3D Curves and their Tangents | Intro to Vector-Valued Functions

Рет қаралды 96,364

4 жыл бұрын

A space curve, or vector-valued function, is a function with a single input t and multiple outputs x(t), y(t), z(t). In this video we introduce these functions and see how to visualize them in 3D. We then turn to the problem of tangent lines to these types of curves. The definition is modeled after tangents to graphs of functions.
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Пікірлер: 114

@benphelps8250 4 жыл бұрын

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@izaiahedwin3038 2 жыл бұрын

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@alex_turing 8 ай бұрын

@@izaiahedwin3038you are right. This is the wrong place to ask. How did you even end up here lmao

@TrampTuts 4 жыл бұрын

Best thing that’s happened to me this year: signing up for your calc class ❤️

@farhansadik5423 Күн бұрын

Unbelievable. It's unbelievable how you teach! I love this so damn muchhhhh

@admiralhyperspace0015 4 жыл бұрын

I can't tell you how much I am loving these lectures.

@alkankondo89 4 жыл бұрын

Great visuals and color-coding! It makes an already-easy-to-understand explanation even clearer!

@ayushstephen3053 3 жыл бұрын

Sir, you are a great teacher. Thank you for all your efforts. May God bless you in all your endeavours.

@DrTrefor 3 жыл бұрын

You are most welcome

@Lostwolf16 4 жыл бұрын

Wow, nice way to visualize it instead of just memorizing formulas and forgetting it later. Thank you

@imtiazursyed1521 3 жыл бұрын

Your lectures are great. The constant smile on your face shows how much you love the subject and how much you love to teach it.

@toomanycharacter Жыл бұрын

I can't think of any channel other than yours with such a wide and high-quality coverage of Calculus. Your videos are a very great service for Calculus students worldwide and especially self-learners, such as myself. The visualisations are very nice on several levels, and the explanations are rigorous as well as intuitive. Thank you.

@yadhuss919 4 жыл бұрын

Best video to understand this topic in a clear manner

@karamay5479 3 жыл бұрын

This man is the reason I stop my Calculus lecture videos, come to youtube, and say, "Trefor will make me love this."

@DrTrefor 3 жыл бұрын

Hahah :D

@undefined.infinity3106 2 жыл бұрын

in youtube, I'm not being watched for just solving some random problems for tests. to get the gist of any topic and feel those are the main objective for me. and you do these things perfectly. your bite-sized lectures and visuals for every topic make me intrigued through the topic

@chyldstudios 4 жыл бұрын

Excellent production value!

@waiyanphyo920 3 жыл бұрын

Just wanna say PERFECT. Thank you for your effort, sir.

@sergeimerekin8193 4 жыл бұрын

You have an incredible channel, thank you!

@user-fv1cd5nx3w 3 жыл бұрын

The 3d visualizations synchronized with your lecture, really help understand the material!

@ferus5583 Жыл бұрын

Great lesson and visuals! thank you so much, Sir!!!

@freshely9309 3 жыл бұрын

Holy moly another great video, you are a life-saver! :')

@Festus2022 4 жыл бұрын

Nice! Love the graphics!

@joeypadua867 3 жыл бұрын

Thanks for this video. It immediately cleared up my confusion.

@brunomartel4639 2 жыл бұрын

intuitive, rigorous, complete,nice animations

@Leoeoeoeoeoeoeooeo Ай бұрын

The best teacher

@212ntruesdale 3 жыл бұрын

Much appreciated. Thank you!

@rrrushan 3 жыл бұрын

That was so amazing!

@olehborys1462 Жыл бұрын

You are a great teacher, your videos help me with my studies. Thanks!

@omarayoubi8135 3 жыл бұрын

we love you a lot you are an amazing professor yes , I am a math teacher but also i really like being a student when i watch your courses ❤

@skvsatish5277 3 жыл бұрын

Thank you so much, it was just amazing

@prathamghavri8591 3 жыл бұрын

Thanks sir !! Really liked the way u explained

@sushma.vallabhuni0985 4 жыл бұрын

Excellent explanation

@victoriacorcimaru1731 Жыл бұрын

FANTASTIC EXPLANATION!!!!!💯❣

@umadbroyo2388 3 жыл бұрын

Not only are you explanation simple and easy to understand but also the way you speak makes me excited about math, I don't know why...

@DrTrefor 3 жыл бұрын

Thank you!!

@umadbroyo2388 3 жыл бұрын

@@DrTrefor 😁

@zuggrr 2 жыл бұрын

You are amazing ! Thank you so much

@user-pg6rd9ew3l Жыл бұрын

sir, you deserve atleast 1M subs

@amritas2400 4 жыл бұрын

Wow. That helped a lot. Subscribed. 💖💖💖

@rodrigoalmeida820 3 жыл бұрын

Kindest professor i've ever seen

@SaminCrypted 2 жыл бұрын

Great one bro. Got some relief.

@pavanajsridhar939 4 жыл бұрын

your multivariable calculus series are just amazing!! they are really helping me utilize my time well during this lockdown!

@xanxusgrim3047 3 жыл бұрын

Thank you for this, pewdiepie i learned a lot

@dinmukhammedtleuzhanuly1225 3 жыл бұрын

Thank u very mush for this video!!!

@juancarlossanchezveana1812 5 ай бұрын

Excelente explicación

@mnada72 3 жыл бұрын

The best 👌.

@sharan9993 3 жыл бұрын

I half read two books on multivariate calculus bcoz i was studying machine learning could not understand anything. Here u r literally explaining them like simple basic maths. Wow thanks a lot. This is how maths should be taught. Great work and big fan of yours sir.

@DrTrefor 3 жыл бұрын

So glad they helped!

@sharan9993 3 жыл бұрын

@@DrTrefor Sir can u tell me from where the maths and basics of machine learning derived from?

@nimnim5149 3 жыл бұрын

what a content ..... superb

@aymmenbatool7254 3 жыл бұрын

This was actually great!

@DrTrefor 3 жыл бұрын

Thank you!

@hinamehndipearls4374 2 жыл бұрын

You are great 👍

@susanjacob937 3 жыл бұрын

Thank you :)

@KaviPriyan-qt6vc 4 жыл бұрын

You are great😍

@markbell8967 3 жыл бұрын

Thank you

@GrandmasKitchenkerala 3 жыл бұрын

incredible class

@DrTrefor 3 жыл бұрын

Thank you!

@a.b.6677 3 жыл бұрын

Beautifully explained

@DrTrefor 3 жыл бұрын

Thank you so much 🙂

@a.b.6677 3 жыл бұрын

@@DrTrefor Thanks to you Professor

@tramquangpho 3 жыл бұрын

The hardest part in teaching calculus is making everything seem obvious, “ but many people fail to do that. Great teaching indeed . One question : you say , the vector r(t+ delta(t) - r(t) is increase in size when divide by t less than 1; but the more t decease and that vector really close to tangent vector , I dont see it increase in size anymore ?

@blankspace1959 Жыл бұрын

I watch this channel through 2 different accounts so I can give it more likes

@continnum_radhe-radhe 2 жыл бұрын

🔥🔥🔥

@jgkostas 2 жыл бұрын

Dr T -- Can you recommend a multi-variable calculus text? I prefer texts will physical explanations and examples. Thanks for the spectacular vectors in 3-space in the videos....

@lehou8320 Жыл бұрын

Dr. Trefor, thank you very much for the lessons. They're really amazing! So... dr/dt is the velocity (vector v), not the tangent vector T, right? dr/ds is T.

@brandonheald9624 3 жыл бұрын

Indeed.

@TheBgracey 4 жыл бұрын

In the formula - r (t) = cos(t)I + sin(t)j + tK Why is a plus sign used? Is the output to be thought of as a vector or as a scalar?

@franekkos574 Жыл бұрын

🙏🏼

@Caleepo 4 жыл бұрын

hello Trefor Bazett, thank you for your nice video, but Ive got a question somehow. How can you exactly know if two different inputs have got the same output. How can you be sure you are dealing with a function ?? If two inputs have got the same output then how can you see it/ calculate it ?

@Caleepo 4 жыл бұрын

@@DrTrefor ah thank you very much Im on my first year of engineering it really made a mess of my head, can't think properly as I used to do in highschool lol

@andrewwoan 3 жыл бұрын

Hi! what software do you use to graph in 3 dimensions like that?

@DrTrefor 3 жыл бұрын

I use MATLAB for most things, but a good option for students to play with that is free is geogebra

@andrewwoan 3 жыл бұрын

@@DrTrefor Thank you very much Dr. Bazett!

@pa7832 Жыл бұрын

Dr. Bazett, what 3D visualization tool do you use? It seems useful as you are able to change your viewing angle etc.

@DrTrefor Жыл бұрын

Everything here is done in MATLAB

@pa7832 Жыл бұрын

Thanks Dr. Bazett! Your videos with the animations are super useful!

@wakeawake2950 3 жыл бұрын

Thank you sir for this video, I want to ask is this the gradient of (r) vector?

@DrTrefor 3 жыл бұрын

Gradient only applies to a scalar function

@wakeawake2950 3 жыл бұрын

@@DrTrefor thnk u sir🙏

@212ntruesdale 3 жыл бұрын

In single variable, the derivative is the slope of the tangent line. When it comes to vector valued functions, is the magnitude of the tangent vector analogous to the slope of the tangent line? So, in the case of a straight line, the tangent vector would just be the zero vector?

@DrTrefor 3 жыл бұрын

Exactly. Another way to think of it is that it is the "speed" aka the length of the velocity vector

@rajisingh5710 2 жыл бұрын

Sir what will be unit tangent vector

@thecarlostheory 2 жыл бұрын

May you please give a geometric or formal derivation of delta t, instead of putting it as a scalar that increase the delta r magnitude vector? For me that feels very artificial, and I don´t like it... Is there another way to derive delta t participation in the equation of tangent vector?

@calcubite9298 8 ай бұрын

at 5:47 is the yellow vector pointing in the wrong direction? I was taught that when are doing (vector A) minus vector B, when A and B have a common starting point, in this case, the origin, that the (vector a minus b) starts at the tip of B and points TOWARDS vector A. Here in this picture, the vector starts at the tip of A and points towards vector B.

@samisiddiqi5411 2 жыл бұрын

9:14 I think we should be taught the Leibniz Notation more in school...

@dylanico887 Жыл бұрын

At 2:30, why do you just randomly consider x^2 + y^2 = 1? Aren't the x and y components respectively cost and sent?

@212ntruesdale 3 жыл бұрын

The fact that the yellow vector stays yellow even after being multiplied by a scalar confused me. The vector that becomes the tangent vector and delta r are not the same. (You do erase the expression for delta r, but I didn’t get as much from that as I would have from a change in colors, to emphasize the fact that the two vectors aren’t the same.) I don’t think this is quibbling either, when the magnitude of the tangent vector has such an amazing interpretation, that being speed when t is time.

@marcbanfi4985 7 ай бұрын

Can a vector-valued function be in only two dimension?

@inquisitiverakib5844 2 жыл бұрын

Tangent Vector 3:27

@satyampanchal-1016 3 жыл бұрын

how do you plot these vector valued functions on 3D?, i mean what software u use?

@DrTrefor 3 жыл бұрын

I use MATLAB

@satyampanchal-1016 3 жыл бұрын

@@DrTrefor i'm a physics student in first year of my under graduation, and i'm looking for such resources, can you briefly tell me what should I do on Matlab? i don't know if its very advanced for someone like me do I need to learn how to use it (like some computer language), actually i have zero clue about this Matlab , can you nudge me in the right direction?

@nomann5244 3 жыл бұрын

what is the name of the software used to plot the 3d graph

@DrTrefor 3 жыл бұрын

I use MATLAB, but lots of options that work great too

@nomann5244 3 жыл бұрын

Thank you for your reply and answer.

@geoffreyfaust3443 2 жыл бұрын

"Leibniz" (as in, derivative notation) should be pronounced like the long i in 'like'

@anishmanandhar1203 3 жыл бұрын

Nicely explained. Would be better if you could explain via delta-epsilon theorem too

@waqasmuneer7951 2 жыл бұрын

Why a vector valued function should have only 1 input?

@therishi4014 3 жыл бұрын

I'm Indian here ,😀 Like if u love Indians 😍😍

@asmcriminaL 3 жыл бұрын

Dude, I just want to make a circle...

@vaderanomaly1573 3 жыл бұрын

thanks but pleaaase get a little mic for your collar

@videorome4782 Жыл бұрын

Where is the problem solving????

@IGJTHOMAS 3 жыл бұрын

Solid content but that echo is hard to accept.

@1364aakash 3 жыл бұрын

Liked? Check. Subscribed? Check.

@laalhussain4234 Жыл бұрын

You speak in Urdu Language

@punditgi 3 жыл бұрын

What happened to "zed "? USA is the only place that says "zee", which makes the USA the outlier in the English speaking world globally.

@DrTrefor 3 жыл бұрын

ha, I spent three years in the US and now I'm mentally stuck using both:D

@punditgi 3 жыл бұрын

@@DrTrefor Understood. I lived for a time in Montreal and learned French, so I very much appreciate our neighbors (neighbours) to the north. Vive le Canada! 🇨🇦