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

Поделиться
HTML-код
  • Опубликовано: 19 янв 2025

Комментарии • 117

  • @benphelps8250
    @benphelps8250 5 лет назад +119

    Pin this comment if you love teaching !!!

    • @izaiahedwin3038
      @izaiahedwin3038 3 года назад +2

      i know im asking the wrong place but does anyone know a way to get back into an Instagram account??
      I was stupid forgot the login password. I would appreciate any tricks you can offer me.

    • @ManojKumar-cj7oj
      @ManojKumar-cj7oj 3 года назад

      @@izaiahedwin3038 use option forgot password

    • @ColonelFluffles
      @ColonelFluffles 3 года назад +1

      @@izaiahedwin3038 Turn it on and off

    • @alex_turing
      @alex_turing Год назад +4

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

  • @TrampTuts
    @TrampTuts 5 лет назад +42

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

  • @imtiazursyed1521
    @imtiazursyed1521 3 года назад +6

    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.

  • @admiralhyperspace0015
    @admiralhyperspace0015 4 года назад +9

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

  • @ayushstephen3053
    @ayushstephen3053 4 года назад +27

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

    • @DrTrefor
      @DrTrefor  4 года назад +5

      You are most welcome

  • @alkankondo89
    @alkankondo89 5 лет назад +38

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

  • @Lostwolf16
    @Lostwolf16 4 года назад +9

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

  • @toomanycharacter
    @toomanycharacter Год назад +1

    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.

  • @なるほどなるほど-z1y
    @なるほどなるほど-z1y 3 месяца назад

    You are literally a god. Like, that might even be an understatement. Your youtube videos are BY FAR the most easily understandable explanations of these difficult topics I’ve ever seen; you manage to explain a topic in 10 minutes better than a professor from elite institutions does in an hour.

  • @undefined.infinity3106
    @undefined.infinity3106 3 года назад +1

    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

  • @yadhuss919
    @yadhuss919 5 лет назад +3

    Best video to understand this topic in a clear manner

  • @chyldstudios
    @chyldstudios 5 лет назад +9

    Excellent production value!

  • @karamay5479
    @karamay5479 3 года назад +1

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

  • @umadbroyo2388
    @umadbroyo2388 4 года назад +1

    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...

  • @farhansadik5423
    @farhansadik5423 5 месяцев назад

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

  • @waiyanphyo920
    @waiyanphyo920 4 года назад +1

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

  • @sergeimerekin8193
    @sergeimerekin8193 4 года назад +6

    You have an incredible channel, thank you!

  • @brunomartel4639
    @brunomartel4639 2 года назад +1

    intuitive, rigorous, complete,nice animations

  • @Festus2022
    @Festus2022 4 года назад +3

    Nice! Love the graphics!

  • @sharan9993
    @sharan9993 3 года назад +1

    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
      @DrTrefor  3 года назад +1

      So glad they helped!

    • @sharan9993
      @sharan9993 3 года назад

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

  • @olehborys1462
    @olehborys1462 Год назад

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

  • @dyadyastepaaa
    @dyadyastepaaa 4 года назад

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

  • @ferus5583
    @ferus5583 2 года назад +1

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

  • @asamikwork
    @asamikwork 4 месяца назад

    You explanation is very clear and helpful thank you for your contribution.

  • @rodrigoalmeida820
    @rodrigoalmeida820 4 года назад +1

    Kindest professor i've ever seen

  • @freshely9309
    @freshely9309 3 года назад +1

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

  • @omarayoubi8135
    @omarayoubi8135 4 года назад +1

    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 ❤

  • @joeypadua867
    @joeypadua867 4 года назад +1

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

  • @SatvikVadisetti
    @SatvikVadisetti Год назад

    sir, you deserve atleast 1M subs

  • @victoriacorcimaru1731
    @victoriacorcimaru1731 Год назад

    FANTASTIC EXPLANATION!!!!!💯❣

  • @GrandmasKitchenkerala
    @GrandmasKitchenkerala 4 года назад +1

    incredible class

  • @SaminCrypted
    @SaminCrypted 3 года назад +1

    Great one bro. Got some relief.

  • @aymmenbatool7254
    @aymmenbatool7254 4 года назад +1

    This was actually great!

  • @pavanajsridhar939
    @pavanajsridhar939 4 года назад +1

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

  • @Leoeoeoeoeoeoeooeo
    @Leoeoeoeoeoeoeooeo 7 месяцев назад +1

    The best teacher

  • @a.b.6677
    @a.b.6677 4 года назад +1

    Beautifully explained

    • @DrTrefor
      @DrTrefor  4 года назад +2

      Thank you so much 🙂

    • @a.b.6677
      @a.b.6677 4 года назад

      @@DrTrefor Thanks to you Professor

  • @xanxusgrim3047
    @xanxusgrim3047 3 года назад +2

    Thank you for this, pewdiepie i learned a lot

  • @prathamghavri8591
    @prathamghavri8591 4 года назад +1

    Thanks sir !! Really liked the way u explained

  • @sushma.vallabhuni0985
    @sushma.vallabhuni0985 5 лет назад +1

    Excellent explanation

  • @zuggrr
    @zuggrr 3 года назад +1

    You are amazing ! Thank you so much

  • @rrrushan
    @rrrushan 3 года назад +1

    That was so amazing!

  • @andrewwoan
    @andrewwoan 4 года назад +2

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

    • @DrTrefor
      @DrTrefor  4 года назад

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

    • @andrewwoan
      @andrewwoan 4 года назад

      @@DrTrefor Thank you very much Dr. Bazett!

  • @Skv112
    @Skv112 3 года назад +1

    Thank you so much, it was just amazing

  • @calcubite9298
    @calcubite9298 Год назад

    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.

  • @tramquangpho
    @tramquangpho 4 года назад

    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 ?

  • @212ntruesdale
    @212ntruesdale 4 года назад +1

    Much appreciated. Thank you!

  • @amritas2400
    @amritas2400 4 года назад +1

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

  • @blankspace1959
    @blankspace1959 2 года назад

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

  • @dylanico887
    @dylanico887 2 года назад

    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?

  • @nimnim5149
    @nimnim5149 4 года назад

    what a content ..... superb

  • @hinamehndipearls4374
    @hinamehndipearls4374 2 года назад +1

    You are great 👍

  • @juancarlossanchezveana1812
    @juancarlossanchezveana1812 11 месяцев назад

    Excelente explicación

  • @lehou8320
    @lehou8320 Год назад

    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.

  • @pa7832
    @pa7832 2 года назад +1

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

    • @DrTrefor
      @DrTrefor  2 года назад +1

      Everything here is done in MATLAB

    • @pa7832
      @pa7832 2 года назад

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

  • @inquisitiverakib5844
    @inquisitiverakib5844 2 года назад

    Tangent Vector 3:27

  • @212ntruesdale
    @212ntruesdale 4 года назад +1

    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
      @DrTrefor  4 года назад

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

  • @dinmukhammedtleuzhanuly1225
    @dinmukhammedtleuzhanuly1225 3 года назад

    Thank u very mush for this video!!!

  • @wakeawake2950
    @wakeawake2950 4 года назад +1

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

    • @DrTrefor
      @DrTrefor  4 года назад +1

      Gradient only applies to a scalar function

    • @wakeawake2950
      @wakeawake2950 4 года назад

      @@DrTrefor thnk u sir🙏

  • @KaviPriyan-qt6vc
    @KaviPriyan-qt6vc 4 года назад +1

    You are great😍

  • @Sssss2t
    @Sssss2t 2 месяца назад

    Thank you very much

  • @markbell8967
    @markbell8967 3 года назад +1

    Thank you

  • @mnada72
    @mnada72 3 года назад

    The best 👌.

  • @jgkostas
    @jgkostas 3 года назад

    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....

  • @TheBgracey
    @TheBgracey 4 года назад

    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?

  • @susanjacob937
    @susanjacob937 3 года назад +1

    Thank you :)

  • @rajisingh5710
    @rajisingh5710 2 года назад

    Sir what will be unit tangent vector

  • @nomann5244
    @nomann5244 4 года назад +1

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

    • @DrTrefor
      @DrTrefor  4 года назад +1

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

    • @nomann5244
      @nomann5244 4 года назад

      Thank you for your reply and answer.

  • @marcbanfi4985
    @marcbanfi4985 Год назад

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

  • @brandonheald9624
    @brandonheald9624 4 года назад +1

    Indeed.

  • @continnum_radhe-radhe
    @continnum_radhe-radhe 3 года назад +2

    🔥🔥🔥

  • @samisiddiqi5411
    @samisiddiqi5411 3 года назад

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

  • @thecarlostheory
    @thecarlostheory 3 года назад

    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?

  • @Caleepo
    @Caleepo 5 лет назад

    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
      @Caleepo 5 лет назад

      @@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

  • @satyampanchal-1016
    @satyampanchal-1016 4 года назад

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

    • @DrTrefor
      @DrTrefor  4 года назад

      I use MATLAB

    • @satyampanchal-1016
      @satyampanchal-1016 4 года назад

      @@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?

  • @waqasmuneer7951
    @waqasmuneer7951 3 года назад

    Why a vector valued function should have only 1 input?

  • @therishi4014
    @therishi4014 3 года назад +1

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

  • @212ntruesdale
    @212ntruesdale 4 года назад

    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.

  • @anishmanandhar1203
    @anishmanandhar1203 4 года назад

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

  • @franekkos574
    @franekkos574 2 года назад +1

    🙏🏼

  • @videorome4782
    @videorome4782 2 года назад

    Where is the problem solving????

  • @geoffreyfaust3443
    @geoffreyfaust3443 2 года назад

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

  • @vaderanomaly1573
    @vaderanomaly1573 4 года назад

    thanks but pleaaase get a little mic for your collar

  • @1364aakash
    @1364aakash 3 года назад +2

    Liked? Check. Subscribed? Check.

  • @asmcriminaL
    @asmcriminaL 3 года назад

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

  • @IGJTHOMAS
    @IGJTHOMAS 4 года назад

    Solid content but that echo is hard to accept.

  • @punditgi
    @punditgi 3 года назад +1

    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
      @DrTrefor  3 года назад

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

    • @punditgi
      @punditgi 3 года назад

      @@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! 🇨🇦

  • @laalhussain4234
    @laalhussain4234 2 года назад +1

    You speak in Urdu Language

  • @khoavo5758
    @khoavo5758 6 месяцев назад

    your shirt needs some ironing, its normal is pointing everywhere and it’s distracting.
    jk of course😊

  • @adityaduggal4489
    @adityaduggal4489 2 года назад

    50 rupay kaato overacting ka