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! 😂
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!!!!
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 :)
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.
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.
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.
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.
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.
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"
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.
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?
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.
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.
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.
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
![The most beautiful equation in math, explained visually [Euler’s Formula]](http://i.ytimg.com/vi/f8CXG7dS-D0/mqdefault.jpg)
![เปิดบ้าน พี่ตูน Bodyslam หลังใหม่คนแรก ที่ภูเก็ต l [Nickynachat]](http://i.ytimg.com/vi/flFwcmyDQSk/mqdefault.jpg)
I'm immensely amazed on his ability to write like this 👏👏
🤦 He reflects the camera image.
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! 😂
I still don't understand how this works
@@abrlim5597 It's as Andrew said, he reflects the image along the vertical axis.
which implies he is writing by left hand. Still impressive for me@@jasonthomas2908
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!!!!
I wish you were the teacher of my son. Really great lessons. My compliments
Yes I wish he was my teacher too ..
@@Chetan_Hansraj me too. he is a great teacher👍👍
He is teaching you through these videos
I just found this channel last night, and I couldn’t keep me away from it😅What a surprising treasure I found luckily!
I am amazed! Took me a while to find this, thank you! Really great to follow 😀
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 :)
I felt like "from zero to hero" in this video, thanks a lot
Thanks a lottttttttt for uploading, I requested for this video the other day. impressively prompt........appreciate it,
Thank you!! This was so fun and informative, and has really helped give an intuition for something I've been struggling with. Merci beaucoup!!
Saving me so much time.
Outstanding. Love your videos.
Thank you for such informative lecture.
Wow! Cool stuff! The graphs and pictures are so helpful! 😂
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.
What a beautiful lecture
What an ABSOLUTE legend!
This is a great video, good job!
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.
maybe we should call them 'cliffs', because you fall all the way from Pi to -Pi
That intro is awesome!!
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!
Great lecture
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.
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.
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 🙏
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.
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"
Correct me if I'm wrong tho
not only is this man capable of explaining complex analysis, but he can also write backwards 🤯🤯🤯. What a guy
Or he is just left-handed (or capable of writing with his left hand). Easy to reverse the video.
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.
Wondering if this is the genesis of uncertainty between time and s-space…hmm 🤔..will wait and see. Thanks!
Shouldn't we dealing with ln since the logarithm are according to e ?
should the last plot of spiral start from x axis, rather than the y axis
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?
fucking great lesson mate
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.
🤯 math is so cool
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.
Can you make one about residue theorem? (I am struggling with Matsubara Green’s functions)
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?
it depends on the direction of the rotation
3:15 , 17:17
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.
칠판 신기하다
화이트보드보다 훨씬 낫네요
@@Exoepxoe 화이트보!!!
@@comment8767 아니요, 검은색 보드 같지만 흰색이에요.
@@Exoepxoe Αγαπώ την Ελλάδα
@@comment8767 Κι εγώ, αγαπώ πολύ την Ελλάδα.
can someone explain the 2 * pi * i in 24:49? I understand the 2*pi makes a circle, but how did the i appear?
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
❤
Real life application of that please ?
rlc circuits
Did anyone notice he's writing BACKWARDS???
the marker sqeak is unbearable 😢