Directional Derivatives | What's the slope in any direction?
Вставка
- Опубліковано 16 лис 2019
- A directional derivative gives the slope in any particular direction, similar to partial derivatives which give the slope just in the x or y directions. We formally define directional derivatives by modifying the familiar limit definition of the derivative for when you move along some vector in the input space. Then we see a very nice feature that we can use the gradient vector grad(f) to make computing directional derivatives easy. If you have the gradient, you can get the directional derivative in the u direction with one easy dot product.
****************************************************
YOUR TURN! Learning math requires more than just watching videos, so make sure you reflect, ask questions, and do lots of practice problems!
****************************************************
►Full Multivariable Calculus Playlist: • Calculus III: Multivar...
****************************************************
Other Course Playlists:
►CALCULUS I: • Calculus I (Limits, De...
► CALCULUS II: • Calculus II (Integrati...
►DISCRETE MATH: • Discrete Math (Full Co...
►LINEAR ALGEBRA: • Linear Algebra (Full C...
***************************************************
► Want to learn math effectively? Check out my "Learning Math" Series:
• 5 Tips To Make Math Pr...
►Want some cool math? Check out my "Cool Math" Series:
• Cool Math Series
****************************************************
►Follow me on Twitter: / treforbazett
*****************************************************
This video was created by Dr. Trefor Bazett. I'm an Assistant Teaching Professor at the University of Victoria.
BECOME A MEMBER:
►Join: / @drtrefor
MATH BOOKS & MERCH I LOVE:
► My Amazon Affiliate Shop: www.amazon.com/shop/treforbazett
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😂😂
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
This is the best explanation of directional derivatives. Please never delete these videos.
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!
Didn't knew that PewDiePie was such a great teacher.
Okay sorry. You are awesome Dr. Bazett.
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!
Some of the videos I just watched them because they were so engaging, despite not being part of my syllabus.
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.
The visual explanation up to 2:40 really helped me understand the main concept better.
Glad it helped!
Omg finally I understand this
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!
Thanks for your explanation. Please never delete this video. You inspire students who want to see the beauty of math. Thanks again.
I am so happy to see your channel getting the recognition it deserves . You really saved me during university period.
Amazing Dr.Trefor.. Never imagined the concepts in this way. Please continue making videos. Big fan
I've studied this in Calculus about four years ago, but never actually learned it. This helped a lot, thank you!
Certainly the best explanation of DD I've seen so far) I had several "wow" moments during this video)
Holy smokes!!! . how can a student not fall in love with you sir ? . Just struck in awe.
This was a stellar video on a topic that I could not wrap my head around. Thank you.
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.
the visuals and your teaching really make it!
Incredible explanation! So detailed and easily understandable!
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.
Maths is more fun if we can visualise it rather than mugging up formulae . We need teachers like you . 😍😍😍😍😍👏
thank you!
This man is a genius at geometric intuition for calculus. Help me alot, thank you.
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))
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.
You make calculus easy to understand and fun, keep up the good work!
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!
This is a great demonstration. Thank you.
amazing content, I always appreciate a skilled mathematician.
Dr Trefor, many will remember you for life time. God bless you.
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
Hey man, I love your videos! Quick question, how do you make those graphs & animations? Python I assume?
Trefor Bazett - Sweet thanks!
i have been searching for simple detailed explanation since very long before i found this.... Thank you very much
Wow, brilliant & beautiful, I watched the video 2 or 3 years ago, & I still enjoy going back to it, kudos Professor
Nice combination of graphs and equations. Good stuff!
why do good teachers and professors exist only online :(. Amazing video
Trefor teaches in person as well.
I wish I had a maths teacher like you
THANK YOU VERY MUCH 🙏
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!
the visual explanation helped me a lot ,I'm extremely happy for some reason after watching this video, thanks a lot.
Earlier I didn't understand this but now I appreciate how beautiful calculus is
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
You are really one of the best teachers.
I have never seen this kind of detailed and articulate explanation
Thanks a lot sir 🙏
4:57 That's what she said.
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!
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
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.
Have never seen such a logical explanation.
Maza Agiya Bahi sahb❤👍
Beautiful Explanation. Thank u so much
I am surprised that only 1.8k thumbs up when 38k people watched it. This video deserves 38k thumbs ups.
Amazing Dr Trefor. The combo of 3blue 1 brown + Dr Trefor= Mastery of the subject.... No need to go anywhere.
Best explanation of directional derivatives I’ve ever seen!
Thank you!
I am so happy UA-cam recommended me your videos.😊
Lots of love from India 🇮🇳❤
Wish others that are struggling find this video, Thank you for making the video.
i always come to your channel whenever im stuck on a topic, you have the best explanations ever!!! thanks!
Very illustrative and visual. 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.
Thank you. Important stuff made simple by your expert video. Outstanding.
Clear & concise. 👏
Wow, this is extraordinary explanation 👏👏👏
Just AMAZING! Thank you!!!
Cool animation!!!!!! I understand it right away! !
great stuff dude! deserves more attention
Thanks this cleared things up for me.
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
I really wished if you were my tutor! Until now I was just memorizing those formulas! Thank-you sir! Love from india!
dude you just saved my life. thank you so much 🙏🙏
Amazing Video ! Supplementing this with my lecture notes ! Thank you professor.
Your diagram was so helpful!! I have been struggling to understand the idea of directional derivatives and this video helped so much!
Simply fantastic !
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:)
So great way explaining this lesson , Very well done prof .
Thank you so much, Dr. Bazett
This one video cleared all my questions on multivariate calculus
The explanation was concise and very clear.
Fantastic way of teaching!!! I recommend the classes here in Brazil!
incredible i was strugling to understand this by reading and visiualizing thank u so much nice explanation along with the killer graphics
You Nailed It !
Brilliant explanation, thank you very much
Thanks for all this wonderful explanation.
Thank you for your time and effort.
You're the greatest teacher I never had... ❤❤❤
Great explanation!
Thank you for this beautiful advanced explanation. Both animations and expressions were excellent :)
Mind blowing !
Thanks a lot Dr.
Very nice explanation, thank you!
You’re the best!!!!! Thank you so much for your help 🙂
Thank you! This video was very helpful!
Love your passion!
Thank you 😀. This video helps me alot.
Thanks Doc, this was really helpful.
thanks, great intuition great teacher, well done sir
Very nice
Easy to understand
Wow🤩 best explanation