Video was pretty good. To get a clear intuition on what exactly an integral in complex analysis mean I recommend the book "Visual complex analysis" by Tristan Needham combined with vector calculus chapter in "Feynman lectures in physics".
Hi there! I just wanted to say that your video on complex analysis is fantastic. I'm starting to learn it again on my own, and your video has been a tremendous help. Great work, and thank you so much!
Didn't I watch this on your other site, focusing on Complex Analysis. I keep going crazy. Not that watching it again is a bad thing as doing so builds strong bones and teeth.
I've made videos on branch cuts for all the important functions. Check out the complex analysis lectures playlist. The discussion of branch cuts starts with the the complex exponential from Euler's formula.
I noticed something in one or your videos. I forgot which one but it was using lobachevsky formula. You had the integral from 0 to inf of sin(x)sec(x)/x and used the Lobachevsky integral formula. Yet, sec(x) is indeed pi periodic but with alternating signs, but it is not continuous which makes the formula non valid. This integral is basically the integral from 0 to infinity of tan(x)/x. The limit as x -> inf doesn’t exist anyways.
@@maths_505 « Bruh », you did indeed at 8:39 of this video ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-SwizwPy-GmE.htmlsi=He6zBt6AhK1s5GjO. I know there are 2 versions I watched all of your videos i love your content, but it remains the sec(x) isn’t continuous
Oh that's an integral that was part of the solution development of another integral. There's nothing wrong with that application cuz you can always break down the integral into a series of integration operators like I did for the proof of the formula.
I have a question about double intégrals: when you have a double intégral from 0 to Infinity, and the integrand is f(x,y) dx dy. My question is when can you inverse dx and dy (like what are the conditions on f ?)
thanks for the video! i didn't understand your proof (since i am a beginner in advanced calculus and analysis)...i don't know these sums are and most importantly - WHY we have this inequality....intuitively, for me, it doesn't make sense. Could you guys (or the admin) please enlighten me on this? Thanks so much, in advance :)
For the inequality, imagine summing the values 1, -2, 3. If you take the absolute value of each element, then do the summation, it has to be greater than the absolute value of the overall sum - because the absolute value of -2 would be +2. The inequality in general is less than or equals (or >= depending on which way round you write it) because the number of negative items in your set of values might be zero (so the sums would be equal).
As for the Riemann sums - that’s really just the definition of integration, written in summation notation. Dividing the area under the curve into rectangles of width delta x, then taking the limit as the number of rectangles approaches infinity (and delta x therefore approaching 0).
