Complex Taylor Series 2: Some Examples

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Michael Barrus

Michael Barrus

Күн бұрын

Пікірлер: 35
@MelThree-tb7kt
@MelThree-tb7kt 11 ай бұрын
I love you man. You've made this so much more digestible than my book
@mdnia6592
@mdnia6592 8 жыл бұрын
Omg thanks so much! The teacher we have at our university just grinds all this theory into us without showing us how to actually calcutlate and use the stuff we learn. And at an ingeneering university you don't need all that theory if you kinda understand it from a mathematical perspective and can use it. The most important thing for us ingeneers is to actually use it! Helped alot! Thanks again:D
@gokuvegeta9500
@gokuvegeta9500 3 жыл бұрын
Engineers*
@amir.r1639
@amir.r1639 Жыл бұрын
Good for you , your now free from engineering courses Im in term 3 of mechanical engineering and Im going to die 😂
@adetunjidaniel5064
@adetunjidaniel5064 2 жыл бұрын
following your complex variables playlist. It has been awesome. Thanks
@evionlast
@evionlast Ай бұрын
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
@mattgiron2090
@mattgiron2090 5 жыл бұрын
great variety of examples, cramming for AP right now so this was great!
@1112634
@1112634 4 жыл бұрын
On the third example the disk of convergence is the disk centered at the origin with radius 1 (|z|
@gokuvegeta9500
@gokuvegeta9500 2 жыл бұрын
But when we use partial fractions the terms split into f(z)=(1/(z-2i))-(1/(z-1)) So the Taylor's series expansion for the first term doesn't have the singularity z=i in it Furthermore when we combine the Taylor series of both terms having radius of convergence R
@neutrino5695
@neutrino5695 11 ай бұрын
Thanks, man. This was amazing
@ruinex7718
@ruinex7718 6 жыл бұрын
Just awesome explaining. Thank you, it helped me alot
@fernxndesofc
@fernxndesofc 2 жыл бұрын
Thanks so much. You helped me a lot.
@gDrLemon
@gDrLemon 7 жыл бұрын
At 8:01. Can someone please tell me why does the derivative of the series start at k=1 and not k=0? Thanks
@Anonymous-od3bl
@Anonymous-od3bl 6 жыл бұрын
when k=0, the value of that expression is 0. To nullify the constant we started from k=1.
@Qits13
@Qits13 8 жыл бұрын
Thank you so much! Helped me a lot!
@bobogao6328
@bobogao6328 6 жыл бұрын
very clear explanation! thank you
@ottodvalishvili7601
@ottodvalishvili7601 5 жыл бұрын
great videos, thanks so much
@hagarsalem4996
@hagarsalem4996 3 жыл бұрын
Could i know name of the book to solve similar problem?
@kattynl
@kattynl 8 жыл бұрын
very helpful... thank you
@edgarkloster6017
@edgarkloster6017 8 жыл бұрын
At 13:09...why is 1/(2i) the same as i/2 ??? (same question for 1/i = i) I had a different solution because i solved it with 1/(2i) (and i in the second term). Is it wrong to calculate it with 1/(2i) (and i) times the series?? please help!
@s0mthingsmells
@s0mthingsmells 8 жыл бұрын
multiply the numerator and denominator by i. for example 1/-i = 1/-i *i/i = (1*i)/(i*-i) = i/1 = i
@zaimelkalai256
@zaimelkalai256 4 жыл бұрын
@@s0mthingsmells im still confused, in your example you multiply the numerators while adding the denominators...
@gokuvegeta9500
@gokuvegeta9500 2 жыл бұрын
@@zaimelkalai256 He rationalised the numerator
@Aziz-sh3wq
@Aziz-sh3wq Жыл бұрын
god bless ya shawty xoxo
@okan3028
@okan3028 5 жыл бұрын
Awesome thank you sir
@kalki9924
@kalki9924 8 жыл бұрын
thank you sir
@PhuongLe-ki7cb
@PhuongLe-ki7cb 3 жыл бұрын
Great
@zoezhuang8514
@zoezhuang8514 7 жыл бұрын
Hi, I have a question on the second example u did. when u say that the series are absolutely convergent inside the circle of convergence. Do u mean the circle with radius 2i or i centered at 0??
@atulitsrivastava9199
@atulitsrivastava9199 7 жыл бұрын
Qianqian Zhuang a circle with radius 2i will also include singularity point z=i so I don't think he is talking about circle with radius 2i cos for expansion the function must be analytic within the circle of radius 2i
@cameronspalding9792
@cameronspalding9792 6 жыл бұрын
For the expansion about z0=1: could you not find a maccularin series of f(z+1) then adapt it to get back to f(z)
@96Willers
@96Willers 8 жыл бұрын
Thanks
@beophobic9653
@beophobic9653 4 жыл бұрын
Dan Just don’t comment if you don’t have anything positive to say, man. Go away.
@edgarcalochcampos1930
@edgarcalochcampos1930 4 жыл бұрын
@@beophobic9653 ?
@gokuvegeta9500
@gokuvegeta9500 3 жыл бұрын
@@beophobic9653 🤡
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