Real Analysis | The Fundamental Theorem of Calculus

We prove both parts of the Fundamental Theorem of Calculus.
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[@goodplacetostop2973]

22:53 Michael: *uploads a video outside of regular schedule* Me: _I’ve been tricked, I’ve been backstabbed and I’ve been quite possibly, bamboozled_

[@grzechu9751]

no homework today?

[@goodplacetostop2973]

@@grzechu9751 Homework is for the 8AM EST video. You can find the today’s homework on the previous video.

[@goodplacetostop2973]

@@grzechu9751 Reasons are that far more people watch the morning video (still EST timezone) compared to the evening video and that Michael doesn’t upload an evening video every day.

[@grzechu9751]

oh i didn't saw that he already add a video today, thanksfor telling, have a nice day

[@hybmnzz2658]

18:10 I think you should define M as the supremum of the function on the interval [a,b] instead of [x,y]. Because for Lipschitz continuity you need to show there exists an M such that for any x,y the inequality follows. Not that for any x,y there exists an M. Our choice of M should NOT depend on x,y. (In fact you could erroneously prove any function is Lipschitz continuous if you do this subtle error of choosing M afterwards)

[@nickvideen4785]

Doesn’t M need to be the sup for the absolute value of the function?

[@arvindsrinivasan424]

I’ve been wanting to see the proof for the generalization of this (Stokes theorem) using differential forms... I know it’s not really real analysis

[@samisiddiqi5411]

I really love this course. We should learn this before Calculus, or at least combine this, Precalculus, and Calculus, into one subject.

[@stefanveskovic4317]

I feel very happy that KZbin recommended your video. Thank you for the best content

[@AltinoSantos]

Thank you very much for your all videos. They help teachers and students a lot. That is an elegant proof of FTC based on MVT. I enjoy your videos, mainly those about calculus. Thanks again.

[@jonaskoelker]

At 12:20 Michael constructs a sequence of partitions P_n such that U(f, P_n) - L(f, P_n) -> 0 as n -> infinity. I'm not sure it follows from this that U(f, P_n) is convergent on its own, and likewise for L(f, P_n). To fix this, let Q_n = P_1 u ... u P_n. Then U(f, Q_{n+1})

[@mathwithjanine]

Awesome video! You are a great teacher!

[@TechToppers]

22:53 When you are earlier than the Guy named, *Good Place to Stop* ! Hey, Michael Sir! Did you screw up again on scheduling stuff?? Or, this was planned so that *Good Place to Stop* comments after me.

[@MsOops12]

I think part 1 of FTC is supposed to be part 2 of FTC and vice versa. At least that's how it's shown on other sites

[@punditgi]

Capstone video. We have arrived at the Promised Land! 😇

[@luissaybe]

Great content, best channel to learn about analysis

[@arturwiadrowski1739]

Professor, I really enjoy your videos. Could you please do one on some identities involving the trilogarithm, for instance about the value it takes at 1/2 or at 1/goldenratio^2?

[@JDMathematicsAndDataScience]

I appreciate these videos. Do you plan on continuing through to Stone-Weierstrass and other topics?

[@aaronhunt4302]

Yeah, the timing of this video is almost spooky. I was reviewing this earlier today 😆... What are the odds???? .... hmm 🤔

[@madhukushwaha4578]

Hii, If you want more harder questions then I will highly recommend you this channel's latest videos #mathsandphysicsfun

[@CM63_France]

Hi, For fun: 1 "all the way up to", 4 "great", 1 "ok, great", 1 "next what we want to do is", 3 "so let's go ahead and", 1 "now let's go ahead and", 3 "so let's may be go ahead and".

[@Mathcambo]

Good teacher

[@ahorribleperson3302]

Is this meant to be visable? (11/19/2020)

[@paominlienguite2397]

Thank you sir... ♥️

[@tuckerhuang4155]

thanks!!!!

[@solcarzemog5232]

NOBODY on KZbin proves the fundamental theorem sequentially. They all prove it backwards, meaning, they use the result to prove the hypothesis.

[@shafiqkhanqureshi9304]

Watching from pakistan

[@jimallysonnevado3973]

What the hell is lipschitz

[@tsunningwah3471]

like

[@grzechu9751]

can you put your also Real Analysis videos in one playlist already?