Calculus 3 Final Review (Part 2) || Double Integrals, Triple Integrals, Change of Variables

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  • Опубликовано: 12 дек 2024

Комментарии • 81

  • @LudusYT
    @LudusYT  5 лет назад +24

    Donations really help me get by. If you'd like to donate, I have links below!!!
    Venmo: @Ludus12
    PayPal: paypal.me/ludus12
    Patreon: patreon.com/ludus1

    • @esfandiyar2350
      @esfandiyar2350 4 года назад

      Hey there. At 28:50 , why do you complete the square as opposed to traditional factoring, which would give you x(x-2) +y^2 = 0

  • @mingyuetang7041
    @mingyuetang7041 5 лет назад +74

    Hands down the best cal3 review video!!! I took multivariable calculus in cal with a super famous professor who has cal3 video on MIT opencourse, and you explain the material even better than him.

    • @LudusYT
      @LudusYT  5 лет назад +6

      Mingyue Tang - I'm happy to hear that it helped! I haven't tried to dissect my teaching style (yet), but I think it just helps that I try to be as relatable as possible. I took calculus 3 about a year ago, so I know where I struggled, what I got frustrated with, and what I wish was explained better.
      I think this makes me more relatable than your average teacher, and hopefully will help students learn more efficiently. Definitely let me know your thoughts!
      Btw, I saw you subscribed. Thanks for helping me get closer to 1k, it really means a lot!

    • @mingyuetang7041
      @mingyuetang7041 5 лет назад +2

      @@LudusYT I definitely will recommend your videos for whoever taking cal3!

    • @LudusYT
      @LudusYT  5 лет назад +1

      Mingyue Tang - Thank you so much!

  • @masonreno8957
    @masonreno8957 2 года назад +103

    Its crazy to me that you can learn every everything in calc 3 in 3 videos. for free.

    • @LudusYT
      @LudusYT  2 года назад +14

      Glad I can help man!!

    • @Alexander-yh3nw
      @Alexander-yh3nw Год назад +25

      its even crazier that you can learn it all a week before the final

    • @Nick._.kucera_
      @Nick._.kucera_ Год назад +4

      @@Alexander-yh3nw Thats what Im currently trying to do lol

    • @matthewryan5822
      @matthewryan5822 Год назад +18

      @@Nick._.kucera_ Twas the night before the final

    • @eddiesamuel3721
      @eddiesamuel3721 Год назад

      tryna learn 4 days before finals @@Alexander-yh3nw

  • @NameMachineBroke
    @NameMachineBroke 5 лет назад +29

    Once again, your videos have helped me prepare for exams since they are comprehensive and put concepts in relation to the other skills students need to succeed in these calculus courses. And once again, I thank you for the time you put into creating these all while maintaining your own academic success. Thanks Josh!

    • @LudusYT
      @LudusYT  5 лет назад +2

      Jake Heckert - thanks so much man!!! I’m really glad I could help you out!

  • @litang1914
    @litang1914 4 месяца назад +1

    I've been struggling a lot this semester (I haven't been putting in the work I should be), but your videos have been helping me SO SO much. You explain everything so well it's insane.

  • @erich3892
    @erich3892 5 лет назад +17

    THANK YOUUUUUUU BROOOO omg dude like im crying rn

  • @liamsexton7758
    @liamsexton7758 3 года назад +4

    So incredibly helpful. Excellent explanations and examples. This is really gonna help me pass my test.

  • @gon2407
    @gon2407 3 года назад +9

    Seeeshhh bro got a sick fade

  • @forceview3
    @forceview3 6 месяцев назад +5

    Well I’m just here seeing what the future holds. Just passed Calc 2 with a 75

  • @tobeejefferson8831
    @tobeejefferson8831 4 года назад +2

    Ludas.. Man.. That trick with Jacobians.. You're a god. Why haven't I seen this? The system of equations is torture. Thank you.

  • @jas.6x
    @jas.6x Год назад +2

    hi ludus, i found this video really helpful! just one quick note: i think the you need to take the abs value of the jacobian when you substitute it into the double integral, so it should've been positive 1/2.

  • @nikolaimikhail7774
    @nikolaimikhail7774 3 года назад +7

    I'm so scared, this final has literally shown up in my nightmares

  • @Dina-he1uc
    @Dina-he1uc 4 года назад +2

    i never understood the inverse of the jacobian thing, my textbook used like a whole page explaining it and it made no sense, yoou made it so simple thank u :)

  • @Armand__
    @Armand__ 4 года назад +2

    that jacobian trick was bomb. thx my guy

  • @geromeabad
    @geromeabad 2 года назад +2

    Got a final today for calc 3 this helped a lot thanks bro!

    • @LudusYT
      @LudusYT  2 года назад

      No problem man!! Glad I could help!

  • @coletongross7951
    @coletongross7951 3 года назад +14

    I think there's a mistake at 1:16:26, you put dy/dv instead of dv/dy. Same answer for the Jacobian but idk if that is a coincidence or not.

  • @jasonrichards5192
    @jasonrichards5192 Год назад

    Thank you for your help. Hopefully I can ace this final!

  • @doradorahaisai
    @doradorahaisai 2 года назад

    Thank you for showing that trick for calculating a Jacobian.

  • @dianaantillon1984
    @dianaantillon1984 5 лет назад +6

    Thanks for this awesome video! I do have a question though. How did you obtain the bounds for theta at 32:15? Thank you!

    • @LudusYT
      @LudusYT  5 лет назад +7

      Glad I could help!! So, forget about the graph for a second, and just think about what polar coordinates look like with your r and theta. r is the distance from the origin, and theta is the angle made with the positive x-axis.
      Now, at the moment, my understanding of this problem is kind of escaping me (I'm a bit stressed with finals), but what it looks like I was getting at was that this graph r=2cos(theta) is present in the fourth and first quadrants, which have angles that range from -pi/2 to pi/2.

    • @christopherrosson2400
      @christopherrosson2400 2 года назад

      How do you find the bounds using math and not intuition

    • @CurrentlyObsessively
      @CurrentlyObsessively 2 года назад

      plug in rcostheta for x and rsintheta for y and solve for r

    • @CurrentlyObsessively
      @CurrentlyObsessively 2 года назад +1

      unless you meant for theta. Which was to set 2costheta equal to 0 and solve for theta. cos only equals 0 at +/- pi/2.

    • @christopherrosson2400
      @christopherrosson2400 2 года назад

      @@CurrentlyObsessively Thank you. Your videos are great by the way

  • @xaviernavarro7236
    @xaviernavarro7236 2 года назад +1

    at 38:43, there is a mistake, you forgot to subtract the 8(sin(0)/4+sin(0)/32). I appreciate the video though; everything else was really understandable and easily grasped, thank you for reviewing for us.

    • @luke8558
      @luke8558 Год назад

      sin(0) is equal to 0, so that term is arbitrary

    • @xaviernavarro7236
      @xaviernavarro7236 Год назад

      @@luke8558 lmao I must've been tired

  • @mathewhanna6410
    @mathewhanna6410 3 года назад +3

    hey @ludus so i understand how you are getting the limits @21:50 but is is okay for the lower limit to be x^2 and the upper to be rad x? For the first integral dy. I feel like that doesnt make sense, can u make a further explanation? Thank you

  • @maishalosker7496
    @maishalosker7496 3 года назад +1

    thank you so much for your videos. I'm also struggling with graphing quadric surfaces. Could you please make a video on that like the way you did for cylinder 28:33

    • @techno2371
      @techno2371 Год назад

      I recommend drawing a simple level set, finding similarities to 2D functions, and looking at the behavior around the axis.

  • @cowblasterr
    @cowblasterr 15 часов назад

    got my final on the 14th 🙏🙏🙏

  • @arturptak544
    @arturptak544 3 года назад +1

    this man is god

  • @hashtech123
    @hashtech123 5 лет назад +2

    hey josh thanking you again for this amazing video, but i request you to make 20 to 30 mins videos for each concept saperately

    • @LudusYT
      @LudusYT  5 лет назад +2

      hashim raza - I’m glad this helped! Definitely, let me know if you have any questions.
      I should have been giving reminders after every other topic to take a break so students don’t get burned out watching. I will definitely have to start doing that.
      While there will be videos that I make that are 20-30 minutes (such as the series on Special Relativity that I have coming soon), I do want to continue making these final review videos longer.
      To be completely transparent, the reason for this is because it helps me get more watch time and so RUclips will be more likely to recommend my video. I’ve made hundreds of videos that are sub 10 minutes, and very few of them have over 100 views.
      I’m essentially mimicking the Organic Chemistry Tutor’s style of making longer videos. This is how I believe he was able to blow up in such a short amount of time. I hope that by making higher quality videos, and making them the same length, I hope to see the same growth.
      Definitely let me know your thoughts!

    • @LudusYT
      @LudusYT  5 лет назад +1

      Hashim raza - I actually may have missed your point. I was more talking about keeping the final review videos long, and that’s what I thought you were requesting. I can absolutely take a look at making in depth videos for each of these concepts. It will take some time though because I have multiple projects in the works for this summer. I will be creating courses and series and a whole bunch of other stuff. I will also hopefully be doing a series on Vector Calculus, with 20-30 minute videos covering each topic such as Line Integrals, Surface Integrals etc. It will be kind of like 3blue1brown but more applicable to academia.

    • @hashtech123
      @hashtech123 5 лет назад +3

      @@LudusYTthese videos are excellent, amazing, i love them and i get your point. thanks for the reply, you're the first youtuber from whom I've gotten a reply.

    • @LudusYT
      @LudusYT  5 лет назад +3

      Hashim raza - I’m glad you like them! I love responding to the comments I get because the majority of them are really positive and encouraging (like yours).
      If you know anyone else who these videos could help be sure to pass them on! We’re about to finally hit 500 subs lol. I’m watching the sub count like a hawk.

  • @sophieperron8446
    @sophieperron8446 День назад

    this vid is life changing. doing gods work fr. hit that subscribe button bc you better than my professor

  • @michaelmalgioglio1532
    @michaelmalgioglio1532 7 месяцев назад +1

    Isn’t the Jacobian supposed to be an absolute value?

  • @leguardianproperty856
    @leguardianproperty856 2 года назад

    Hey Ludus, may I know what's kind of the tool you use to write note like to did in your RUclips videos ? I guest it's an Apple ipad with pencil, right? Your teaching is awesome!

  • @zaimelkalai256
    @zaimelkalai256 4 года назад +4

    shouldn't the jacobian in the last problem be 1/2 because it is absolute value of determinant?

    • @vanilla-vx3pd
      @vanilla-vx3pd 3 года назад +1

      That's also what I was wondering

    • @eikhiyatun7677
      @eikhiyatun7677 2 года назад +1

      Yeah, it’s suppose to be a positive 1/2, not negative.

  • @osmanf9901
    @osmanf9901 Год назад

    My boy got the haircut after part 1 😂😍

  • @youreyesarebleeding1368
    @youreyesarebleeding1368 2 года назад

    For the first triple integral, shouldn't the bounds for Z be from 1 to 1+x+y? We know the bounds for x are from 0 to 1, and for y it's from 0 to sqrt(x) -- thus the minimum for both X and Y is 0 -- and 1+0+0 = 1, giving a minimum value of 1 for Z.
    edit: Nevermind, i didn't read the problem fully, it says, "above the region in the x-y plane"

  • @SiddKid01
    @SiddKid01 3 года назад

    @ 20:32 how do you just know that point is (1,1).

  • @Jackymomo1
    @Jackymomo1 2 года назад +1

    i thought you had to take the absolute value of the jacobian?

  • @dcon_11
    @dcon_11 4 года назад +1

    At 1:19:05, how did e^0 turn to 1/2?

    • @LudusYT
      @LudusYT  4 года назад +3

      it was e^0/2, and since e^0 is 1, e^0/2 is 1/2. Sorry I was rambling and not saying things correclty.

    • @dcon_11
      @dcon_11 4 года назад

      Gotcha, thanks so much!

  • @nathanteig7108
    @nathanteig7108 2 года назад

    When converting the z, why did you make z from 0 to 2r instead of just 0 to 2?

  • @indianjitsingh8838
    @indianjitsingh8838 4 года назад

    i think you made a mistake at 1:05:31. isnt sin^2(x)=(1-cos(2x))/2. You did not divide by the 2

  • @georgesadler7830
    @georgesadler7830 Год назад +1

    Professor Ludus, thank you for an outstanding video/lecture on Double Integrals, Triple Integrals and Change of Variables in Calculus Three. Setting up and solving each problem in this video is good, however equal signs are missing in between each problem and the solution. Professor Ludus, as you indicated. in the video, you are going very fast on each problem, please slow down so all students can absorb this complex material. Whenever a student took Calculus Three for the first time, it is huge struggle to understand the material. The best way to learn Calculus Three is by teaching /tutoring it to students. Self-study is another way to master the concepts in Calculus Three. Please correct these errors in the video.

  • @xk6gg32010
    @xk6gg32010 2 года назад

    Do you offer virtual tutoring services?

    • @LudusYT
      @LudusYT  2 года назад

      Yes, email me at luduslearningyt@gmail.com

  • @admirmujkanovic8159
    @admirmujkanovic8159 2 года назад

    What type of drawing pad are you using?

    • @alannafey
      @alannafey 2 года назад

      I believe he's using an iPad with an apple pencil

  • @sweetness4j1
    @sweetness4j1 5 лет назад

    i think you made a mistake with the limits at 57:38

    • @LudusYT
      @LudusYT  5 лет назад

      Can you give me some context so I can help you?

    • @sweetness4j1
      @sweetness4j1 5 лет назад +1

      See 0 to 1 is both on r and cos, but you only got it on for r

    • @LudusYT
      @LudusYT  5 лет назад +4

      So, I think you're confused with how I'm separating the integrals (correct me if I'm wrong).
      Long story short, cos^2(theta) doesn't have an r in it, so we don't have to integrate over r, we can separate it out into it's own theta integral. We end up separating this into two separate integrals, one with thetas and one with r's. This will only work when two functions are being multiplied, NOT if they are being added.

  • @esfandiyar2350
    @esfandiyar2350 4 года назад +7

    LMAO 1:01:25

  • @thunderd7904
    @thunderd7904 Год назад

    33:20

  • @tiagojoelcoronel3143
    @tiagojoelcoronel3143 8 месяцев назад

    fucking legend

  • @gracepierle6648
    @gracepierle6648 Год назад

    Thank you 🙏🙏🙏🙏michigan math sucks