the rabbit hole” with this concept because it just doesn’t mean anything until you visualise it. Your videos really helped me, thank you 🙏
It is a wonderful thing to see your passion about mathematics, I'm assure you it is contagious and I love you because of it. I wish best for you with my all heart. Please do continue to make videos like that.
My new favourite video of yours, the mountain example was great :) You taught me calc1 at Uvic last year and now you are teaching me calc 3. A true godsend, thanks Trefor!
great videos, Trefor, I have been looking for the explanations with geometrical insights vs just algebra on the board. This really helps to "see" the math. thanks!
Of course I enjoyed it. For better understanding of the Gradient, I searched this subject, fortunately, I saw you and I just clicked! Thank you so much
This video is spot on! Very nice. You just clarified gradient, level curves and the directional derivative in an intuitive way. I know understand the meaning behind the math. Thank you so much!
@@sumittete2804 The direction of the gradient tells you the direction of steepest ascent, and the magnitude tells you the slope of that ascent. Opposite the gradient vector, is the direction of steepest descent. The rate of change of the function is minimized, if the input point travels perpendicular to the gradient vector. The contour lines are perpendicular to the gradient vector. The principle behind Lagrange multipliers comes from this idea. Given that the point in question follows a constrained path, the candidates for the local extreme value of the function's output will occur when the path and the contour line, share a common direction.
I like to think of the normal vector to the contour plot as the shortest distance between two points is a straight line. And when the distance between them next contour is infinitesimal. It is a parallel line. And anything other than normal is going to be more than just going normal.
This is awesome. You're uploading right as I'm learning this material in class, and it's super helpful. I'm a math and education major too - this is such a great conceptual explanation. Thank you!
i have been looking for a video to help me understand directional derivatives and the gradient for a week and this one was the most helpful!! the visual examples are amazing :)) thank you
Also really important how you pointed out grad f as in the x-y plane as that also can be very confusing initially thinking about it as the gradient itself but of course that’s why we need 😊
13:30 is important. Del f is into the mountain which is still normal to the curve and it is logical as del f components are in i and j directions. We move in x and y and the result is change in z which the magnitude of the gradient tells us.
![Div, Grad, and Curl: Vector Calculus Building Blocks for PDEs [Divergence, Gradient, and Curl]](/img/1.gif)
I was very confused when people said the gradient was "normal" to the curve. I thought they meant the function itself, not the "level curve". Now it makes complete sense! Thanks!
Same!
Is rate of change of function minimum in the direction of tangent vector or in the direction opposite to gradient vector ?
@@sumittete2804 rate of change of the function is minimum in the direction of the tangent vector i.e. in you move perpendicular to the gradient vector
@@Suyogya77 But if i move opposite to gradient vector i.e 180° I'm getting rate of change of function as negative which is less than 0. Moving along tangent vector the rate of change of function is zero. So how ??
@@sumittete2804 do you use telegram or something?
My professor rambled on for 2 hours and I didn't understand anything. Here you are explaining it perfectly in 15 minutes. THANK YOU SO MUCH
dude I love ya. that cleared everything about gradients in my mind. Thanks a lot bud.
Glad it helped!
Man if my college calculus profs. were as articulate as Dr. Bazett..I would have gotten better grades in those classes. I'm now a retired software "geek" and really love watching these presentations. Very few folks who understand advanced math (and EE-Comp Sci) are good at teaching it to "undergrads". Of course I love the animations also.
Couldn't agree more, lot of lectures I have i can barely understand what they are trying to present. It's pretty funny that a you tuber can present ideas in a much more clear and straight forward matter.
@@codstary1015 LOL, Its pretty naive of you to assume that Dr.Trefor is just another youtuber!
Thank you so much. I read my textbook and understood about half of this material and watched this video a couple of times and now understand the gradient vector much better. You really helped me.
Glad it was helpful!
Beautifully presented! It's such a cool topic, and using mountains as an analogy makes everything so intuitive.
Great derivation and application! The derivation of the gradient-vector formula and its justification were both quite easy to follow!
I have never seen such a beautiful explanation ever of Gradients love you
Thank you for this video. You are a very clear example of the fact that you don't need 3Blue1Brown levels of visual editing in order to explain something intuitively and clearly.
I am a civil engineer , now a days I am pursuing master's in structural engineering ,in structural engineering we use these concepts to find maximum stresses/strains , Before this video I tried a lot but couldn't get into the depth of concept but after watching this video ,I got the concept of it ,animations are very helpful .thankyou and keep up the good work.
I usually don't comment on videos but that's the best explanation i've ever watched to understand... i had this confusing for a long time and this lecture cleared that up! you deserve more subs!
after visualizing these concepts it became easier for me to perform the mathematical formulas thank you so much sir for the valuable information
Man, you really teach what's important to understand the concepts, and you explain yourself perfectly! Amazing! You've gained a new subscriber 😁
Thank God I found this channel 🙌
The great combination of theory and a real example of a mountain in Vancouver. I enjoy the lesson series of Calculus so much.
I found myself really “down the rabbit hole” with this concept because it just doesn’t mean anything until you visualise it. Your videos really helped me, thank you 🙏
Best math channel on RUclips!
you'll make us love calculus and maths!!
thanks for including practical example of Vancouver island
haha I had fun with that part!
my favorite math teacher on youtube
Thank you!
It is a wonderful thing to see your passion about mathematics, I'm assure you it is contagious and I love you because of it. I wish best for you with my all heart. Please do continue to make videos like that.
Ahhh, finally I fully got it, thx man:) The map help a lot. I knew what gradient is, but i strugled to get the geometric meaning
Glad it helped!
I am doing all possible steps to take this channel to a bigger audience
My new favourite video of yours, the mountain example was great :) You taught me calc1 at Uvic last year and now you are teaching me calc 3. A true godsend, thanks Trefor!
Thanks Conor, really appreciate that. Good luck with math 200!
had seen the videos pop up in the search results and never found the time to have a look. Now just did : I'm a fan! Thanks Prof. Bazett! :)
great videos, Trefor, I have been looking for the explanations with geometrical insights vs just algebra on the board. This really helps to "see" the math. thanks!
Of course I enjoyed it.
For better understanding of the Gradient, I searched this subject, fortunately, I saw you and I just clicked!
Thank you so much
this video is one of the greatest one's that you can find on this topic
my mind is blown, finally I understand how the tangent unit vector gives a direction along which f(x,y) is constant, Thx alot Dr.
glad it helped!
This video is spot on! Very nice. You just clarified gradient, level curves and the directional derivative in an intuitive way. I know understand the meaning behind the math. Thank you so much!
Amazing explanation!!!! thank you so much, you make great influence in the world..
Amazing lecture!
It essentially proves the notion that the gradient is orthogonal to the level set.
Thanks a lot Sir Trefor.
You are welcome!
Is rate of change of function minimum in the direction of tangent vector or in the direction opposite to gradient vector ?
@@sumittete2804 The direction of the gradient tells you the direction of steepest ascent, and the magnitude tells you the slope of that ascent. Opposite the gradient vector, is the direction of steepest descent.
The rate of change of the function is minimized, if the input point travels perpendicular to the gradient vector. The contour lines are perpendicular to the gradient vector.
The principle behind Lagrange multipliers comes from this idea. Given that the point in question follows a constrained path, the candidates for the local extreme value of the function's output will occur when the path and the contour line, share a common direction.
This video is amazing. First time I'm seeing these concepts clearly since I started taking this course.
Example of a mountain was superb to explain gradient..thanks bro
Fantastic explanation. Now I understand the gradient for our purposes lies in the xy plane and that it points into the mountain.
I like to think of the normal vector to the contour plot as the shortest distance between two points is a straight line. And when the distance between them next contour is infinitesimal. It is a parallel line. And anything other than normal is going to be more than just going normal.
Man, you are Richard Feynman of our time
That is high praise!
@@DrTrefor more than him!
Literally the truth🫡☺️
Not high praise , the amount of hard work you have done to develop these is phenomenal ❤
@@Abdullahezzat1893of course not. What a stupid reply🤦🏽♂️
Your demonstration is just amazing Sir....the best explanation of gradient vector on RUclips....
Thanks a ton!
rewatched it several times, started losing hope but then it clicked and I was like 'wait that makes sense!'
This video is really helpful. Thank you so much,👏
Perfectly explained. Thank you sir
Such a brilliant video, it truly heps
great example, thank you for your video
This is awesome. You're uploading right as I'm learning this material in class, and it's super helpful. I'm a math and education major too - this is such a great conceptual explanation. Thank you!
Excellent explanation
i have been looking for a video to help me understand directional derivatives and the gradient for a week and this one was the most helpful!! the visual examples are amazing :)) thank you
amazing and so interesting! keep it up
Love your teaching sir...""LOVE""
excellent video as always, nice example :)
Great illustration, thank you!
understood the beauty of multivariable calculus and gradient operator. Thanks a lot sir :)))
Happy to help!
Great video that gives a brilliant straight explanation for the gradient vector. Hope to have your class in UVic.
I wish there was the option of giving more than one like. Superb explanation!
your bio says you try to do "evidence based pedagogical practices". This is just beautiful man. Hope you come up with more intuitive calculus videos
Absolute trivial explanation.
A legend is living among us!!!!!!!!!
Fantastic way of teaching!!! I recommend the classes here in Brazil!
Also really important how you pointed out grad f as in the x-y plane as that also can be very confusing initially thinking about it as the gradient itself but of course that’s why we need 😊
You’re literally perfect
Thank you sir ❤! You are clearing my such deep buried doubts .
Amazing explanation. Thank you!
This channel is truly underrated
thank you so much for clearing the doubt. The video was very helpful.
Best math channel. Massive respect. Thank you sir..❤️
The Geometric element is fascinating. But the algebraic dot product provide a solid conclusion.
Such a clarity in your explanation....thank you so much sir, you cleared my hardest doubt...😊😊❤❤😊❤❤❤
very informative
Thanks so much it helped me understand the gradient concept.
I love so much u are a genius teacher
Absolutely fantastic explainer! Way to go!
Just amazing
Brilliant explanation again :). It would be very good if you linked the previous explanations, i.e., the tension vector.
Great video, made it easy to understand. Thanks, professor Trefor!
Oh god it helped me so much thanks sensai
thankyou so much! this one's great!!🌟
I love you, thank you!
Great explanation! Thanks alot
thanks a lot for the great explanation
Super thanks Dr.
May you be blessed
Think you sir,,,,,,,Respect from Bangladesh 🇧🇩🇧🇩🇧🇩🇧🇩🇧🇩
Thanks a lot sir 🔥🔥🔥
great job.
That's amazing zing zing
13:30 is important.
Del f is into the mountain which is still normal to the curve and it is logical as del f components are in i and j directions.
We move in x and y and the result is change in z which the magnitude of the gradient tells us.
thank you
Very well-explained.
Glad you think so!
wow. great explanation
Amazing, Thank you!
Good works! Thank you.
after 99999years of searching, I finally found a video that could make me understood
Wonderful video
Simply Brilliant
Thank you!
amazingly clear. thank you
Really enjoyed
In starting, too many concepts to grasp. But the example in end was very interesting.
It's awesome interpretation💖
Awesome video!
Amazing explanation! Thank you so much!!
Glad you enjoyed it!
Wow LTT has an educational channel
I suppose to drop out and join RUclips University
Thanks