These videos are awesome! A suggestion (for future courses) for 10:23, could we use the argument that the nth root of a given number "a" can also be represented as (a)^(1/n). So as n->inf, 1/n->0, meaning that we get (a)^0=1. The same applies for (n)^(1/n). No matter big n becomes, since 1/n is almost 0, almost anything raised to 0 is 1. Not exactly, a proof, but I think it'd be helpful for comprehension.
I'm enjoying this series so far! I am a bit thrown by some notation... at 22:15, on the slide "Applying these New Facts...", braced definitions for the real and imaginary parts become darkened. It reminds me of a piecewise-defined function, but I haven't seen a brace used mid-expression like that before. I'm assuming there is an implied multiplication just before the braces.... If anyone can verify, correct, or reveal some nuance I missed about this, I'd gladly repay the favor with a like :)
Yeah. I am teaching some of this to my completely average 7 year-old daughter and she gets it. I wonder why they waste people’s time in school learning useless stuff when they can learn this.
This playlist is saving my life right now. Thank you!
Thank you for such a clear presentation....!!!!!!
awsome! For the first time I understand everything about the complex numbers
These videos are awesome! A suggestion (for future courses) for 10:23, could we use the argument that the nth root of a given number "a" can also be represented as (a)^(1/n). So as n->inf, 1/n->0, meaning that we get (a)^0=1. The same applies for (n)^(1/n). No matter big n becomes, since 1/n is almost 0, almost anything raised to 0 is 1. Not exactly, a proof, but I think it'd be helpful for comprehension.
I'm enjoying this series so far! I am a bit thrown by some notation... at 22:15, on the slide "Applying these New Facts...", braced definitions for the real and imaginary parts become darkened. It reminds me of a piecewise-defined function, but I haven't seen a brace used mid-expression like that before. I'm assuming there is an implied multiplication just before the braces....
If anyone can verify, correct, or reveal some nuance I missed about this, I'd gladly repay the favor with a like :)
Thank you so much, your lectures are awesome
How do you prove the rules stated on the slide starting at 11:00?
Robin Wilson
Monotone convergence theorem
it is good even for a 9 year old
Yeah. I am teaching some of this to my completely average 7 year-old daughter and she gets it. I wonder why they waste people’s time in school learning useless stuff when they can learn this.
@@Thefare1234 exactly my son is already solving differential equations, his school is still teaching 4*5 by circling 20 circles.