Complex Analysis L04: The Complex Logarithm, Log(z)

[@fanwellnyereyemhuka8378]

You are an amazing lecturer sir.I need more of these.You make my life easier.Keep it up.

[@pizzacrust7029]

My professor is not good at getting any of this information across, he's incredibly intelligent, but is very bad at teaching. Your video taught me more in thirty minutes than i learned in multiple lectures. Thank you for the work you put out, it's really made a huge difference in my understanding of complex analysis!!!!

[@juniorcyans2988]

I just found this channel last night, and I couldn’t keep me away from it😅What a surprising treasure I found luckily!

[@dennerguilhon]

I'm immensely amazed on his ability to write like this 👏👏

[@andrewrezendes]

🤦 He reflects the camera image.

[@ralphhebgen7067]

Yes! That also amazed me no end until I understood that people write normally on a glass pane and film it from behind! I am still amazed he can write like this, though - the maths is lucid and clear! 😂

[@abrlim5597]

I still don't understand how this works

[@jasonthomas2908]

@@abrlim5597 It's as Andrew said, he reflects the image along the vertical axis.

[@ShengceZhang-wj9pp]

which implies he is writing by left hand. Still impressive for me@@jasonthomas2908

[@andreacomparini9381]

I wish you were the teacher of my son. Really great lessons. My compliments

[@Chetan_Hansraj]

Yes I wish he was my teacher too ..

[@hoseinzahedifar1562]

@@Chetan_Hansraj me too. he is a great teacher👍👍

[@rob4187]

He is teaching you through these videos

[@mosquito001]

Get your son into the university of washington

[@brendawilliams8062]

Proof that first come is motivation

[@ItsDeveshA]

Damn-I had done this topic in my college and there-we were explained a bit and given the formula. But your video literally made me fall in love with the Beauty of Mathematics. I genuinely feel that the professors that bring life to the Subject should be the only ones allowed to teach-else, you kill the LOVE FOR THE SUBJECT and eventually students end up hating the subject(where in reality, they hated to just mug the things up and see it all superficially). Thanks for the video Steve :)

[@lucapetrescu6990]

not only is this man capable of explaining complex analysis, but he can also write backwards 🤯🤯🤯. What a guy

[@XJWill1]

Or he is just left-handed (or capable of writing with his left hand). Easy to reverse the video.

[@mehmet2247]

I felt like "from zero to hero" in this video, thanks a lot

[@Cindsardella]

I am amazed! Took me a while to find this, thank you! Really great to follow 😀

[@JAYasankarPillai7]

Thanks a lottttttttt for uploading, I requested for this video the other day. impressively prompt........appreciate it,

[@xinglinli9874]

Saving me so much time.

[@ralphhebgen7067]

Perfect - many thanks for that lucid and clear explanation. The only thing I would have liked to have added is the notation “arg(z)” and “Arg(z)”, which is often used. It’s clear enough what that is from the video, though.

[@ViridiansVivarium]

Thank you!! This was so fun and informative, and has really helped give an intuition for something I've been struggling with. Merci beaucoup!!

[@AnirbanMukhopadhyayeed]

Thank you for such informative lecture.

[@annanor9009]

Thank you so much for these videos! The word "branches" in this context feels very strange to me. When I hear "branches," I imagine a tree-like structure, where there are junctions that have multiple choice of "direction" to go in, whereas the branches as illustrated here appear to be segments of a continuous spiral.

[@JamesMartin-vn5dq]

maybe we should call them 'cliffs', because you fall all the way from Pi to -Pi

[@nokidding152]

That intro is awesome!!

[@dansantner]

Outstanding. Love your videos.

[@abelmedina-aispuro3716]

What a beautiful lecture

[@ericchasseur3904]

At 26:00. I think there is a mistake here. What for sure is correct is : integral of 1/z dz = 2*pi*i on a closed contour around z=0. However, integral of Log(z) dz on a circle arond z=0 where it makes sense (with complex numbers with phase in ]-pi,pi[, excluding the values -pi and pi because Log is not defined on negative real numbers) = - 2*pi*i. With a negative sign.

[@curtpiazza1688]

Wow! Cool stuff! The graphs and pictures are so helpful! 😂

[@vahiddanesh4661]

What my professor couldn't teach us in 10+ lectures, you just taught in 30 minutes. I wish I see you one time in-person!

[@fabdelap2971]

Sir. The log you are using is the log base e and is usually written as Ln. In France we call it the "natural logarithm". So it is certainly not restricted to the complex numbers.

[@samuelahibo339]

Yes but I think what he means is that Ln is used more with real numbers and Log with complex numbers, I remember my "Lycée" teacher saying that "log" with lower case l, is the logarithm that we know with any base (or 10), and "Log" Upper case L is usually use to mean base e or "logarithme népérien"

[@samuelahibo339]

Correct me if I'm wrong tho

[@killoffman]

What an ABSOLUTE legend!

[@andrcarb]

This is a great video, good job!

[@abelmedina-aispuro3716]

Great lecture

[@jamesjohn2537]

Nice lectures, am a self studying student of calculus, studying calculus II, and this lectures complex analysis start making sense to that of powers series, trig. functions more of lower math I learned a long the way. kind of nice and keep my motivative of why learning calculus! thanks sir.

[@Chetan_Hansraj]

Thank you soo much for this , just One suggestion the overall master volume of the video is quite low , would be great if it's a bit louder . Thanks 🙏

[@jimlbeaver]

Wondering if this is the genesis of uncertainty between time and s-space…hmm 🤔..will wait and see. Thanks!

[@belwizdadimed3967]

If f is a function defined from set E to set F which is f: E -> F , we know by definition that each x in E has at most one picture in F. How come you call a function an object that associates one value from E to an infinite values in F??? You should restrict to the principal to call the complex log a function. May be you can define an infinite sequence of functions fn indexed by integer n. Per Bourbaki consistency is key in mathematics not in physics.

[@gabrielchircu422]

We know that |z| can be found by Pythagoras' theorem and is uniquely defined. However, Log(z) has a constant real component log(R), i.e. log(|z|), whereas the imaginary component jumps in steps of 2pi. What is then |Log(z)|? It looks as tough it varies according to the phase of Log(z) therefore it has an infinite number of values. Where is the contradiction?

[@Impatient_Ape]

Steve, is your background painted with something like Vantablack, Musou Black, or Black 3.0? I can't see any edge artifacts from using a green screen technique, so it got me wondering.

[@QetyzPsn]

🤯 math is so cool

[@copernicus6420]

Shouldn't we dealing with ln since the logarithm are according to e ?

[@lamdawave]

Question 15:40 One question Sir, can we also go in the negative direction by specifying the phase angle to be theta - 2 pi, theta - 4pi etc?

[@Exoepxoe]

it depends on the direction of the rotation

[@antonzub672]

Can you make one about residue theorem? (I am struggling with Matsubara Green’s functions)

[@Saweera786]

Hello sir, could you please make a video of any particular algorithm that is used for acceleration signals affected by excitation sources and low frequency components in the streaming environment.

[@stevenzhang5294]

should the last plot of spiral start from x axis, rather than the y axis

[@shawnyao7850]

can someone explain the 2 * pi * i in 24:49? I understand the 2*pi makes a circle, but how did the i appear?

[@shawnyao7850]

I guess Steve's intentionally leaving a lot of blanks on complex integrals and skipping to the end result of CIF. Will stay tuned until I read the latter part of the series haha

[@brendawilliams8062]

Professor Norman Wildberger can reach Cauchy or closed intervals formulas if you live triangles

[@emir2750]

fucking great lesson mate

[@extendedwhizz1637]

3:15 , 17:17

[@asmithgames5926]

Did anyone notice he's writing BACKWARDS???

[@radadadadee]

There is no such thing as a "multi-valued function". "In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y". EXACTLY ONE. The example you gave about +/- in the square root, are the solutions to the corresponding equation. And by the way, the symbol for square root is ONLY for the positive result.

[@epicchocolate1866]

That is false. That is the definition of a “single valued function”

[@radadadadee]

@@epicchocolate1866 check out Wolfram's entry and you'll realize that there is no such thing as a multi-valued function. The word "function" there is a misnomer perpetuated by morons like you and your kind.

[@뾱뾱-c9n]

칠판 신기하다

[@Exoepxoe]

화이트보드보다 훨씬 낫네요

[@comment8767]

@@Exoepxoe 화이트보!!!

[@Exoepxoe]

@@comment8767 아니요, 검은색 보드 같지만 흰색이에요.

[@comment8767]

@@Exoepxoe Αγαπώ την Ελλάδα

[@Exoepxoe]

@@comment8767 Κι εγώ, αγαπώ πολύ την Ελλάδα.

[@sarkarsubhadipofficial]

❤

[@zrmsraggot]

Real life application of that please ?

[@Exoepxoe]

rlc circuits

[@lessnightlights8535]

the marker sqeak is unbearable 😢