Calculus Review: The Derivative (and the Power Law and Chain Rule)

[@Andres186000]

I unironically really enjoy the sound of the squeaky markers.

[@dennislui2938]

Steve, Prof Brunton, is one of my favorite Mathematics educators, up there along with Gilbert Strang. Besides, one time I forgot how to spell his last name, so I searched for eigensteve, and bam! Found him right away. 😅 Thanks for all the amazing videos and the efforts!!!

[@fabiofarina9579]

About remembering what we studies years ago. One of my professors, that eventually became a really close friend after my PhD, once told me that what we really know is what we remember once we forget. It's a thought that I still keep in mind after so long

[@sardorabdirayimov]

Well said!

[@johnstuder847]

One of your best lectures. Thank you for all of them.

[@acestapp1884]

Great talk, and thanks for the series. When learning the chain rule, the thing that tripped me up was that the x in f(x) and in g(x) are different x's. Using f(y) or f(u) makes the substitution much easier since there's no confusion between the x you are substituting in and the x you are substituting for. Or rather, the substitution can be accomplished syntactically, without requiring semantics about the particular x. This also makes checking your work much easier.

[@pierricbross]

Thanks for all of your new series videos! It's so well done and it's really helping me with my engineering maths course.

[@MavrikSoundsOfficial]

Thanks dude... The explicit breakdown of the rules are doing it for me... I did calculus 1 and 2 but never fully understood (or had a memorable method) for chain rule... I came up with something from your video that now I'll never forget... I just needed someone to jumpstart the process for me and this video has done that... excited about the other videos in the playlist!

[@curumo_curunir]

Thank you very much. The lecture is very insightful and helpful. I feel lucky to able to watch your videos.

[@hoseinzahedifar1562]

Very thanks... Homeworks: 1- In time 22:54: Drive the chain rule relationship (the derivative of f(g(x))) by using the definition of the derivative of a function f(x) (d/dx f(x) = lim (f(x+dx)-f(x))/dx, as dx->0), and take out why it would actually give you this expression: d/dx (f(g(x)) = f'(g(x)) * g'(x) ? Hint: you can google "chain rule", and take some ideas from Wikipedia...

[@sardorabdirayimov]

After watching it, It reminded me my lyceum years, where we used to solve all math formulas like in formula1, including derivatives. It was great times!

[@tascker0]

simply the best explanation I got. Thanks a lot.

[@virushk]

what a fascinating approach... would like a bit more emphasis on intuition though :P

[@martinsanchez-hw4fi]

All of your videos are awesome. Just think there is an error when stating the chain rule. In 22:21, that f'(g(x)) you later write it as df/dx(g(x)), but is the derivatige with respect to that inner function. Making u=g(x), we have f'(u)u'(x)=df/du * du/dx

[@shyamchauhan5269]

In the chain rule of dvtv; did you make error while writing? I think df(g(x))/dx = df(g(x))/dg(x) * dg(x)/dx, right?

[@mllo2003]

Eloquent and substantial. Great lecture !!

[@Eltrissi]

Great great work Professor. Many thanks for this interesting refresher .

[@makavelilcf]

great lecture, however the chain rule I would write differently: d f(g)/ d x = df/dg * dg/dx

[@danch_ranch6594]

I always get fascinated by how Steve manages to write all this backwards😂

[@chrisharri7376]

Hi Steve, thank you very much for all your great videos! Although I already graduated in ME and had this, this classes are an amazing learning/ recap resource!! At 18:24 I was just wondering if this should be of Big Omega instead of Big O as it is lower bounded by n^2 instead of upper bounded?

[@robvp71]

Wow, excellent lesson!

[@marcfruchtman9473]

Teaching from behind a clear writing board, requires so much more skill... it is amazing how easily you do it. I have to wonder what happens when you try to write on paper! LoL. Not only that but to write out all the formulas backwards from normal... that's simply astounding.

[@meunomemauricio]

If you watch some of his early videos in the channel you can see that he is left handed. He's writing normally on the glass and mirroring the video in editing. But even though it's a "trick", I still think it's quite ingenious :D

[@marcfruchtman9473]

@@meunomemauricio Ah, well that is a cool trick! Thanks for the info!

[@curtpiazza1688]

WOW! Great review! Thanx! 😂 🎉 😊

[@taimuralishams304]

@steve brunton Derivative of a complex polynomial generated yet another polynomial of 1 degree less than the original polynomial. I understand that when one point is inserted into derivative of a polynomial, it will output one single value which would be the slope of original polynomial at that concerned point. My point is why derivative of a complex higher order polynomial outputs another polynomial at first place and what is its meaning graphically ? Thanks

[@TheChemicalProcessEngineer]

done many thanks

[@harikrishnanb7273]

Is the rate of change, multiplication or addition?

[@gemy6188]

But I think delta X = 0 to power any number will be one not Zero ? 19:39

[@user-mg5oz2ls9u]

Are you writing in reverse direction? If yes, then its cool.

[@AVRiegel]

He's left-handed, so I'm afraid he "just" mirrors the video afterwards ... But yeah, it would definitely be cool.

[@krishnendudas8573]

The way our brain works or reacts based on changes in multiple parameters is also a use case of differential calculus. Is it true?

[@James-md8ph]

Nice explanation 🙂

[@stavroguine3239]

Okay I am quite new at this, so I guess it's an stupid question: How can i download the Jupyter notebook from the website? When I am clicking on the .ipynb file it's just opening a new webpage with text (JSON I guess)

[@shreddingstranger]

To use Jupyter you need to have Python installed on your pc. If you don't have Python installed yet, I'd recommend downloading Anaconda Distribution. This has a package manager, that has a lot of usefull packages (including Jupyter) for Python already pre-installed.

[@stavroguine3239]

@@shreddingstranger Hi Richard, thank you for your answer. I have installed python and I am able to launch Jupyter Notebook. My problem is to download the files from the course website. I am ending up on a webpage with text which is not python: faculty.washington.edu/sbrunton/me564/python/L01_weather.ipynb

[@shreddingstranger]

@@stavroguine3239 Oh, I misunderstood. Rightclick>save link as.. and than opening that saved link with Jupyter should work. (Or saving the link directly to your Jupyter working directory)

[@stavroguine3239]

@@shreddingstranger It worked, idk why I didn't try this.Thanks for the help!

[@An_Attempt]

Good revew.

[@SaravanakumarKarunanithi]

Thank you.

[@krillnyetheshrimpguy6152]

beard is lookin' good!

[@Thesportynerd16]

this is so epic

[@lioneloddo]

Something that I have never understood. If we need a later time to get the speed from position, then it means that we can never have simultaneity or coincidence between position and speed. Position is always known before speed. There is a delay between position and speed. Is it the reason why in quantum mechanics, we can can not perfectly know both the position and the speed ?

[@karatsurba4791]

Speed is derived from position. So, not sure what you mean by "simultaneity between speed n position". QM is probabilistic in nature. So you can determine the likelihood position of a particle.

[@lioneloddo]

@@karatsurba4791 Speed is derived from position. Yes, and how do you do your derivation? You use two positions at two different times. So it's not complicated to understand that speed (or velocity) can not be known at the same time as position. When you know P1, position at moment 1, you don't know yet the velocity.

[@karatsurba4791]

@@lioneloddo Velocity is rate of change of position. So, if you know P1 (starting position) & P2 (final position) & you know the time 't' it takes to reach from P1 to P2, then you have velocity. It's terms of formula it'll be (P2 - P1) / t .

[@lioneloddo]

@@karatsurba4791 I don't agree. t = T2-T1. The only way to have simultaneity between position and velocity is to make the same assumption as Leibniz. You have to suppose that differentiation is out of the world. Leibniz used the letter "d" to indicate that it's only true out of the physical world, in the infinitesimal world.

[@karatsurba4791]

@@lioneloddoMay be it wasn't obvious. 't' is the time taken from P1 to P2, so that's T2-T1, where the time 't' is infinitesimally small.

[@queasybeetle]

Thanks. Super useful for understanding backprogation in neural nets.

[@PhuongAnhNguyen-ei4mu]

god bless you

[@jamalan7417]

ledge

[@zivhellman2806]

Please pronounce the name of Leibnitz correctly. He was a sufficient genius to deserve us getting his name right

[@DanKleeman]

[@cukkoogaming4755]

Wow he could write backward lol