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
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!
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 :)
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!
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. ^ ^
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.
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))
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.
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.
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.
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!
As an engineering student who did well in Calc 2. I'm struggling to visualize calc 3 and study for my midterm. This really saved me and it was an amazing explanation. Thanks
@@gabrielcruzati3717 I'm guessing it depends on your university because here in Canada, my uni is doing this in calc 2 as well but other universities don't
pure gold. Great presentation. I'm really enjoying working through all the partial derivative vids in the play list. Reviewing them before moving on to the optimisation videos.
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.
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
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
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!
The video was amazing....but I really do have a question how was it that dx/ds and dy/ds was equated to u1 and u2?...m sorry of the question was stupid
such a difficult thing to conceptualize is deserving of such graphics as these. Why do remote learning professors suck so much?? This helped a ton. I was still shaking on my geometric understanding of the partial deriv.
this helps a lot i am taking calc 3 in the summer in 6 weeks, and basically, i have to study 2 chapters a 2week , these videos help a lot on the question ," why we do this"
@Dr. Trefor Bazett Thanks for explaining it in such an easy and systematic way. Just one question, if you can visually explain it, 1) for secant case where two points are lets say (1,1) and (2,5) then why adding slope of secant line in x direction and slope of secant line in y direction is equal to slope of secant line from (1,1) to (2,5). 2) Or in limiting case at point (1,1) why slope in the direction of going from (1,1) to (2,5) is the sum of slopes of tangent in x direction and y direction. In other words why we extract slope of tangent line in any direction just by adding slopes of tangents in x and y directions. I mean why we add them why not multiply or do some other thing. (Also please explain that what it means to say that partial derivatives are linear so we add them to get slopes in any other direction)
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
From the expression of the directionnal derivative. Whatever the u vector is, if the gradient vector is 0 then the directional derivative is 0. But i can imagine curves where the the gradient is 0 with some direction where the derivative is not 0.
I'm an undergrad and believe me this is the first time i understood anything about calculus hats off man👍
thats the power of Internet
you made it to calc 3 without ever understanding anything about calculus?
@@mikzin630😂😂
@@mikzin630 It's easy. You can literally memorize your way through single variable calculus if you are solid in algebra.
self-studying this over the summer.... wish u were my teacher!! thank you
Yo, me too!
doing it over winter. Yes, I am a bit mental.
@@gonderage Ya , i long too
@SHADAB ANSARI , u 2 :)
He's your teacher thanks to the internet
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
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!
The visual explanation up to 2:40 really helped me understand the main concept better.
Glad it helped!
This is the best explanation of directional derivatives. Please never delete these videos.
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 :)
Some of the videos I just watched them because they were so engaging, despite not being part of my syllabus.
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!
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. ^ ^
Glad it helped!
I love your enthusiasm. Calculus is beautiful once one has grasped the logic behind algebraic framing of questions.
This video is INSANE. Learned more from this than a 2-hour lecture from my professor 😭
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.
Omg finally I understand this
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))
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.
Holy smokes!!! . how can a student not fall in love with you sir ? . Just struck in awe.
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!
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.
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.
Didn't knew that PewDiePie was such a great teacher.
Okay sorry. You are awesome Dr. Bazett.
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!
Amazing Dr.Trefor.. Never imagined the concepts in this way. Please continue making videos. Big fan
As an engineering student who did well in Calc 2. I'm struggling to visualize calc 3 and study for my midterm. This really saved me and it was an amazing explanation. Thanks
Man, you are fine. Here in Brazil, this is my calc II :´)
@@gabrielcruzati3717 Em Portugal tb
@@gabrielcruzati3717 I'm guessing it depends on your university because here in Canada, my uni is doing this in calc 2 as well but other universities don't
Yeah ,here in Greece in the particular department im in, multivariable calculus is basically calc ll.
Dr Trefor, many will remember you for life time. God bless you.
Thanks for your explanation. Please never delete this video. You inspire students who want to see the beauty of math. Thanks again.
A genius of teaching. You're a special gift to us students, thank you dr. Bazett :)
Certainly the best explanation of DD I've seen so far) I had several "wow" moments during this video)
Wow, brilliant & beautiful, I watched the video 2 or 3 years ago, & I still enjoy going back to it, kudos Professor
Best explanation of directional derivatives I’ve ever seen!
Thank you!
pure gold. Great presentation. I'm really enjoying working through all the partial derivative vids in the play list. Reviewing them before moving on to the optimisation videos.
I am so happy RUclips recommended me your videos.😊
Lots of love from India 🇮🇳❤
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.
I am surprised that only 1.8k thumbs up when 38k people watched it. This video deserves 38k thumbs ups.
This man is a genius at geometric intuition for calculus. Help me alot, thank you.
idk why but his way of explaining things is so engaging. it really is amazing 🤩🤩.
Glad you enjoyed!
I've studied this in Calculus about four years ago, but never actually learned it. This helped a lot, thank you!
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.
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.
Thank you so much for your kind words:)
I wish I had a maths teacher like you
THANK YOU VERY MUCH 🙏
Amazing Dr Trefor. The combo of 3blue 1 brown + Dr Trefor= Mastery of the subject.... No need to go anywhere.
Wish others that are struggling find this video, Thank you for making the video.
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
4:57 That's what she said.
Have never seen such a logical explanation.
This was a stellar video on a topic that I could not wrap my head around. Thank you.
I really wished if you were my tutor! Until now I was just memorizing those formulas! Thank-you sir! Love from india!
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
This one video cleared all my questions on multivariate calculus
Maths is more fun if we can visualise it rather than mugging up formulae . We need teachers like you . 😍😍😍😍😍👏
thank you!
I am so happy to see your channel getting the recognition it deserves . You really saved me during university period.
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!
The explanation was concise and very clear.
I have never seen this kind of detailed and articulate explanation
Thanks a lot sir 🙏
You're the greatest teacher I never had... ❤❤❤
the visual explanation helped me a lot ,I'm extremely happy for some reason after watching this video, thanks a lot.
The video was amazing....but I really do have a question how was it that dx/ds and dy/ds was equated to u1 and u2?...m sorry of the question was stupid
Very illustrative and visual. Thank you.
the visuals and your teaching really make it!
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
You are really one of the best teachers.
i have been searching for simple detailed explanation since very long before i found this.... Thank you very much
such a difficult thing to conceptualize is deserving of such graphics as these. Why do remote learning professors suck so much??
This helped a ton. I was still shaking on my geometric understanding of the partial deriv.
incredible i was strugling to understand this by reading and visiualizing thank u so much nice explanation along with the killer graphics
this helps a lot i am taking calc 3 in the summer in 6 weeks, and basically, i have to study 2 chapters a 2week , these videos help a lot on the question ," why we do this"
week not 2week
Thank you. Important stuff made simple by your expert video. Outstanding.
@Dr. Trefor Bazett Thanks for explaining it in such an easy and systematic way. Just one question, if you can visually explain it, 1) for secant case where two points are lets say (1,1) and (2,5) then why adding slope of secant line in x direction and slope of secant line in y direction is equal to slope of secant line from (1,1) to (2,5). 2) Or in limiting case at point (1,1) why slope in the direction of going from (1,1) to (2,5) is the sum of slopes of tangent in x direction and y direction. In other words why we extract slope of tangent line in any direction just by adding slopes of tangents in x and y directions. I mean why we add them why not multiply or do some other thing. (Also please explain that what it means to say that partial derivatives are linear so we add them to get slopes in any other direction)
Nice combination of graphs and equations. Good stuff!
Cool animation!!!!!! I understand it right away! !
Maza Agiya Bahi sahb❤👍
Earlier I didn't understand this but now I appreciate how beautiful calculus is
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
Very nice
Easy to understand
why do good teachers and professors exist only online :(. Amazing video
Trefor teaches in person as well.
Your visuals give life to Mathematical concepts.
Question: at around 8:57 is gradient born 🐣 from the Directional derivative?
So great way explaining this lesson , Very well done prof .
i always come to your channel whenever im stuck on a topic, you have the best explanations ever!!! thanks!
dude you just saved my life. thank you so much 🙏🙏
You make calculus easy to understand and fun, keep up the good work!
I wonder how people used to imagine and read surfaces just seeing the equations in the past and now we are here with animations😍
Thank you, clear explanation. I guess if u was not a unit vector, it would still work as s -> 0?
thank you so much for the content. this helps me a lot for my calc 3 class.
Wow, this is extraordinary explanation 👏👏👏
great video, great explanation, thanks form Mexico.
Thank you!!
Your diagram was so helpful!! I have been struggling to understand the idea of directional derivatives and this video helped so much!
Incredible explanation! So detailed and easily understandable!
Wow🤩 best explanation
This is a great demonstration. Thank you.
amazing content, I always appreciate a skilled mathematician.
wow better than a Cambridge maths course lecturer 😑
Fantastic way of teaching!!! I recommend the classes here in Brazil!
thanks, great intuition great teacher, well done sir
Question: Relating it to the another video, does it mean that we have proved that that is the min rate of change?
From the expression of the directionnal derivative. Whatever the u vector is, if the gradient vector is 0 then the directional derivative is 0. But i can imagine curves where the the gradient is 0 with some direction where the derivative is not 0.
Thank you 😀. This video helps me alot.
Thank you for this beautiful advanced explanation. Both animations and expressions were excellent :)
totally masterpiece, making a cool subject even cooler, what a professor :)
Hey man, I love your videos! Quick question, how do you make those graphs & animations? Python I assume?
Trefor Bazett - Sweet thanks!
Great explanation!
epitome of conceptual clearing
thank you so much! I've been trying so hard to understand the slope of directional derivatives on the graph! This helped a lot!
Glad it helped!