Example: Computing the Line Integral of a Vector Field (i.e. Work Done)

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  • Опубліковано 29 лис 2024

КОМЕНТАРІ • 77

  • @kylestang5703
    @kylestang5703 6 днів тому +1

    3:45 "I don't have to think very hard about what it's going to be because it's just what I know." Wise words

  • @j.o.5957
    @j.o.5957 3 роки тому +23

    I'm on a mission to watch and like every single one of the vector calculus class videos

    • @DrTrefor
      @DrTrefor  3 роки тому +7

      haha, alright looking forward to your comment on the last video:D

  • @Mortgageman145
    @Mortgageman145 9 місяців тому +1

    I’m a high school student studying classical E&M in my spare time and this video series on vector calculus has been a life saver especially when it comes to Maxwell’s equations. Thanks

  • @Independent_Variable
    @Independent_Variable 4 роки тому +27

    The timing on these videos is amazing! New to the channel, but I have devoured hours of content with no end in sight. Thank you for the enthusiasm shown on every single video, and thank you most of all for the clean and fresh perspectives you always provide. I appreciate you very much Dr. Bazett.

    • @DrTrefor
      @DrTrefor  4 роки тому +6

      So glad they are helping!

  • @shriasingh260
    @shriasingh260 16 днів тому

    I'm passing my Btech maths course thanks to this man. Literally, you're making me love calculus and I can't believe it.

  • @physicsismyfiancee...1353
    @physicsismyfiancee...1353 3 роки тому +6

    God pls make my mathematical skill like this man .great, today I have understood what i am searching for

  • @x_ma_ryu_x
    @x_ma_ryu_x 2 роки тому +2

    Wow. This was 1.5 years late. Haha. Doing my masters now and realized i passed the exam for this without fully comprehending during my bach. This is amazing. I literally spend my whole Saturday watching your videos. Thanks a lot. This channel will become huge.

  • @christopheverre4848
    @christopheverre4848 7 місяців тому +1

    Your videos on line integrals for scalar fields and vector fields have made so much more sense that what I've been reading elsewhere. Thank you.

  • @annarooney3492
    @annarooney3492 3 роки тому +3

    SIR.... YOU HAVE HELPED ME IMMEASURABLY!!! your videos have explained in 7 minutes what my lecturer could not do in 2 weeks. thank you!

  • @whodhruvjoshi
    @whodhruvjoshi 3 роки тому +12

    Hello Dr. Bazett , Your video lectures has been a boon for students like us and it's really interesting to dwell into the concepts graphically . But there is a request if you could please increase the no of examples , then it would be cherry on the top.😊
    Love from India .♥️

  • @cosmefulanito6386
    @cosmefulanito6386 3 роки тому +4

    Thank you for your enthusiasm, as a depressed student due to the pandemic i must say thank you, you are great help

  • @qamarmoavia4031
    @qamarmoavia4031 4 роки тому +2

    Thank u very much for explicit,effective,interesting explanations ..You are my teacher now ..
    your videos goes straight into my brain without any difficulty .... I should start loving math Now

  • @sanjibghosh1185
    @sanjibghosh1185 3 роки тому +2

    Ur videos r awesome for imagination and understanding,,, respect from india🙏🙏🙏🙏

  • @mohammadhomsee8640
    @mohammadhomsee8640 2 роки тому

    I am new to this channel, and I really hope to be one of your students, currently I am studying Math 3 course in university, my professor is very far from explaining the real meaning of any integral, he is only teaching us how to compute thing, in other word, he is just giving as some sort of rules to memorize and apply it, that' it !, In the other hand, you are giving as the real meaning, the real concepts of how things work !!, I really appreciate your work, Thank you so much !!

  • @arsenalaman6493
    @arsenalaman6493 4 роки тому +5

    Again .....I will say amazing video sir....thank you for it.....You again explained well with example.....And Im first to comment. 🙂

  • @robertoberidojr.435
    @robertoberidojr.435 3 роки тому +1

    Your a gift from heaven

  • @pilearn1266
    @pilearn1266 2 роки тому

    have to say I saw the full playlist and wow helps so much

  • @Alannnn14
    @Alannnn14 4 роки тому +2

    Excellent, just when I needed it!!!

  • @sumitkumarsahoo7601
    @sumitkumarsahoo7601 3 роки тому +2

    great effort sir, you will reach the peak soon

  • @chathushkaranasinghe4888
    @chathushkaranasinghe4888 3 роки тому +1

    I found this video series yesterday. This is amazing sir🔥 Nice explanations. Thank you

  • @jonpritzker9709
    @jonpritzker9709 Рік тому

    Could you link to some resources for examples to work on? I see someone else commented they want more examples, and I agree. You have example videos dotted throughout the playlist, if there could just be more of them. Like two or three examples per topic, just label em and it's easy to skip if we want. Your explanations are amazing, graphics too, your time and effort is greatly appreciated.

  • @dimaswift
    @dimaswift 4 місяці тому

    thank you, exactly what I needed 🎉

  • @cosmopaul8773
    @cosmopaul8773 3 роки тому +2

    Thank you for your work. Very helpfull.

  • @user-jm6gp2qc8x
    @user-jm6gp2qc8x 4 роки тому +1

    Yay! Been enjoying your videos so much.

  • @wasa1997
    @wasa1997 2 роки тому +1

    Instead of taking the dot product, can we still instead multiply by the magnitude of dr/dt? It makes the integration much easier since the magnitude is 1. The answer seems to be the same, so I'd assume it's a "yes"?

  • @AnilSharma-qf5lh
    @AnilSharma-qf5lh 4 роки тому +4

    Great video. So nicely explained.
    Which board/software do you use sir?

    • @DrTrefor
      @DrTrefor  4 роки тому

      I have a greenscreen behind me, I write on a dell tablet but could be anything, and then I use an actually obsolete writing software called madewithmischeif

  • @williamangus7576
    @williamangus7576 3 роки тому +2

    Can you clarify the relationship (if any) between the orientation of the x/y axes and the îhat/jhat unit vectors. Intuitively, I sense they need not be aligned and the work done (pi) will be the same. (Like starting out from a different point on the circle, but still going round 360 degrees.)

  • @viktorsegersall4449
    @viktorsegersall4449 7 місяців тому

    Thank you very much for this! I tried the same example but where the direction is clockwise on the unit circle. Hence, in the same direction as the vector field in the example. How does changing direction affect the line integral? My intuition says it should be just \pi but I am having problems coming to this conclusion by just evalueating the integral.

  • @اجملالمقاطعمنوعات-قناةعامر

    Hello sir, Can you clarify why did you assign (0, 180) as the integral limits ?

  • @ileanadominguez6055
    @ileanadominguez6055 2 роки тому

    Thank you very much for your videos!

  • @HosRo4161
    @HosRo4161 Рік тому

    Excellent!

  • @rt722
    @rt722 3 роки тому

    I may be missing something simple here but how can you guarantee that dr/dt is a unit tangent? My understanding is it must be unit tangent in order to be dotted with the vector field.

  • @Mohamedezzeldin-k8h
    @Mohamedezzeldin-k8h Рік тому

    After coming from electromagnetic field course vector calc hits really different

  • @anupriya7366
    @anupriya7366 3 роки тому

    How do we know that circle's parametric is that? Because general parametric point on circle with unit radius is ( cos t, sin t), I'm not able to figure out that r(t) vector.

  • @rodionraskolnikov6989
    @rodionraskolnikov6989 10 місяців тому

    Amazing!

  • @ismailsevimli6424
    @ismailsevimli6424 2 роки тому

    How did you specify the direction to the curve when you are parametrizing it? I didn't understand how CCW or CW will be expressed. I guess just need to change the interval of t like from 0 to 2Pi to 2pi to 0

    • @khanjeer4038
      @khanjeer4038 4 місяці тому

      You would need to change the parameters , it would be cost*i - sint*j

  • @scrappybuilds
    @scrappybuilds 4 роки тому +1

    I appreciate you

  • @MarekGonet
    @MarekGonet 12 днів тому

    Excellent
    But I spend a lot of time, why do you ignore the cost*sint expression. I know now, that it disappears during integrating.

  • @TheFpsPlayer01
    @TheFpsPlayer01 3 роки тому +1

    good job

  • @ashutoshranjan4644
    @ashutoshranjan4644 3 роки тому +1

    Its awesome

  • @zauberer1259
    @zauberer1259 4 роки тому +1

    thank you

  • @shubhamg23
    @shubhamg23 4 роки тому +2

    Why Take the curve in CCW Sense?...

    • @DrTrefor
      @DrTrefor  4 роки тому +2

      We could do either way. By convention we usually take CCW which is sort of like the convention of taking and outward normal vector vs inward.

  • @johnf7993
    @johnf7993 3 роки тому +1

    0:31 glitch in the matrix

  • @anonym498
    @anonym498 Рік тому

    what if we choose to move particle clockwise. How would it affect the answer?

    • @khanjeer4038
      @khanjeer4038 4 місяці тому

      That would change the paremeters , it would be cost*i -sint*j

  • @ahoora46
    @ahoora46 2 роки тому +1

    0:33

  • @continnum_radhe-radhe
    @continnum_radhe-radhe 2 роки тому +2

    🔥🔥🔥

  • @bijumonr559
    @bijumonr559 4 роки тому +3

    👍👍👍

  • @slipnova951
    @slipnova951 3 роки тому

    this is a line integral but it is not connected to area like in the previous videos
    little confused

  • @hrkalita159
    @hrkalita159 3 роки тому

    Sir, why the graph of F(x) is like this, arrows are connected tips and tails?

    • @DrTrefor
      @DrTrefor  3 роки тому +1

      We can't plot a vector starting at EVERY POINT so what we do instead is make a regular spaced grid and just plot the vectors starting at those grid points. THey only connect if the vectors are long enough.

  • @wisegamer706
    @wisegamer706 7 місяців тому

    legend

  • @hqs9585
    @hqs9585 3 роки тому

    how would you introduce the CW rotation to get positive work?

    • @SergioGarridoPaco
      @SergioGarridoPaco 3 роки тому +1

      by parametrization of the unit circle, instead of cos(t) i + sin(t) j you change the sign in sin(t)

  • @SuperDeadparrot
    @SuperDeadparrot Рік тому

    Could we not use the fact that C is a closed figure containing no poles?

    • @DrTrefor
      @DrTrefor  Рік тому

      Yes, it is only pedagogically out of place in the sense that my vector calculus playlist is blind to complex analysis.

  • @sergiolucas38
    @sergiolucas38 3 роки тому

    nice example :)

  • @physicslover1950
    @physicslover1950 4 роки тому

    Well done. Does the formula F.T.ds= F(r(t)).(dr/dt)*dt means that F=F(r(t)) and T.ds=(dr/dt)*dt the second one is confusing.

    • @physicslover1950
      @physicslover1950 4 роки тому +2

      Oh sorry I got it now. ds is simply |dr| and T is dr/|dr| 😀

  • @briandwi2504
    @briandwi2504 2 роки тому

    Great video! I note the unusual spelling of your forename. I wonder if you are of Welsh decent as that is how the Welsh would spell it.

  • @wiz144
    @wiz144 Рік тому

  • @hubenbu
    @hubenbu 2 роки тому

    Am I learning physics or something? Ok, just some pretty basic concept revisited.

  • @smolzfierx1099
    @smolzfierx1099 2 роки тому

    "All that mathers is the height", I dont think it is true

    • @fernandojackson7207
      @fernandojackson7207 2 місяці тому

      Ask women. They won't date you if you're below 6'. But, really, for the vector field F(x,y) xi+0j, this is fully determined by the height , i.e., the field at a fixed height yo will be identical.

  • @scrappybuilds
    @scrappybuilds 4 роки тому +2

    I appreciate you