Curves, Parameterizations, and the Arclength Parameterization

love from iit bombay

You are so good! This is proper teaching

Can you bring special course on Vector calculus.

Which book you are following for this course??

Really well explained. I especially like the intuition given and the graphics generated to support your teaching. Thanks !

Extremely grateful for these lectures! Thank you sir!

i love you

Can someone explain, why the r(t) is described using cos(t) i + sin(t) j ? Why not using the circle formula x² + y² = radius instead?

講得很好ㄟ 哥 謝謝你 我的超人

thanks this review is helping as a prerequisite for tensor calculus!

finally found someone who teaches because he likes teaching, I should puy my tuition for you sir,

Ohk i am gonna be honest with you .....i am trying to sketch a curbve of an impeller vane and this video is fuckin useless and timewaste

thanks for making calculus so easy and fun to study.

Marvelous💯💯

"... what parametrization does, that it tells us where all the points on the circle at some specific time t". sometimes such sentences are the thing needed to fill the gaps. And such sentences comes from someone who really understands the topic. Thank you!

Wish I had you as my professor!

Dr. Bazett can you help me?
How to parametrize a circle in 3D space from three points?

if position vector (r) represents the displacement, here in the curve(circle), r is normal to the curve. Similarly, if the derivative of r represents the velocity, here in the curve(circle) velocity is along the tangent to the curve. but displacement and velocity must be in same direction. Isn't it? I'm a bit confused over here...

Nice breakdowns.

"whereas the time parameter here is reflecting the specific choices for a specific particle on a specific path along this curve so which do you prefer" could you explain this statement more ?

A huge new discovery: the domain of time is defined in terms of 0 and Pi, there must be some intrinsic connections between the physical concept of time and this mathematical notation Pi.

outstanding sir , but if possible speak a bit slow......

There is actually a rational parametrization for the equation x^2+y^2= 1 it is [(1–t^2)/(1+t^2), 2t/(1+t^2)]

Thank you so much for these fantastic videos!

Love how we get a breakdown of why police care more about the rate of change of your position vector as opposed to your arc length parameterization.

I took vector calculus (Calc IV) in undergrad but my professor left off all the intuition/application and so most of the topics didn't make much practical sense. Really excited to go through this series!

Thank you very much sir 🔥🔥🔥

thank you

The videos are great but listening to this guy lecture is eye opening.

your videos are great.

Sir !
I am not getting it can you please help me
I am in hot water right now

Awesome video, I love how quickly you brought together multiple topics I've been learning about in my Calculus 4 class. Thanks for such clear explanations!

Step 1: Read textbook and put formulas into Anki.
Step 2: Watch Dr. Trefor Bazett
Step 3: Practice
Step 4: Ace test

Wow this was a lot more interesting and applicable than my lecturer. Thanks! You're amazing.

I have always enjoyed watching your videos. Thanks for math more enjoyable.

thank you for this, now i finally get it

The best explanation I've seen. I just failed my multivariable calculus course but your videos will be a valuable help during my next chance. Thank you!

thanks so much for taking the time to make this playlist its super helpful for undergrad physics here in the uk :)))

Thank you __From India 🇮🇳

Short and concise, wonderful work! (As always). I'm starting to learn Diff. Geometry and this was helpful! Take care, love from Spain. PD: congrats on hitting the 100k, you deserve it :)

I've never seen a video with such an impressive like/dislike ratio and I can see why.

I hope you make money off of these videos because you deserve to. Thank you for all the help. You've helped me understand all my calc II - IV concepts, and I'm very grateful

Thank you Dr.
From Saudi

Please recommend me a book to learn vector calculus basics

Ma sha Allah extraordinary way of teaching 👍🏿