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Theorem 0:13 Useful facts 0:53 Example 1 Maclaurin series for f(z)=1/(3+6z)² 5:20 Example 2 expand f(z)=(z-1)/(3-z) around z_0=1 Example 3 obtain the Maclaurin series for f(z)= i/(z-i)(z+2i) 11:56 Example 4 expand ln(1+z) in a Maclaurin series 14:26

Thank you so so much. Group theory is such a hard subject for me.. This might get me the points to pass the exam!

Excellent tutorial. Thanks!

Best introduction on Strong Induction I have seen on TH-cam. Elegantly presented sir.👍

It looks like there is a slight mistake at 29:01, the -10 changes to zero during the R3+R4->R4 operation when it shouldn't. So I think parametric form should look like: x1 = x5 - x3 x2 = x3 - x5 + 10 x3 is free x4 = 10 - x5 x5 is free

Very nice explanation Michael! Thank you

proof by induction, is a fraud

Thanks a lot professor for your efforts. I follow you from Algeria.

Why is matrix multiplication defined this way? 😮

His voice is so calming haha

EXCELLENT LECTURE- -WHERE IS RODE ISLAND ? THANK U SIR - AMARJIT -INDIA

perfect video, exactly the level i need. Thanks

🙏🙏

Amazing and clear explanation. Thanks a lot

Thank you!

the parametrizations: z(t) = t-it and z(t) = t+it makes the computation easier. (line y=-x, and line y=x)

Thanks

Injective is dual to surjective synthesizes bijection or isomorphism. Syntax is dual to semantics -- languages, communication. If mathematics is a language then it is dual. "Always two there are" -- Yoda.

Injective is dual to surjective synthesizes bijection or isomorphism. Syntax is dual to semantics -- languages, communication. If mathematics is a language then it is dual. "Always two there are" -- Yoda.

It turns out that in this example partial fraction decomposition provides a simpler path to the solution without the need for an algebraic "trick". Just to be clear, I'm not slamming this approach but this only works if you see the trick. Partial fractions always works but it is not always simpler.

This whole video was analyticawesome!

Can someone tell me where the log(x) of the furthest on the right integral went to?

Thanks, man. This was amazing

amazing teacher

I love you man. You've made this so much more digestible than my book

Thank you... excellent lesson. I understood the parts I didn't understand for days.

man wtf is this topic watched the whole thing and understood absolutely nothing

I have a higher math midterm on Tuesday. You’re a lifesaver!

Do u can write it for a general (x+iy)^(x+iy)

thank you so much

Good work

Adamsn ab 12:06

Hi , am confused , the video is about taylor series but i see Maclaurine series examples

Very helpful video.

Thanks for the video! 😊

Are there practical applications for complex trigonometric functions? I have seen complex numbers used for solving polynomials, analyzing circuits, and harmonic motion; but I've never needed to take the cosine of a complex number.

Listen to what he says between 5:19 and 5:52 Nary a truer word has ever been spoken.

The best math channel on youtube is back!

Superb!!! thank you

Thank you Michael. Great explanation!

Most beautiful

These videos are a great treatment of complex; ideal for somebody like me who's revisiting the subject after many years.

Silly question here. Is the t in Goursat silent?

What amazing explanation. Ty so much

Fantastic!

god bless ya shawty xoxo

Nice 👌

I owe you a lot. Thank you so much sir. I just learned a whole lot more in just two days of watching your video compared to weeks of lessons in my campus. College would be way better with more people like you.

how do you know how many times to differentiate

شكرا ♥️