The Formula for Taylor Series

  Рет қаралды 170,784

blackpenredpen

blackpenredpen

Күн бұрын

Пікірлер: 173
@ArtStyleEdge
@ArtStyleEdge 6 жыл бұрын
Man i was about to sleep..Nevermind i will watch this first!
@alexandrebriard9175
@alexandrebriard9175 4 жыл бұрын
When you watch this video after 3B1B : *you know i'm kind of a mathematician myself*
@aaronaugust7904
@aaronaugust7904 3 жыл бұрын
I know it is pretty randomly asking but does anybody know a good site to stream newly released series online?
@franklindrake3225
@franklindrake3225 3 жыл бұрын
@Aaron August I dunno atm I've been using Flixportal. Just google for it =) -franklin
@aaronaugust7904
@aaronaugust7904 3 жыл бұрын
@Franklin Drake thanks, I went there and it seems like they got a lot of movies there :D I appreciate it !!
@franklindrake3225
@franklindrake3225 3 жыл бұрын
@Aaron August no problem xD
@Draginx
@Draginx 3 жыл бұрын
This guy is awesome, I love maths, physics, and engineering, and this guy explains everything so great!
@benjamingiribonimonteiro9393
@benjamingiribonimonteiro9393 6 жыл бұрын
Thanks for featuring me at the beggining! Love your channel
@blackpenredpen
@blackpenredpen 6 жыл бұрын
Benjamin Giriboni Monteiro : )))
@benjamingiribonimonteiro9393
@benjamingiribonimonteiro9393 6 жыл бұрын
@@blackpenredpen :)
@CalculusPhysics
@CalculusPhysics 6 жыл бұрын
i think the thumbnail has a slight typo, shouldn’t it be n! in the denominator, not simply n?
@diabolicallink
@diabolicallink 6 жыл бұрын
Chloe I thought so too
@alejrandom6592
@alejrandom6592 3 жыл бұрын
3:04 e^x + sinx "can't even do the common denominator" *laughs in complex definition*
@ado22222
@ado22222 3 жыл бұрын
but where did he get the sinx from?
@alejrandom6592
@alejrandom6592 3 жыл бұрын
@@ado22222 from his imagination
@ado22222
@ado22222 3 жыл бұрын
@@alejrandom6592 oh ok so its not like he is saying 1/1-x somehow equals to sinx right? Cool Because i though he meant that and it was really driving me nuts
@alejrandom6592
@alejrandom6592 3 жыл бұрын
@@ado22222 yeah don't worry it was just an example ;)
@angelmendez-rivera351
@angelmendez-rivera351 6 жыл бұрын
Papa Taylor has blessed us.
@baoradeon878
@baoradeon878 4 жыл бұрын
Love the way he explained how does the Taylor series work. THANK YOU
@____Paul____
@____Paul____ 8 ай бұрын
I appreciate that you started with showing the usefulness of Taylor Series before diving into the details of how to use it! Edit: This video is only showing the formula, not how to work with Taylor series.
@phorusrhacidaeaves811
@phorusrhacidaeaves811 Жыл бұрын
can anyone help to explain what he said 'best friend' on 4:57 to be?😅😅😅
@BenjaminKeilty
@BenjaminKeilty 6 жыл бұрын
For anyone curious about the "unless you add a circle" comment at 0:40: The mediant en.m.wikipedia.org/wiki/Mediant_(mathematics) is pretty cool and useful in math competitions if you know how to use it
@abhilashsaha9931
@abhilashsaha9931 4 жыл бұрын
You are God.
@djchavaz
@djchavaz Жыл бұрын
For 1/(1-x) expansion using infinite geometry series is true when -1
@jamesoneill5070
@jamesoneill5070 2 жыл бұрын
This formula was developed by Brook Taylor, an English mathematician (1685-1731) so it's over 300 years old.
@OLApplin
@OLApplin 6 жыл бұрын
:O ! FOURIER SERIES ! I just can't wait (my favorite math subject ever)
@rob876
@rob876 6 жыл бұрын
1/2 an hour plus a 1/3 of an hour = 30 mins plus 20 mins = 50 mins = five sixths of an hour. 0.83333... = 8/10 + 1/30 = 48 mins + 2 mins = 50 mins.
@benjaminbrady2385
@benjaminbrady2385 6 жыл бұрын
Can't wait for that Fourier series video!
@ski34able
@ski34able 4 жыл бұрын
I am soooo glad I clicked no this video! Best explanation on youtube so far
@PrynPucksomporn
@PrynPucksomporn 7 ай бұрын
Finally, this vid is 10x understandable than my lecture
@ArhamKhan05
@ArhamKhan05 Жыл бұрын
thats amazing sir great explanation thanks ❤
@opufy
@opufy Жыл бұрын
5:15 Taylor (the dad) series haha
@KotaCraig
@KotaCraig 3 жыл бұрын
I hope you know how many people you've helped! Thank you!
@kendalwilliams5128
@kendalwilliams5128 Жыл бұрын
I loved how you explained it. Thanks!
@math4math608
@math4math608 6 жыл бұрын
Hopefully, Fourier Series will be AS GOOD AS THIS VIDEO! Thanks, Very Detailed Explanation!
@charleswoodard8478
@charleswoodard8478 3 жыл бұрын
Astounding how little attention this material attracts as opposed to more high concept rigamarole and dramatized frivolities done in the name of fame. This should depose the current mainstream passtimes, we’d be far better off…
@sayhan3631
@sayhan3631 3 жыл бұрын
Amazing video ! I enjoyed watching it
@moaydsparklug8311
@moaydsparklug8311 6 жыл бұрын
Hi I'm physicist , fall in love with taylor series helped me alot of times ,anyway I like your videos 😁
@slayervii2280
@slayervii2280 6 жыл бұрын
First I was like why is the first term of the series in the thumbnail equal to infinity then I realised there was no factorial sign on the "n"
@torung9606
@torung9606 Жыл бұрын
omggg i love youuuu
@ragnarlothbrok4090
@ragnarlothbrok4090 4 жыл бұрын
Thanks! You got me through High School!!!!
@quantumcity6679
@quantumcity6679 6 жыл бұрын
Awesome job... I'm curious about next video 😘
@AlessandroZir
@AlessandroZir 9 ай бұрын
good! the comparison with decimals was very useful;
@iremkarakas6770
@iremkarakas6770 3 жыл бұрын
this man i really love you .
@ado22222
@ado22222 3 жыл бұрын
sorry dumb question. why would 1/(1-x) become sinx at 3:03
@suellenalmeida3040
@suellenalmeida3040 5 жыл бұрын
I have been loving your videos! Thank you so much :D
@jibran8410
@jibran8410 6 жыл бұрын
so using that f^0 (a) = 0! x Cn can you say that Cn = f(a) ? where n is 0
@matj12
@matj12 6 жыл бұрын
A note for 1:13: If you find it hard to remember the digits of 1/3, there is a mnemonic for the first 25 digits: kzbin.info/www/bejne/hJrRo4eNZqeraLs
@blackpenredpen
@blackpenredpen 6 жыл бұрын
Hahaha, nice!!!!
@alejandroill
@alejandroill 5 жыл бұрын
0:40 “unless you have a circle right here” ??? I’m so confused
@tpstrat14
@tpstrat14 4 жыл бұрын
the main problem you had in that moment is that you didn't hear him say "let's not talk about that". He shouldn't have even mentioned it LOL. Because of course anything in math can be expanded on. ANYTHING. In other words, you can always get confused at any point if the teacher tries to expand the idea beyond what you're ready for.
@abhilashsaha9931
@abhilashsaha9931 4 жыл бұрын
Look up the word "mediant"
@albatrosslove8654
@albatrosslove8654 Жыл бұрын
there is summation (n=o to inf ) but you are diff n -times means this is finite then how can we take the limits upto inf
@bogdancorobean9270
@bogdancorobean9270 6 жыл бұрын
One thing I don't quite get is how do we know we can represent functions as power series. I mean, why would someone 200 years ago or whenever would have thought of trying something like this? I know it works out, but it seems so unintuitive. Same for power series solutions to differential equations.
@ssdd9911
@ssdd9911 6 жыл бұрын
4ier series next?
@blackpenredpen
@blackpenredpen 6 жыл бұрын
s sdd Yup, I call it fouryay
@gregoriousmaths266
@gregoriousmaths266 4 жыл бұрын
Lol fouryay
@nafissaatlagh206
@nafissaatlagh206 6 жыл бұрын
Hell we need a love reaction in youtube 😐❤
@eustacenjeru7225
@eustacenjeru7225 2 жыл бұрын
good explanation
@zahraa-dm5cy
@zahraa-dm5cy 4 жыл бұрын
0:09 my goal for this year .......
@emrealpozavc783
@emrealpozavc783 6 жыл бұрын
Thank you, can you make a video about lagrange error bound ?
@omkarsinghchauhan3053
@omkarsinghchauhan3053 6 жыл бұрын
i love that thing he holds in his hand btw it is mike or anything else
@angelmendez-rivera351
@angelmendez-rivera351 6 жыл бұрын
Omkar Singh Chauhan it is a Mike
@user-wu8yq1rb9t
@user-wu8yq1rb9t 3 жыл бұрын
You can find any relation between Taylor (the mathematician) and Taylor (the singer; Taylor Swift) ?!! *Taylor Series* and *Taylor Swift* !!?
@carultch
@carultch 2 жыл бұрын
That's most likely just a coincidence. The Taylor series is named after Brook Taylor.
@MrHK1636
@MrHK1636 6 жыл бұрын
Hello, I need help in this problem: If there is a polynomial such that f(x+5)=f(5-x) with 4 real roots. How should you calculate sum of all roots. Don't tell me what answer is. I want a little hint 😅
@MrHK1636
@MrHK1636 6 жыл бұрын
And that condition is true for all real values of x
@snillie
@snillie 6 жыл бұрын
Since f(x+5)=f(5-x), that means if r_1 and r_2 are roots, you can immediately know what the other two roots are (assuming that knowing r_1 doesn't lead you to r_2 and vice versa). If you can find the other two roots, you should be able to solve the problem c:
@MrHK1636
@MrHK1636 6 жыл бұрын
Thank you, right answer is 20, isn't it?
@sajankumarkar8237
@sajankumarkar8237 10 ай бұрын
Shouldn't 1/2 + 1/3 be 5/6?
@aphelmusonda5253
@aphelmusonda5253 Жыл бұрын
youre a hero sir, thank you
@jurihorstmann645
@jurihorstmann645 3 жыл бұрын
To sad that she stopped making proofs to start a music career. Taylor Swift is a math genius!
@carultch
@carultch Жыл бұрын
This is named after Brook Taylor. A completely different person.
@giuseppeagresta1425
@giuseppeagresta1425 9 ай бұрын
​@@carultchit's a joooooke
@epicsushi5817
@epicsushi5817 7 ай бұрын
@@carultchr/woosh
@macglone
@macglone 7 ай бұрын
That was physically painful. Well done!
@douro20
@douro20 5 жыл бұрын
Is it the same Taylor for whom the Taylor Manual is named?
@carultch
@carultch Жыл бұрын
It's named for Brook Taylor
@wuwu1598
@wuwu1598 11 ай бұрын
Thank you, father
@AlbinoJedi
@AlbinoJedi 4 жыл бұрын
Can you explain setting a=0 or any other number and why? I don't get the "centering".
@dawsonbowhay6796
@dawsonbowhay6796 4 жыл бұрын
A Taylor series is infinite, but in practice we may only use the first few terms of the Taylor series as a close approximation to the true function. Therefore, all the [infinite] remaining terms that aren't used are equal to the error between the approximation and the true function. If you graph the true function and the approximation, you will see that there will be zero error at x=a, but as x gets further away from the value a, the error increases. You might choose a certain value of a based on which values of x you want your approximation to be accurate for. Or, you might have to use a non-zero value of a if the function is undefined at x=0 (take for example y = 1/x, where you can't divide by zero so a=1 would probably be used).
@iamimran5880
@iamimran5880 5 жыл бұрын
Very nice sir live from India
@loukafortin6225
@loukafortin6225 6 жыл бұрын
Nice video there! I'm one year ahead of my first classes of calculus, so I'm having a hard time to find a way to calculate the arc length of the function f(x)=x^3. I can't get pass the step : int of sqrt(x^4+1/9)dx. Please help xO. I definitely KNOW there's a way arghhh and it's haunting me lol
@angelmendez-rivera351
@angelmendez-rivera351 6 жыл бұрын
Unfortunately, you cannot find the antiderivative of this function in terms of single-variable elementary functions. There is just no answer you can give using arithmetic operations, exponents or powers, trigonometric functions, hyperbolic functions, or the inverses or compositions of any of the above. Wolfram Alpha gives an answer that requires imaginary numbers and uses special elliptical integrals.
@loukafortin6225
@loukafortin6225 6 жыл бұрын
@@angelmendez-rivera351 oh okay! I needed this to stop getting upset of not finding anything. 'guess I shouldn't mess with those things too much. Anyways, thanks!
@bigalturn1
@bigalturn1 4 жыл бұрын
can you derive the Lagrange Error Bound formula please
@tarekhajjshehadi4670
@tarekhajjshehadi4670 6 жыл бұрын
Do you know what's so special about the number 1729?
@blackpenredpen
@blackpenredpen 6 жыл бұрын
Tarek Hajjshehadi yes
@AndDiracisHisProphet
@AndDiracisHisProphet 6 жыл бұрын
yes
@marcellomarianetti1770
@marcellomarianetti1770 6 жыл бұрын
Yes, we all know
@ironmc7972
@ironmc7972 6 жыл бұрын
1729 can be written in sum of 2 cube numbers in 2 ways. 1729=12^3+1^3 and 1729=10^3+9^3
@メ乇しム尺
@メ乇しム尺 6 жыл бұрын
@@ironmc7972 That's right, but what makes 1729 so special is that it's the smallest number that can be written as a sum of two cubes in two different ways
@alejandroill
@alejandroill 5 жыл бұрын
"My biggest goal to 2020 is to get selected to the Brazilian team in IPhO 2021"
@JureRatkovic
@JureRatkovic 6 жыл бұрын
"Let's look at the jerk of that... no just kidding"
@gourabghosh5574
@gourabghosh5574 6 жыл бұрын
A circle of radius 1 cm rotates and move like a wheel around another circle of 3 cm radius and returns to its initial position. How many times does the citcle of radius 1 cm rotate? The answer is 4. Explain why it is not 3 ie Problem with the solution (circumference of the bigger circle/circumference of the smaller circle)
@Wecoc1
@Wecoc1 6 жыл бұрын
You want us to make your homework, pal?
@UrielMartínezLópez-z9u
@UrielMartínezLópez-z9u 11 ай бұрын
U the GOAT Saludos a toda la raza de la FESC
@_PowerPlay_55
@_PowerPlay_55 Ай бұрын
great man!
@khalilmohammed2297
@khalilmohammed2297 3 жыл бұрын
Thank you so much
@Kumar-oe9jm
@Kumar-oe9jm 6 жыл бұрын
How to kill a constant? bprp 2019: by integration
@y.z.6517
@y.z.6517 6 жыл бұрын
How to kill a positive number? By differentiation.
@principiamathematica5414
@principiamathematica5414 6 жыл бұрын
When the note becomes notice!
@gediman0512
@gediman0512 2 жыл бұрын
you are a great man..keep it up...in addition to this I would asked you one thing.I would like to physics could you announced the best lecturer for physics like you..
@poornimabalachandran1004
@poornimabalachandran1004 4 жыл бұрын
Good job👍👏👏
@الفيزياء-ب2ي
@الفيزياء-ب2ي 4 жыл бұрын
1/2+1/3=5/6 no 2/5 :) 0:32
@oil1263
@oil1263 Жыл бұрын
this guy is fking underrated,
@cptn_n3m012
@cptn_n3m012 6 жыл бұрын
Can you integrate the gamma function ?
@angelmendez-rivera351
@angelmendez-rivera351 6 жыл бұрын
leo bonneville You can, you simply cannot express it in terms of any other well-studied functions, as far as I understand. At best, you can numerical approximations for the definite integral, and the indefinite integral can only be expressed as the definite integral of another function, which is itself not solvable in terms of elementary functions.
@Roshankongala
@Roshankongala 3 ай бұрын
what is professor holding in his left hand?💀
@guliyevshahriyar
@guliyevshahriyar Жыл бұрын
thanks a lot
@roshannanayakkara5865
@roshannanayakkara5865 Жыл бұрын
Excellent
@dr.rahulgupta7573
@dr.rahulgupta7573 4 жыл бұрын
Excellent presentation Sir.Thanks with sincere regards. DrRahul Rohtak India
@abtahi._
@abtahi._ 2 жыл бұрын
beautiful
@armandoski-g
@armandoski-g 4 жыл бұрын
7:45 you're an all star
@louisecaustur7996
@louisecaustur7996 4 жыл бұрын
that was beautiful :o
@subhopal
@subhopal 6 жыл бұрын
FIND OUT THE DERIVATIVE OF x! WRT x
@subhopal
@subhopal 6 жыл бұрын
If f(x)=x! then, f'(x)=?
@subhopal
@subhopal 6 жыл бұрын
Find the derivative of factorial x wrt x
@yoavcarmel1245
@yoavcarmel1245 6 жыл бұрын
it is something with the gamma function, you cannot get a nice solution for that :(
@srpenguinbr
@srpenguinbr 6 жыл бұрын
x! is a discrete function Unless you consider the Pi function, which does give an answer, but in terms of improper integrals or other special functions
@srpenguinbr
@srpenguinbr 6 жыл бұрын
If you don't consider the pi function, then x! is not differentiable.
@ggssjoker4931
@ggssjoker4931 3 жыл бұрын
TQVM
@sebastianmeier5002
@sebastianmeier5002 6 жыл бұрын
🔥🔥🔥
@BlokenArrow
@BlokenArrow 6 жыл бұрын
1/2 plus 1/3 does equal 2/5 in statistics.
@angelmendez-rivera351
@angelmendez-rivera351 6 жыл бұрын
BlokenArrow How?
@XESolar
@XESolar 6 жыл бұрын
So good!
@bullinmd
@bullinmd Жыл бұрын
Cantor proved it is impossible to "count" real numbers.
@OonHan
@OonHan 6 жыл бұрын
1/2 + 1/3 is not 2/5 :(((
@PhilBoswell
@PhilBoswell 6 жыл бұрын
There is a specific operation which does in fact work this way, but the name escapes me right now. The operation which combines a/b and c/d to give (a+c)/(b+d) has the interesting property that it guarantees a new fraction which lies between the two source fractions and is very helpful in various proofs, the nature of which also escapes my memory right now. Look, it's Friday and it's been a tiring week, OK? Somebody else pick up the thread? ;-)
@clubstepdj
@clubstepdj 6 жыл бұрын
you call it "the dad", papa flammy call it "papa taylor"
@manuelodabashian
@manuelodabashian 6 жыл бұрын
Thanks!
@MozwGamer
@MozwGamer 5 жыл бұрын
If I fail Calculus 3, I'll a top subscriber by next year
@Patapom3
@Patapom3 6 жыл бұрын
Amazing!
@pratikmanurkar9421
@pratikmanurkar9421 6 жыл бұрын
Nice
@lucasfrykman5889
@lucasfrykman5889 6 жыл бұрын
Can you prove the Taylor series tho?
@blackpenredpen
@blackpenredpen 6 жыл бұрын
Lucas Frykman What do u mean?
@angelmendez-rivera351
@angelmendez-rivera351 6 жыл бұрын
What do you mean “prove the Taylor series”? What about it needs proof?
@ayoubsbai6339
@ayoubsbai6339 5 жыл бұрын
i love you :)
@maginobionrequiem9167
@maginobionrequiem9167 6 жыл бұрын
COMEDY KING XD
@bullinmd
@bullinmd Жыл бұрын
I'd rather use MacLaurin Series.
@cleahey6350
@cleahey6350 4 жыл бұрын
love you x
@gulzira7642
@gulzira7642 5 жыл бұрын
How are you
@angelmendez-rivera351
@angelmendez-rivera351 6 жыл бұрын
Mr. Cao, I have a number theory challenge for you. Consider the pair of numbers n - k and k + 1, where n is a natural number and k = 0, 1, ..., n - 1. For what values of n are n - k and k + 1 co-prime (relatively prime, they share no common factors) for all k? In other words, for what values of n is gcd(n - k, k + 1) = 1 for all k satisfying the conditions I established?
@АлексейШубин-н8й
@АлексейШубин-н8й 6 жыл бұрын
Hi, go int 1/(x^n+a^n)dx, n=2k, n=2k+1
@angelmendez-rivera351
@angelmendez-rivera351 6 жыл бұрын
Алексей Шубин Not a particularly special exercise or problem. Since a is an arbitrary real number, we know there exists some b such that b^(2k) = a^(2k + 1). This simplifies the problem to anti-differentiating 1/(x^(2k) + b^(2k)).
@SoyFerchow
@SoyFerchow 6 жыл бұрын
I love you.
@akyberdiew8797
@akyberdiew8797 2 жыл бұрын
👏
@xylellaa
@xylellaa 6 жыл бұрын
I love you
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