Curves, Parameterizations, and the Arclength Parameterization

[@_kantor_]

So glad I'm studying physics in a time where there is so much high quality vids of kinda advance math. You're great! Thank you so much! Lots of appreciation from Tel aviv

[@DrTrefor]

You're most welcome! Glad to have some subs from Israel!

[@naman4067]

Me too

[@hrperformance]

Mate I could agree more

[@omargaber3122]

@@DrTrefor you mean palastin!!

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free palestine

[@shehabeldinhousein5875]

"... 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!

[@NuclearPhysix]

Driving from London once, I noticed a police car getting interested in the magnitude of my position vector. So I slowed down naturally. Love you, Professor

[@DrTrefor]

Ha!

[@NuclearPhysix]

@@DrTrefor You teach in a clear way that I love. I wish I had you as my Professor when I did that Engineering degree. You got me when you expressed speed as a position vector, made so much sense. Subbed!

[@farrukhsaif108]

@@NuclearPhysix Speed would be the *magnitude of the rate of change of your position vector*

[@diveintoengineering6089]

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!

[@anotheryoutuberperson38]

Did you pass the second time around?

[@gentlemandude1]

Dr. Bazett, I often come to your videos thinking that I fully understand the topic, but inevitably during my viewing, you mention something that I hadn't considered. Thank you for presenting such wonderful and comprehensible mathematical insight. You're videos are gems!

[@DrTrefor]

Thank you! It is tricky for sure as my current videos are presuming a lot of multicariable calc stuff. If you ever get lost, feel free to comment and I can link the relevant prereq video hopefully👍

[@b49satyarani32]

@Professor ~ ur video is so much visualising.

[@tateallen9972]

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

[@addifalcone2817]

I’ve never been more grateful to find someone on youtube. This is helping me out so much for my calc 3 final tomorrow! Thank you!!

[@DrTrefor]

Good luck!

[@RyanMcCoppin]

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!

[@andrewkoulogeorge2569]

The goat himself

[@AninditaII]

Sir, I have seen many videos on advanced math but wow ,your videos make me feel it, incredible, and others leave me in half way of the course, u r a lifesaver , gonna watch all playlist.....

[@DrTrefor]

It's my pleasure:)

[@carter613]

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

[@anaslahrichi]

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

[@AidanHomewood]

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

[@lukefarley8984]

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

[@user-nz5ml4de5s]

Extremely grateful for these lectures! Thank you sir!

[@DrTrefor]

Glad you like them!

[@joaquintorres834]

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 :)

[@DrTrefor]

Thank you!!

[@nathanbrazil9345]

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!

[@udaysingh5167]

thanks for making calculus so easy and fun to study.

[@newyorkguy158]

I'm taking vector analysis right now and am so excited at what I am learning from your videos. The conceptual explanations are very good.

[@DrTrefor]

Glad to hear that! Excited to see your comment when you get to the end:)

[@ahmedmusa517]

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

[@adityaswamy9647]

Amazing Explanations Professor Love from India Thank you

[@hdheuejhzbsnnaj]

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.

[@Harry-ub2fv]

Again thanks, man!. Whenever I wanna understand some topic of multivariable calculus you've made that topic video.:)

[@DrTrefor]

So glad it’s helping:)

[@sutapamaji2510]

Thank you __From India 🇮🇳

[@truongngo638]

You are so good! This is proper teaching

[@theroyalplayer4033]

thanks sir This video helps me a lot....love from India❣️❣️

[@ananthanarayanan9378]

Awesome video! Pls cover complete vector calculus soon. Ur explanation is very gud and makes these complex topics easily comprehensible for beginner students like me. Pls continue this series😃

[@DrTrefor]

Thank you! The vector calculus series is coming out 3 days a week and will be done in about one more month:)

[@anupriya7366]

Aahhhh, here is the explanation of parameterization, found it,hashhh. Thanks professor

[@thapaharis]

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

[@strigiformsW]

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

[@DrTrefor]

Lol awesome

[@Hunter-zp9xb]

3:27 the curve is one dimensional but it exists in a three dimensional space, just as the circle is also a one dimensional manifold in a two dimensional space. Thus the smallest number of parameters tells you the dimension.

[@sdsa007]

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

[@naseemakel7588]

Thank you Dr. From Saudi

[@rafiakhan7279]

Ma sha Allah extraordinary way of teaching 👍🏿

[@isaacr7791]

Wish I had you as my professor!

[@shanmugapriyam2623]

Need an online course from u Beautifully explained🤟

[@bananamanjunior7575]

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)]

[@matanshtepel1230]

Thank you! So excited for these vids 😊

[@DrTrefor]

Glad you like them!

[@matanshtepel1230]

@@DrTrefor they're excellent 😁

[@Ehsanfarzin-iu9rh]

Thank you so much, Dr. Bazett, for your incredible and in-depth teaching. I truly appreciate it! 🙏 Could you please recommend a textbook that aligns with this course?

[@youkaihenge5892]

Taking Calc 3 in Spring! Pretty excited for it. 😄

[@DrTrefor]

Nice! You're going to love it, multivariable is so much cooler than single variable imo

[@lanog40]

How is it going so far? It's fun for me!

[@hrperformance]

Thank you so much for these fantastic videos!

[@simtholileqaukeni8878]

Nice breakdowns.

[@continnum_radhe-radhe]

Thank you very much sir 🔥🔥🔥

[@billhopkins8330]

Very helpful explanation!!!

[@DrTrefor]

Glad it helped!

[@adresscenter]

Very good quality channel Thx!

[@DrTrefor]

Thank you!

[@roivinikmossel2998]

your videos are great.

[@jet468]

thank you

[@scholar-mj3om]

Marvelous💯💯

[@UllyanneFreire]

thank you for this, now i finally get it

[@harshakontham4534]

love from iit bombay

[@newyorkguy158]

What is your choice of textbook for MV and Vector Calculus?

[@DrTrefor]

The "standard" full service calc books are Thomas and Stewart, both are fine

[@fotballfredrik1]

GOAT

[@momen8839]

Awosome...I want to know history of vector calculus and its relation with physics. particularly (flux,curl,circulation)

[@DrTrefor]

We're definitely going to have a lot of connections to physics, particularly a bit later in the series:)

[@momen8839]

@@DrTrefor Is this any book present these conceptions with historical approach?

[@dinamustafa6115]

"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 ?

[@MATT123Gaming]

430 likes and not ONE DISLIKE?!?!

[@DrTrefor]

That's actually a pretty sick ratio

[@MATT123Gaming]

@@DrTrefor so sick that math breaks for it🤯

[@PREMKUMAR-kv1zp]

Can you bring special course on Vector calculus.

[@DrTrefor]

I have a whole playlist on this!

[@hikmatullahpakhtoon3694]

Sir! As equation of a circle is not a function in x and y variable or i can just in cartesian coordinates. but sir ,after parameterising that equation does it become a function or not?

[@DrTrefor]

Well yes, but not in the same sense. It is a function from [0,2pi] to a subset of R^2. So not the graph of a function from R to R like you might be imagining.

[@hikmatullahpakhtoon3694]

@@DrTrefor thank you sir.

[@hubenbu]

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.

[@prashanthkumar0]

cool... vector calculus❤️❤️❤️❤️❤️

[@DrTrefor]

Love vector calc so much:D

[@prashanthkumar0]

@@DrTrefor yeah... but unfortunately i won't be able to give it some time... because nowadays im busy in teaching myself chemistry for board exam ... i have paused my coding also ...

[@DrTrefor]

Haha yup have to pass the exams first:D

[@physicsmathsworld2033]

Awosome 😀❤️❤️❤️❤️❤️

[@elchanu1239]

How to parametrize a curve while maintaining dimensional accuracy. Like, say I want a curve that looks like the exponential curve but I want the curve to have dimensions of length L. What do I do? Do I do it like x(t) = se^t, and y = st?

[@jasonarmondo4619]

7:41 ' doesnt depend on the specific path along the curve", but isnt this just the curve , since the curve defines the path? Or do you mean going along the curve at different speeds, which correspond to different time parameterizations of the curve (as opposed to *the* arclength parametrization, which has unit speed the whole way'

[@DrTrefor]

It's like a highway. The highway is fixed. How you drive down the highway, faster or slower, doesn't change anything.

[@turkishlegends4499]

Which book you are following for this course??

[@DrTrefor]

Thomas calculus

[@user-ql8wm4gy3v]

講得很好ㄟ 哥 謝謝你 我的超人

[@miguelposada3684]

love the video, audio a bit crucnhy prob the mic

[@forresthu6204]

Hi Dr Bazett, which textbook should i use in order to follow this playlist?

[@antonia5423]

Vectors exam in a week. Let’s go B)

[@sabinacharya5117]

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...

[@Falinaschi]

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

[@delsonmcgriffin1989]

4:22

[@mortezakhoshbin]

i cant thank you enough...

[@DrTrefor]

you're most welcome!

[@ArmenianDude88]

no kappa, explanation slapped

[@danieltambunan9717]

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?

[@DrTrefor]

It’s the difference between describing a road and describing a particular way that a car drives along the road, with for instance a velocity you can compute at each point.

[@krzysztofciuba271]

OK.Hm, then what is the unit tangent vector (of any curve)? On the definition It (this unit for r (t), r'(t)=v) =: (vector)v (t)/v(t)/(magnitude and also (this unit for r(s);s-arclength= dr(s)(vector)/ds =((dx(s)/ds;dy(s)/ds;dz(s)/ds))and this =1 (on: ds=v(s)ds,then v(s)=ds/ds=1); /v(s)/=/v(t)/(the magnitude)-is it ok? I want t be sure! (I see a huge problem with the use of it or rather ignoring in the application to 4-d spacetime interval: the unit of (spacetime interval), or the unit of time parameter, esp. the unit of proper time- a huge mess in textbooks since....A.Einstein and P.Langevin's,AD 1911 lecture hoax! Again: the unit arc tangent vector and the unit of arclenght=1(or not?).It is just another geometric argument contra ...textbooks' idiocies (on "time dilation"'s interpretation.

[@krzysztofciuba271]

in few minutes i discovered even on KZbin I am right (in Prof. Leonard's lecture); u missed in your lecture: dr(s)/d(s)=1. A proof of all 110 years of writings about "proper time" (definition, symbol)is a perfect BS without defining the unit of proper time and the unit arc tangent of spacetime interval/unit arclength!

[@captaingerbil1234]

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

[@DrTrefor]

That actually is pretty crazy. If anyone ever dislikes this, I’m mad at you lol

[@captaingerbil1234]

​@@DrTrefor Well my good Doctor, may it remain forever untainted.

[@karthiks8665]

Please recommend me a book to learn vector calculus basics

[@daniyaaaqil371]

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

[@ludwigimbihl4965]

i love you

[@syz911]

7:10 min What is the "ass?"

[@aizazhussainaizazofficial1202]

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

[@MarkCliffeIsGay]

Great video. It would've been helpful to see an example at the end though, even an easy one. Otherwise thanks!