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Curves, Parameterizations, and the Arclength Parameterization 

Dr. Trefor Bazett
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WELCOME TO THE START OF VECTOR CALCULUS. Full playlist here: ►VECTOR CALCULUS (Calc IV) • Calculus IV: Vector Ca...
In this video we give an overview of one of the foundational concepts: curves. We will contrast the idea of a curve and path, talk about different parameterizations, the tangent vector, arclength, arclength parameterizations and contrast when to use the arclength parameter versus a time parameter. A lot of these topics are covered in more depth back in my Calc III: Multivariable Calculus playlist, so check out that below as well.
0:00 Curves
1:00 Parameterizations
3:10 Tangent Vector
4:25 Arclength
7:23 Arclength vs Time Parameter
THE MULTIVARIABLE PLAYLIST: ►MULTIVARIABLE CALCULUS (Calc III): • Calculus III: Multivar...
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17 авг 2024

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Комментарии : 127   
@_kantor_
@_kantor_ 3 года назад
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
@DrTrefor 3 года назад
You're most welcome! Glad to have some subs from Israel!
@naman4067
@naman4067 2 года назад
Me too
@hrperformance
@hrperformance 2 года назад
Mate I could agree more
@omargaber3122
@omargaber3122 Год назад
@@DrTrefor you mean palastin!!
@mianokasha1462
@mianokasha1462 3 месяца назад
free palestine
@shehabeldinhousein5875
@shehabeldinhousein5875 Год назад
"... 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
@NuclearPhysix 3 года назад
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
@DrTrefor 3 года назад
Ha!
@NuclearPhysix
@NuclearPhysix 3 года назад
@@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
@farrukhsaif108 2 года назад
@@NuclearPhysix Speed would be the *magnitude of the rate of change of your position vector*
@gentlemandude1
@gentlemandude1 3 года назад
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
@DrTrefor 3 года назад
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
@b49satyarani32 3 года назад
@Professor ~ ur video is so much visualising.
@diveintoengineering6089
@diveintoengineering6089 3 года назад
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
@anotheryoutuberperson38 8 месяцев назад
Did you pass the second time around?
@addifalcone2817
@addifalcone2817 3 года назад
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
@DrTrefor 3 года назад
Good luck!
@tateallen9972
@tateallen9972 3 года назад
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
@andrewkoulogeorge2569
@andrewkoulogeorge2569 3 года назад
The goat himself
@RyanMcCoppin
@RyanMcCoppin 2 года назад
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!
@AninditaII
@AninditaII 3 года назад
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
@DrTrefor 3 года назад
It's my pleasure:)
@carter613
@carter613 2 года назад
The videos are great but listening to this guy lecture is eye opening.
@AidanHomewood
@AidanHomewood 3 года назад
Wow this was a lot more interesting and applicable than my lecturer. Thanks! You're amazing.
@anaslahrichi
@anaslahrichi 11 месяцев назад
Really well explained. I especially like the intuition given and the graphics generated to support your teaching. Thanks !
@joaquintorres834
@joaquintorres834 3 года назад
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
@DrTrefor 3 года назад
Thank you!!
@lukefarley8984
@lukefarley8984 3 года назад
thanks so much for taking the time to make this playlist its super helpful for undergrad physics here in the uk :)))
@nathanbrazil9345
@nathanbrazil9345 2 года назад
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!
@user-nz5ml4de5s
@user-nz5ml4de5s Год назад
Extremely grateful for these lectures! Thank you sir!
@DrTrefor
@DrTrefor Год назад
Glad you like them!
@udaysingh5167
@udaysingh5167 Год назад
thanks for making calculus so easy and fun to study.
@adityaswamy9647
@adityaswamy9647 3 года назад
Amazing Explanations Professor Love from India Thank you
@newyorkguy158
@newyorkguy158 3 года назад
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
@DrTrefor 3 года назад
Glad to hear that! Excited to see your comment when you get to the end:)
@ahmedmusa517
@ahmedmusa517 Год назад
finally found someone who teaches because he likes teaching, I should puy my tuition for you sir,
@Harry-ub2fv
@Harry-ub2fv 3 года назад
Again thanks, man!. Whenever I wanna understand some topic of multivariable calculus you've made that topic video.:)
@DrTrefor
@DrTrefor 3 года назад
So glad it’s helping:)
@Ehsanfarzin-iu9rh
@Ehsanfarzin-iu9rh 11 дней назад
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?
@sutapamaji2510
@sutapamaji2510 3 года назад
Thank you __From India 🇮🇳
@ananthanarayanan9378
@ananthanarayanan9378 3 года назад
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
@DrTrefor 3 года назад
Thank you! The vector calculus series is coming out 3 days a week and will be done in about one more month:)
@truongngo638
@truongngo638 10 месяцев назад
You are so good! This is proper teaching
@hdheuejhzbsnnaj
@hdheuejhzbsnnaj 2 года назад
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.
@theroyalplayer4033
@theroyalplayer4033 3 года назад
thanks sir This video helps me a lot....love from India❣️❣️
@rafiakhan7279
@rafiakhan7279 3 года назад
Ma sha Allah extraordinary way of teaching 👍🏿
@anupriya7366
@anupriya7366 3 года назад
Aahhhh, here is the explanation of parameterization, found it,hashhh. Thanks professor
@isaacr7791
@isaacr7791 Год назад
Wish I had you as my professor!
@shanmugapriyam2623
@shanmugapriyam2623 8 месяцев назад
Need an online course from u Beautifully explained🤟
@sdsa007
@sdsa007 Год назад
thanks this review is helping as a prerequisite for tensor calculus!
@thapaharis
@thapaharis 3 года назад
I have always enjoyed watching your videos. Thanks for math more enjoyable.
@youkaihenge5892
@youkaihenge5892 3 года назад
Taking Calc 3 in Spring! Pretty excited for it. 😄
@DrTrefor
@DrTrefor 3 года назад
Nice! You're going to love it, multivariable is so much cooler than single variable imo
@lanog40
@lanog40 3 года назад
How is it going so far? It's fun for me!
@naseemakel7588
@naseemakel7588 3 года назад
Thank you Dr. From Saudi
@strigiformsW
@strigiformsW 3 года назад
Step 1: Read textbook and put formulas into Anki. Step 2: Watch Dr. Trefor Bazett Step 3: Practice Step 4: Ace test
@DrTrefor
@DrTrefor 3 года назад
Lol awesome
@Hunter-zp9xb
@Hunter-zp9xb 3 года назад
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.
@matanshtepel1230
@matanshtepel1230 3 года назад
Thank you! So excited for these vids 😊
@DrTrefor
@DrTrefor 3 года назад
Glad you like them!
@matanshtepel1230
@matanshtepel1230 3 года назад
@@DrTrefor they're excellent 😁
@simtholileqaukeni8878
@simtholileqaukeni8878 2 года назад
Nice breakdowns.
@hrperformance
@hrperformance 2 года назад
Thank you so much for these fantastic videos!
@forresthu6204
@forresthu6204 Месяц назад
Hi Dr Bazett, which textbook should i use in order to follow this playlist?
@continnum_radhe-radhe
@continnum_radhe-radhe 2 года назад
Thank you very much sir 🔥🔥🔥
@elchanu1239
@elchanu1239 2 месяца назад
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?
@bananamanjunior7575
@bananamanjunior7575 2 года назад
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)]
@roivinikmossel2998
@roivinikmossel2998 2 года назад
your videos are great.
@billhopkins8330
@billhopkins8330 3 года назад
Very helpful explanation!!!
@DrTrefor
@DrTrefor 3 года назад
Glad it helped!
@adresscenter
@adresscenter 3 года назад
Very good quality channel Thx!
@DrTrefor
@DrTrefor 3 года назад
Thank you!
@jet468
@jet468 2 года назад
thank you
@harshakontham4534
@harshakontham4534 10 месяцев назад
love from iit bombay
@dinamustafa6115
@dinamustafa6115 2 года назад
"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 ?
@scholar-mj3om
@scholar-mj3om Год назад
Marvelous💯💯
@UllyanneFreire
@UllyanneFreire 3 года назад
thank you for this, now i finally get it
@PREMKUMAR-kv1zp
@PREMKUMAR-kv1zp 10 месяцев назад
Can you bring special course on Vector calculus.
@DrTrefor
@DrTrefor 10 месяцев назад
I have a whole playlist on this!
@newyorkguy158
@newyorkguy158 3 года назад
What is your choice of textbook for MV and Vector Calculus?
@DrTrefor
@DrTrefor 3 года назад
The "standard" full service calc books are Thomas and Stewart, both are fine
@hikmatullahpakhtoon3694
@hikmatullahpakhtoon3694 3 года назад
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
@DrTrefor 3 года назад
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
@hikmatullahpakhtoon3694 3 года назад
@@DrTrefor thank you sir.
@Falinaschi
@Falinaschi Год назад
Dr. Bazett can you help me? How to parametrize a circle in 3D space from three points?
@momen8839
@momen8839 3 года назад
Awosome...I want to know history of vector calculus and its relation with physics. particularly (flux,curl,circulation)
@DrTrefor
@DrTrefor 3 года назад
We're definitely going to have a lot of connections to physics, particularly a bit later in the series:)
@momen8839
@momen8839 3 года назад
@@DrTrefor Is this any book present these conceptions with historical approach?
@MATT123Gaming
@MATT123Gaming 3 года назад
430 likes and not ONE DISLIKE?!?!
@DrTrefor
@DrTrefor 3 года назад
That's actually a pretty sick ratio
@MATT123Gaming
@MATT123Gaming 3 года назад
@@DrTrefor so sick that math breaks for it🤯
@danieltambunan9717
@danieltambunan9717 Год назад
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
@DrTrefor Год назад
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.
@turkishlegends4499
@turkishlegends4499 11 месяцев назад
Which book you are following for this course??
@DrTrefor
@DrTrefor 11 месяцев назад
Thomas calculus
@jasonarmondo4619
@jasonarmondo4619 3 года назад
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
@DrTrefor 3 года назад
It's like a highway. The highway is fixed. How you drive down the highway, faster or slower, doesn't change anything.
@sabinacharya5117
@sabinacharya5117 Год назад
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...
@fotballfredrik1
@fotballfredrik1 3 года назад
GOAT
@krzysztofciuba271
@krzysztofciuba271 2 года назад
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
@krzysztofciuba271 2 года назад
in few minutes i discovered even on RU-vid 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!
@user-ql8wm4gy3v
@user-ql8wm4gy3v Год назад
講得很好ㄟ 哥 謝謝你 我的超人
@hubenbu
@hubenbu 2 года назад
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.
@daniyaaaqil371
@daniyaaaqil371 2 года назад
Sir ! I am not getting it can you please help me I am in hot water right now
@miguelposada3684
@miguelposada3684 6 месяцев назад
love the video, audio a bit crucnhy prob the mic
@prashanthkumar0
@prashanthkumar0 3 года назад
cool... vector calculus❤️❤️❤️❤️❤️
@DrTrefor
@DrTrefor 3 года назад
Love vector calc so much:D
@prashanthkumar0
@prashanthkumar0 3 года назад
@@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
@DrTrefor 3 года назад
Haha yup have to pass the exams first:D
@physicsmathsworld2033
@physicsmathsworld2033 3 года назад
Awosome 😀❤️❤️❤️❤️❤️
@karthiks8665
@karthiks8665 3 года назад
Please recommend me a book to learn vector calculus basics
@antonia5423
@antonia5423 3 месяца назад
Vectors exam in a week. Let’s go B)
@delsonmcgriffin1989
@delsonmcgriffin1989 2 года назад
4:22
@mortezakhoshbin
@mortezakhoshbin 3 года назад
i cant thank you enough...
@DrTrefor
@DrTrefor 3 года назад
you're most welcome!
@ArmenianDude88
@ArmenianDude88 5 месяцев назад
no kappa, explanation slapped
@captaingerbil1234
@captaingerbil1234 3 года назад
I've never seen a video with such an impressive like/dislike ratio and I can see why.
@DrTrefor
@DrTrefor 3 года назад
That actually is pretty crazy. If anyone ever dislikes this, I’m mad at you lol
@captaingerbil1234
@captaingerbil1234 3 года назад
​@@DrTrefor Well my good Doctor, may it remain forever untainted.
@ludwigimbihl4965
@ludwigimbihl4965 Год назад
i love you
@syz911
@syz911 Год назад
7:10 min What is the "ass?"
@aizazhussainaizazofficial1202
@aizazhussainaizazofficial1202 2 года назад
outstanding sir , but if possible speak a bit slow......
@MarkCliffeIsGay
@MarkCliffeIsGay 5 месяцев назад
Great video. It would've been helpful to see an example at the end though, even an easy one. Otherwise thanks!
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