Complex Analysis: what is a contour integral?

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Complex Analysis: what is a contour integral?

Рет қаралды 19,358

Maths 505

Күн бұрын

Пікірлер: 38

@ryankelly9772 10 ай бұрын

common Maths505 W

@TI5040 10 ай бұрын

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".

@quanle1539 2 ай бұрын

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!

@AB-nu5we 10 ай бұрын

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.

@user-wt6oe8nm7y 10 ай бұрын

Although my math is bad,I still watch most of your videos idk I probably enjoy watching someone solving hard problems

@maths_505 10 ай бұрын

Thanks bro

@silentmath3198 9 ай бұрын

awesome video

@ikarienator 10 ай бұрын

That's a very nice introduction! Can you cover the branch cut next time? I think I have never really understood it.

@maths_505 10 ай бұрын

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.

@fuckayo-ti1fj 10 ай бұрын

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 10 ай бұрын

Bruh I have never evaluated that integral. And there are 2 versions of Lobachevsky's formula and I've proved both of em.

@fuckayo-ti1fj 10 ай бұрын

@@maths_505 « Bruh », you did indeed at 8:39 of this video kzbin.info/www/bejne/iajMq6qGrpJ6o6csi=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

@maths_505 10 ай бұрын

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.

@pandavroomvroom 10 ай бұрын

pretty cool

@tifn4g190 10 ай бұрын

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 ?)

@maths_505 10 ай бұрын

Continuity of the function.

@tifn4g190 10 ай бұрын

@@maths_505 there isn't any condition on the convergence of the integral?

@maths_505 10 ай бұрын

@tifn4g190 isn't that plainly obvious????? Convergence is always key.

@spiderjerusalem4009 10 ай бұрын

Did you use shakarchi's complex analysis 🤔

@maths_505 10 ай бұрын

Who?

@maths_505 10 ай бұрын

I use lang, dettman and gamelin for complex analysis

@notsodope834 Ай бұрын

Ok but 1/z dz integral is not ln(z) here😢

@worldnotworld 26 күн бұрын

OK Cool

@giacomocervelli1945 10 ай бұрын

Why did you upload this here and not on the second channel? (Just out of curiosity)

@maths_505 10 ай бұрын

Experimental purposes

@youknowwhatlol6628 6 ай бұрын

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 :)

@KusacUK 6 ай бұрын

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).

@KusacUK 6 ай бұрын

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).