100 thoughts on “Lec 2 | MIT 18.03 Differential Equations, Spring 2006

  • October 20, 2010 at 8:30 pm
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    29:37 xaxaxax that was great xD

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  • December 10, 2010 at 9:23 pm
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    i do not understand what the men in black were about. They also appeared in the electromagnetism lecture. May someone please inform me what that is about

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  • April 25, 2011 at 6:36 am
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    My teacher was awfull next to this guy when I did that class

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  • July 12, 2011 at 1:18 am
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    lol at 9:54 watch how he pockets the chalk.
    LMAO

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  • September 8, 2011 at 2:35 am
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    he needs to explain where hAn comes from a bit better.

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  • September 22, 2011 at 7:09 pm
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    What the heck happened at 29:40!?
    What was that!? A kind of commercial or a special break!?
    uHAUHuhauhUAHUhuaHUHA

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  • September 28, 2011 at 4:09 am
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    @darylicked
    using the eqn: y = mx+c

    (delta)Y + c = m(delta)X + c
    (delta)Y = hAn

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  • January 3, 2012 at 3:46 pm
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    this is awesome

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  • January 8, 2012 at 4:20 am
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    @Tsoy1984 yay!

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  • January 15, 2012 at 12:39 am
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    @fdlbeats not with grammar like that

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  • January 23, 2012 at 11:31 am
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    Sir How we assume that the next Yn+1 element also comes on the same curve and has slope "An" as those of Yn.How this is possible as per Euler's.It may come with negitive slope.Consider a sine wave suppose at the maximum Yn=1 (The maximum value of sine wave) Here Yn+1 Element does not have the same slope as Yn. We cannot suppose it as An.Please clarify this.

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  • January 30, 2012 at 11:39 am
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    awesome lesson

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  • January 30, 2012 at 11:39 am
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    Interesting video

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  • January 30, 2012 at 11:36 pm
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    whats his name?

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  • February 20, 2012 at 10:48 pm
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    OMG you just made me understand the first three weeks of class in 50 minutes. So THIS is what you pay for at a university….wow….

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  • February 25, 2012 at 1:51 am
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    Euler is too high. 😀

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  • March 2, 2012 at 4:43 pm
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    2:54 I actually did! XD When I was trying to deduce the equations of motion of bodies affected by gravity that's the first thing I made up to give me an approximation. I guess I'll skip this one.

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  • March 2, 2012 at 4:45 pm
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    @raydredX It's the first time I hear this has a name. People seem to like to give long names to simple things.

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  • March 3, 2012 at 5:31 pm
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    I struggled to learn all this over 4 weeks of 1 and half hour lectures and this guy made it crystal clear in 50 mins….

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  • March 6, 2012 at 11:23 am
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    @euanfoster thats a typical "rook at me, im going to torronto" thing to say

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  • March 7, 2012 at 4:10 am
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    @ellliotlai Haha

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  • March 9, 2012 at 9:10 pm
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    29:37 What just happened? I'm confused…

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  • March 30, 2012 at 5:10 pm
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    good stuff…

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  • April 2, 2012 at 7:42 am
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    I've seen it in other MIT videos. It's so painfully awkward.

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  • April 2, 2012 at 7:48 am
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    cool story bro

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  • April 2, 2012 at 7:50 am
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    his chalk, his rules.

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  • April 2, 2012 at 2:00 pm
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    Why thank you dear sir chap.

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  • April 11, 2012 at 11:04 pm
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    29:36 "THAT MEANS YOU, PRETTY BOY"

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  • April 24, 2012 at 8:13 pm
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    It doesn't come the same curve, it only comes close (hopefully). Most solutions to deq's can't be expressed as well defined functions such as sin. Therefore they can only be approximated which is what this method is for. It is similar to irrational numbers being expressed in decimal form. It can't actually be done be it can be approximated to varying degrees of success that are often close enough for practical use.

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  • October 25, 2012 at 7:28 pm
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    thanks a lot, great lecture.

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  • November 4, 2012 at 9:41 pm
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    anyone have an idea of what the homework-pitfall could be? Something that destroys the fait in numerical methods forever… Somehow seems good to know 🙂

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  • November 9, 2012 at 8:45 pm
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    this is great. thanks, Prof!

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  • November 10, 2012 at 12:38 pm
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    I love it!

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  • December 3, 2012 at 3:53 pm
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    brilliant… 😛

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  • December 9, 2012 at 12:30 pm
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    my little box of treasures 😀

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  • December 9, 2012 at 5:08 pm
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    23:28 WTF?

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  • December 9, 2012 at 7:00 pm
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    40:47, this prof is hilarious

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  • December 11, 2012 at 8:31 pm
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    Why isn't his name on these videos?

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  • February 3, 2013 at 8:25 am
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    let's say that I am in LOVE with this old man 🙂

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  • February 12, 2013 at 3:57 am
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    MIT doesent have HD cameras or what?

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  • February 27, 2013 at 12:24 pm
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    We meet again 240p.

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  • March 30, 2013 at 12:07 am
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    Best part of the lecture.

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  • May 6, 2013 at 4:19 am
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    29:35.. what???? LOL

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  • May 14, 2013 at 6:19 pm
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    OKkkay will you plese tell me the reference of euler too high too low ? cuz i didnt get this joke because of being not american.

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  • May 21, 2013 at 2:14 pm
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    I found watching PatrickJMT's explanation on Euler's Method helped me better understand this professor's lecture.

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  • May 27, 2013 at 1:39 pm
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    I don't think they had HD cameras in 2003.

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  • May 27, 2013 at 3:58 pm
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    Perhaps you should read the title of the video again 😛

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  • June 20, 2013 at 2:33 pm
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    240p knew I was coming didn't it…

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  • June 20, 2013 at 2:47 pm
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    His notation for euler's method is incorrect. He should've use the linearization. Much more understandable.

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  • July 24, 2013 at 4:51 pm
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    This was actually recorded in 2003. The videos were later used for a class in Spring 2006. This info is from MIT in the comments of the first lecture.

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  • August 18, 2013 at 4:00 am
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    His comments around 44:00 are completely wrong!
    For a particular step size h Runge-Kutta achieves h^4 accuracy, so halving the step size improves the accuracy by 16 times.
    If you use Euler's method with a step size of h/4, so that both methods perform the same amount of work, he says that Euler's method also gives a 16 times improvement, but this is NOT true. Euler's accuracy is order h so you only get an improvement of 4 times
    There's a reason people use higher order methods!!!

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  • September 5, 2013 at 4:17 am
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    we still used the terms concave up/down in my AP Calc class….

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  • September 9, 2013 at 1:40 am
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    29:37 lol whaat

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  • September 21, 2013 at 6:22 am
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    Funny professor 🙂

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  • October 12, 2013 at 11:31 pm
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    I can't help but think, as I watch lectures from Yale, MIT, etc., that the material at my lowly Midwestern state university contain the same material covered in a similar manner (only much, much cheaper). There is also a much lower suicide rate at my university than in the Ivy League.

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  • October 16, 2013 at 4:29 am
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    ……….and also much less prominent intellectual leaders

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  • October 21, 2013 at 4:07 pm
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    these lectures are great!

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  • January 3, 2014 at 2:49 am
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    Calculous to the rescue! 
    In calculous we trust

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  • March 10, 2014 at 1:07 am
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    Great Lecture!, thank You MIT!

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  • August 18, 2014 at 7:40 am
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    shouldn't y" = 2x because the derivative of y^2 in terms of x equal zero?

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  • February 3, 2015 at 7:26 pm
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    holy crap these lectures are so much easier to follow than at my school!

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  • April 7, 2015 at 5:53 pm
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    I love Mattmatic its only way we can talk to – Aliens in space =)..

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  • September 4, 2015 at 12:46 am
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    thanks for making mathematics simple prof

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  • September 4, 2015 at 4:25 pm
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    Euler too high

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  • September 30, 2015 at 2:39 pm
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    "halve the step size, halve the error"
    Shouldn't that mean that if you halve the step size once, you know how big half the error is. And if you then add/subtract that error twice you should get the true (almost) value of the function?

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  • October 2, 2015 at 2:50 pm
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    i don't get how he got the other side of the triangle to be h*An. That would only work if the slope was equal to the hypotenuse and I just don't see how that's true.

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  • October 7, 2015 at 8:28 pm
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    I've started quoting these lectures like movies… I might be a nerd. "SAME!" "My little box of treasures."

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  • December 6, 2015 at 2:38 pm
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    22:39 26:53 29:36 LOL, I love this guy. 😀

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  • December 16, 2015 at 11:20 am
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    dont be late~~~~~~~~~~~~~~~~~~~~

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  • January 17, 2016 at 7:20 am
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    Of course the comment that euler being exactly right is not an option is said tongue-in-cheek, but the humor to be noted is that the points on the annoying line from earlier that is both an integral curve and an isocline (but not easily drawable) is the gift that keeps on giving, as it corresponds to such a situation, since y''=0 for all x along its length.

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  • February 5, 2016 at 10:25 pm
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    Thanks Prof,you are great!!

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  • June 8, 2016 at 7:24 pm
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    Such a great teacher…What a pleasure to learn maths with you. Thanks!!

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  • July 15, 2016 at 7:39 pm
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    A quick question. What if there are 2 differential equations? Such as dx1/dt = f(x1,x2) dx2/dt = g(x1,x2). Anyone please…

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  • July 25, 2016 at 10:36 am
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    对理解微分方程很有用,来自BUPT。

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  • July 31, 2016 at 6:26 pm
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    Why can't one use a numerical method incorporating the second derivative [from the Taylor series] so that accuracy is better [which for second order function will give accurate results]. i.e. y(n+1)=y(n)+h*y'(n)+h^2*y''(n)/2
    The second derivative can be induced from the first derivative as shown in this lecture at 21:45

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  • September 4, 2016 at 2:11 pm
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    Why y(n+1)-yn= h.An??????

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  • October 9, 2016 at 12:00 pm
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    love how mit perform the lectures with chalks .no one these days take the trouble of writing on the board and actually do their jobs . great lecture ^^

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  • October 9, 2016 at 1:11 pm
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    27:00 PRECIOUS

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  • December 9, 2016 at 5:00 am
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    GATE examination tension brings me there,thans prof

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  • January 17, 2017 at 10:22 pm
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    We say 'plus' and 'minus' in the U.K. Not just in mathematics either, I work in aviation, 'outside air minus 2'. I only use 'Negative' as an adjective, "the value is negative" but I consider the value '-2' to be more of a complete identity. I don't think that we're describing 2 as negative, we're identifying a unique value that is 'minus two'. That's just our convention though.

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  • March 5, 2017 at 1:34 pm
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    This Euler is a genius. He has contributed in every form of math. Graph theory was his child. Father of Number theory. Also in DE. He must have been a genius among geniuses.

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  • March 18, 2017 at 10:02 am
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    I like the lecture.
    BUT I didn't like the jokes.

    Does anyone else find his attempts at being funny and entertaining a bit annoying? I understand it that the great majority really likes all this "Euler too high" jokes, and I'm ok with that. It just seemed strange to me that nobody said that they can be irritating when you are following the line of math reasoning and have to constantly stumble upon these. I mean, otherwise he's going with the material at a good pace, then suddenly out of the blue: "feed the cold" etc. and you have to wait until he's done with it.

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  • May 16, 2017 at 6:00 pm
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    What's the first pitfall that Prof. Arthur wants us to find out? Is it the 'error accumulation'?

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  • July 4, 2017 at 7:05 pm
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    don't be late…

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  • July 17, 2017 at 1:38 pm
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    23:28 "UEHEUEHO" love those vocalizations

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  • July 17, 2017 at 1:39 pm
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    23:37 LOL

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  • September 10, 2017 at 1:37 pm
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    Sir, commendable job!! 👏🏽
    Euler too high made my day 🙂

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  • November 11, 2017 at 8:36 am
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    a great teacher

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  • December 28, 2017 at 3:10 pm
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    Can't we use the second derivative to calculate y_(n+1)?

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  • February 18, 2018 at 11:45 pm
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    Bolsonaro 2018 ! See ya !

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  • February 26, 2018 at 8:28 pm
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    13:24

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  • March 15, 2018 at 6:33 pm
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    teachers like him are angels i wish i could have got the same

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  • March 29, 2018 at 5:18 am
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    DON'T BE LATE!!!!!

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  • May 27, 2018 at 4:17 pm
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    Idk how to express it.. but the way he explains the concepts is just so clear and straightforward. Truly this must be what it means to be a really good professor.

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  • May 27, 2018 at 5:11 pm
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    DON'T BE LATE lmao

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  • June 8, 2018 at 8:01 pm
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    Great lecture

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  • May 3, 2019 at 9:20 pm
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    I clicked on this video to make me sleep and yet I watched the whole video learned something 😂

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  • May 14, 2019 at 9:49 pm
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    Thank you for the clarity.

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  • July 12, 2019 at 5:58 pm
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    We can calculate the energy of a spinning gold ring where the integral is the energy of the speed of the charged platinum spinning in the center of the ring magnetally separated.

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  • September 10, 2019 at 1:41 am
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    What was the Pitfall #1? Any1?

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