I think you had a small mistake. The complex number is actually supposed to be on the fourth quadrant meaning the arg is actually=-arctan(a/q) BTW I love your videos man you're extremely intelligent, seriously keep it up man!
Thank you for another beautiful video. From 6:04 on, I think that you missed (n-1) solutions according to the argument that should be: Arg = 2 k π/n + ..., for all k: 0
Very nice video. May be, I‘m wrong but the argument of z = s - i*a lies in the forth quadrant of the complex plane instead of the second. So, the argument is just 2pi - tan^-1(-a/s) if arg between 0 and 2pi ?
I think you had a small mistake. The complex number is actually supposed to be on the fourth quadrant meaning the arg is actually=-arctan(a/q)
BTW I love your videos man you're extremely intelligent, seriously keep it up man!
Man I missed You G, glad to see you came back with one of my favorite types of problems.
Hell yeah! :)
I really miss this man's daily uploads during the holiday season, legit would watch him right before bed or right when I wake up.
@@daddy_myers IKR! finding this channel was rhe highlight of my vacation.
@@manstuckinabox3679 Same here! 😊
F**k man you guys are the best mathbros a guy could ask for🥺❤
@@maths_505 And you're the best Math bro AND teacher we could've ever asked for! 😊❤️
Was about to do this integral with this method
You can also try cauchy residue theorem
❤❤❤
Marvelous !! Really, really love it. !!!
Bro please make a video on Glauert Integral, having a hard time with it.
Thank you for another beautiful video.
From 6:04 on, I think that you missed (n-1) solutions according to the argument that should be:
Arg = 2 k π/n + ..., for all k: 0
It's common practice to take only the principal branch
However there is one thing I missed; the complex number is in the 4th quadrant not the 2nd
At 4:56 it is supposed to be fourth quadrant
Yes you're right
Sir, please could you recommend a good book for complex analysis (from the basics to advanced & practice problems included)?
@@7calculus applied complex variables by john dettman.
Amazing book!
Thank you sir
Very nice video. May be, I‘m wrong but the argument of z = s - i*a lies in the forth quadrant of the complex plane instead of the second. So, the argument is just 2pi - tan^-1(-a/s) if arg between 0 and 2pi ?
Yes my mistake
It's in the 4th quadrant
No problem.
Or -pi + atan(alpha/sigma). Convention is: it lies between -pi and pi.
2:55 Why didn't you just sub u=t*(sigma-i*alpha) so you could use the Gamma function instead of a Laplace transform?
Yeah the complex number is in the 4th quadrant, not in the 2nd
May I ask about the restriction on the exponent of the t variable? Why greater than -1 necessarily?
Its required by the laplace transform
When n = alpha = sigma = 1 you shoud get 1/2.
does it matter if alpha is positive? since cos is an even function
What does argument of something mean?
Input of a function. Like for e^x, x is the argument.
sig/sig^2+@^2...ma il mio risultato è corretto?
Sir ,i just came up with that similar one last evening.
(0 to 1000pi)e^cos(theta)*cos(sin(theta))=n(pi);n=?
Incomplete Gamma function ?