Complex Analysis 04: Harmonic Functions

Complex Analysis 04. Harmonic functions and the harmonic conjugate

[LoxagosSnake]

Gotta be the most explanatory, concise, thorough math teacher out there! Thanks for supplementing what my stupid textbook thought should be clear.

[DavidPhamthegort]

Absolutely phenomenal. Thank you for the concise, informative video!

[thegoldenratioandbeyond]

Great video, but minor differentiation mistake at 11:27 Im component

[roiorzach]

Mathematical mathematics Memes brought me here lol

[HilariousSibanda]

Am trying to find the conjugate function of u = x²-2x-y² but With reference to 5:54, my Vx is not purely a function of x but 2y and I can't see where am making the mistake. Please kindly assist.

[piotrschmidt]

best explanation of complex analysis on youtube, thanks from Poland

[andyshow]

By the way, Prof...I am from Toronto, Canada, your lecture is very very nice and thoroughly explained - prolific. Thanks so much.

[caribbeankpoplover]

This helped me sooo much! Thank you~! ^-^

[dedukahopkinsinstitute]

At 11:10 there is a mistake and at 11:30 also and at both places there must be another nagative sign.But answer is anyway correct

[andyshow]

Hi Prof...Since we know that the function is "analytic" and "continuous"...(along the x-axis)...I've made a silly mistake as -(1/2)*Re(z)^2 by setting (y=0). Then after thoroughly examining the case, I just figured out that you are absolutely right..."the whole (z) function should be analytic"! Stupid me...!

[boquanerwinchen]

Is there a video that goes more into the properties of harmonic functions?

[zanderzoot]

I really wish I was intelligent enough to understand ANYTHING that was said here.
Sad I know but only reason I came here is due to the subject being mentioned in the film Good Will Hunting, I wanted to know what it was about.
Absolute respect but I'm still non the wiser. 😳

[emlmm]

So, in essence, a harmonic function is a basis for all harmonic functions that are specific to its conjugate? Also, how should one go about proving analytic continuation?

[anuragmehta]

why does V component only differ by a constant

[HimanshuDewruwanHapuarachchi]

Thank you very much. found very helpful.

[nicholaskinney]

Can somebody help, I'm feeling a bit dense. At 8:12 when we want look at the function along the real axis. To me it looks like we should set x = y to kill the imaginary part but its stated that this corresponds to setting y = 0? Can someone help reiterate the trick that uses analytic continuation?

[dondodo]

can someone help?? how can he get the result in 12:02 ? i don't really understand. i do appreciate for helping me. thanks

[deadfish]

how did you find the imaginary part of 1/z directly??

[aishikbhattacharya]

Another mistake while integrating at 11:27

[amitrathod]

At 3:56 how is the partial derivative of u wrt to x equal to y?