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!

@juanbautistasoria757

4 ай бұрын

Same!

@sumittete2804

4 ай бұрын

Is rate of change of function minimum in the direction of tangent vector or in the direction opposite to gradient vector ?

@Suyogya77

4 ай бұрын

​@@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

@sumittete2804

4 ай бұрын

@@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 ??

@Suyogya77

4 ай бұрын

@@sumittete2804 do you use telegram or something?

This is just brilliant. Clear voice, sound logic and great example.

dude I love ya. that cleared everything about gradients in my mind. Thanks a lot bud.

@DrTrefor

3 жыл бұрын

Glad it helped!

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

Beautifully presented! It's such a cool topic, and using mountains as an analogy makes everything so intuitive.

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.

@codstary1015

Жыл бұрын

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.

@focusmaestro4013

Жыл бұрын

@@codstary1015 LOL, Its pretty naive of you to assume that Dr.Trefor is just another youtuber!

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!

I have never seen such a beautiful explanation ever of Gradients love you

Great derivation and application! The derivation of the gradient-vector formula and its justification were both quite easy to follow!

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 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!

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!

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.

The great combination of theory and a real example of a mountain in Vancouver. I enjoy the lesson series of Calculus so much.

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! :)

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

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

Man, you really teach what's important to understand the concepts, and you explain yourself perfectly! Amazing! You've gained a new subscriber 😁

This video is amazing. First time I'm seeing these concepts clearly since I started taking this course.

Best math channel on KZread!

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.

@DrTrefor

3 жыл бұрын

Glad it was helpful!

I am doing all possible steps to take this channel to a bigger audience

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.

Thank God I found this channel 🙌

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.

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!

@DrTrefor

3 жыл бұрын

Thanks Conor, really appreciate that. Good luck with math 200!

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 🙏

after visualizing these concepts it became easier for me to perform the mathematical formulas thank you so much sir for the valuable information

Great video, made it easy to understand. Thanks, professor Trefor!

Best math channel. Massive respect. Thank you sir..❤️

excellent video as always, nice example :)

Absolutely fantastic explainer! Way to go!

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

@DrTrefor

3 жыл бұрын

Glad it helped!

amazing and so interesting! keep it up

this video is one of the greatest one's that you can find on this topic

Great video that gives a brilliant straight explanation for the gradient vector. Hope to have your class in UVic.

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

Perfectly explained. Thank you sir

Brilliant explanation again :). It would be very good if you linked the previous explanations, i.e., the tension vector.

This video is really helpful. Thank you so much,👏

you'll make us love calculus and maths!! thanks for including practical example of Vancouver island

@DrTrefor

3 жыл бұрын

haha I had fun with that part!

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

Thank you sir ❤! You are clearing my such deep buried doubts .

thank you so much for clearing the doubt. The video was very helpful.

Such a brilliant video, it truly heps

Example of a mountain was superb to explain gradient..thanks bro

Amazing explanation. Thank you!

Super thanks Dr. May you be blessed

awesome stuff! i love this subject

I wish there was the option of giving more than one like. Superb explanation!

thankyou so much! this one's great!!🌟

great example, thank you for your video

Amazing explanation!!!! thank you so much, you make great influence in the world..

Fantastic explanation. Now I understand the gradient for our purposes lies in the xy plane and that it points into the mountain.

Such a clarity in your explanation....thank you so much sir, you cleared my hardest doubt...😊😊❤❤😊❤❤❤

Your demonstration is just amazing Sir....the best explanation of gradient vector on KZread....

@DrTrefor

3 жыл бұрын

Thanks a ton!

Great explanation! Thanks alot

Excellent explanation

rewatched it several times, started losing hope but then it clicked and I was like 'wait that makes sense!'

Awesome video!

Thanks so much it helped me understand the gradient concept.

Amazing explanation! Thank you so much!!

@DrTrefor

3 жыл бұрын

Glad you enjoyed it!

This channel is truly underrated

Love your teaching sir...""LOVE""

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.

@DrTrefor

3 жыл бұрын

glad it helped!

amazingly clear. thank you

Good works! Thank you.

thanks a lot for the great explanation

Excellent!

Really enjoyed

Amazing, Thank you!

A legend is living among us!!!!!!!!!

wow. great explanation

Wonderful video

Oh god it helped me so much thanks sensai

bruh, u nailed it🙏🙏

I love you, thank you!

You’re literally perfect

Thank you so much🙏 You're amazing. 😊😎

It's awesome interpretation💖

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.

Just amazing

understood the beauty of multivariable calculus and gradient operator. Thanks a lot sir :)))

@DrTrefor

3 жыл бұрын

Happy to help!

very informative

you r a god.love your videos

Amazing lecture! It essentially proves the notion that the gradient is orthogonal to the level set. Thanks a lot Sir Trefor.

@DrTrefor

3 жыл бұрын

You are welcome!

@sumittete2804

4 ай бұрын

Is rate of change of function minimum in the direction of tangent vector or in the direction opposite to gradient vector ?

@carultch

4 ай бұрын

@@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.

Absolute trivial explanation.

great job.

Thanks a lot sir 🔥🔥🔥

Love you sir!

Very well-explained.

@DrTrefor

3 жыл бұрын

Glad you think so!

I love so much u are a genius teacher

my favorite math teacher on youtube

@DrTrefor

3 жыл бұрын

Thank you!

I love it Great sir

Simply Brilliant

@DrTrefor

3 жыл бұрын

Thank you!

what an amazing video!!! Please make a video on divergence on curl too...it would be very helpful

@rupanzilmamunprince

3 жыл бұрын

@@DrTrefor Wow!! Eagerly waiting for them

woww..!! Subscribed

@DrTrefor

3 жыл бұрын

thank you!

Thanks a lot sir...

Thank you very much

GREAT video, solid explanation. but i have a question. was the gradient defined originally in terms of the directional derivative?