Newton's Method

[xenophyr]

hey mr patrickJMT! is this the same as fixed point iteration?

[unknown8088928]

Dude thanks a lot

[santiagoGBN]

I just wanted to leave a comment saying thanks. My teacher this semester isn't the best I've had, and these videos of yours help me understand things he doesn't explain very well, no matter how many times I ask c:

[HotAssHeels]

anybody wanna help with my maths homework??? :( :( im stuck!

[kwakers1]

THANK YOU!

[elfadil95]

Why did he choose the value 3 instead of 3 for his first value/

?

[p8in2008]

Or you can do 1000^1/7 = same number

[InstantRam3n]

thank you so much man! i have a calc exam tomorrow and you saved me! :D

[MrSwedenik]

@InstantRam3n Same!

[1081617]

your hand is cute and i don't like men

[samy9387]

its actually newton- raphson method

[SoccerStar26]

Deep down inside I kind of hope you're a realistic version of Sheldon Cooper (Big Bang Theory) it makes me want to learn math more

[patrickJMT]

@SoccerStar26 nah, i am not such an obnoxious prick

[mykothopea]

@patrickJMT bazinga

[fungsit]

I'm wondering now that the root can be found by setting f(x) = 0, why bother so much using Newton's method? What's the point of newton's method? Can anyone explain that to me?

[sikel1]

@fungsit In the simple case of this example an explicit solution for x when f(x) = 0 is easy, x = 1000^1/7. However, in practise you would never use this method for this type of problem. Other problems where an explicit solution is not available or where it is too computationally intensive to calculate, e.g. a large dimensional vector space problem, it is very useful. We can use Newton's method to give us a 'good' estimate of the solution in just a small number of iterations.

[username6333]

1080P

[nakedrussian]

Thank you for these vids. You just totally saved my ass.

[Maydaysdifference]

beautiful tangent lines............lol

[sheller57shorty]

Thank you so much! I've been trying to understand this for 4 hours and your video just made it click. Thank you!

[WarrantsSG]

wow thanks man, your explanation is good :D

[firen0va]

Your a realy good teahcer

[InLostConfusion]

thank you very much!!

[spgale]

FINALLY I GET THIS. THANK YOU. probably still going to fail tomorrow, but at least i know something

[TheRedLady1430]

Fig Newton who? btw thnx for ur vids.. helped me a great deal!

[mikelamid]

is it really named after Fig Newton???

[patrickJMT]

@mikelamid this method is sweet (and tasty!), so yes, yes it is.

[w1lhelm]

thanks for this

[Cancer98765]

THANK YOU

[stekzors]

Helped alot, thank you.

[whyalwaysneedthis]

how do you know the root must be between 2 and 3 at the first time? I dun really know which no i should pick for x1?

[j723s]

awesome! Thanks dude

[MA1102R]

this is amazing!

[hrishikeshac]

thanks!

[TheNumber2Pencil546]

i have gone through SO MANY of your videos and "liked" just about every one. haha now all my suggestion videos for my youtube account are math tutorials

[patrickJMT]

@TheNumber2Pencil546 thanks for liking them!

[darkflyes]

I'm the kind of guy who relies heavily on step by step examples and equations while doing my work. The video was really helpful, I hope you make many more like this. Thanks a lot!

[wernis17]

Thanks for this video, I have found that with my calc, I work out x1. And then I replace all the xn with "ANS" and then after that I just keep pressing "=" and it spits out all the answers. Brilliant Video, Writing a test tomorrow! This will save me!

[iamtheCarterP]

You could also put in your initial x value then hit STO>X. So the initial value was 3, you hit 3 STO> X then u type the function in your calculator x - (x^7-1000)/(7x^6) then at the end of that function you do STO>X, so what will be in your calculator will be x- (x^7-1000)/(7x^6)STO>X. Every time you hit the = it will take that value and make it X. Just keep hitting = until your answer is within the error limit given.

[KrisjanisWL]

this is faster than algebra if you have a calculator with more difficult functions. just enter your x value and hit "=". Then enter "ANS" - [whatever your function is]("ANS")/[derivative]("ANS") and hit "=" over and over again until the number stops changing. It honestly takes less than a minute.

[NguyenEmpir3]

By just looking at the equation, how can we tell when Newton's method will not work and if it did not work, what are other ways to find the x-intercepts?

thanks.

[dsephobe]

thx a lot! but excuse me, would u mind help me to understand why d(sin x)/dx = cos x, d(cot x)/dx=-(cscx)^2, etc etc etc....? those messy stuff confuses me all lifetime long...can u help?

[bonzwah1]

considering that to solve for the x sub n+1 value you need to be able to compute f(x) for any x value, why use newton's method at all. With the ability to solve for f(x) for any x, one could likely end up at the zero faster from a guess and check method, especially since we already know the general shape of the graph usually. certainly algebraically solving for the zero would be much quicker. Im not trying to be a jerk, just trying to find an answer that our calc teacher cant provide us with.

[TheXoftware]

Thanks Patrick. Really love watching your videos, they are a great supplement to my math teacher when I am at home doing my homework! I try to make your sure I give you a thumbs up every time I watch your videos.

[KeeperOfTheLore]

Great explanation! You made me understand in 7:30 minutes what my teacher couldn't in 2 classes 1:40 hours each!

Thanks a lot!

[SimplyMesmerizing]

Well I guess since there are zeroes at every value, you probably don't need to do any math at all??

[Thegyptianone]

this is weird. the function they gave me is f(x)=0. how do i do a problem like that? thanks

[lfroggyl]

/watch?v=3sLJo_ym4VU Here is a nice short video that sums up Newton's Method. Watch after watching Patrick

[TheCubanoboy]

As long as you dont pick an x value that has anomalies like horizontal tangent or vertical tangent then newton's mwthod always works , you only have to pick wisely your first x value !

[LadyDancer55]

Very very useful, better than my maths teacher really. You really know what you're saying and how to bring it across and it's simple in just under 10 minutes. Brilliant.

Though we use excel to help us with it, but still this makes me understand it more rather than being alienated by TECHNOLOGY!! Cheers!!

[consciousactions]

Thank you! :)

[KARLCECILHUFF10478]

hey man you gotta shot me some notes on that! i will send you personnel message

[KARLCECILHUFF10478]

i like your video it is new to me and i watch it alot

[hellosoul22]

How can you tell whether the graph of f(x) is a parabola and has multiple zeros?

[patrickJMT]

@hellosoul22 degree two polynomial - use the discriminant

[TRAVISH87]

can u make a video for some bisection method examples and secant method.. PLLLEEAASSSEEE!!!

[kris1ult]

Einstein will always be the best ;)

[shinomora]

Man every time I struggle against a problem you seem to have the answer and you explain so well... thanks!!!!

[8osman8]

So if you don't know the graph of the fuction you couldn't figure out what x1and x2 would be, right?

[ace2a66d20]

couldn't you just take the 7th root of 1000

which ends up being 2.682695795

[patrickJMT]

@ace2a66d20 holy shite, i never thought of that

[bryandPR]

@patrickJMT

wow, patrick. this is the first time I see you being sarcastic/rude to someone...

[ian559fresno]

@patrickJMT OMG Patrick! There are children watching Calculus videos you know!

[patrickJMT]

@ian559fresno oh please

[BanderHM]

@ace2a66d20 if I'm in the middle of nowhere; i.e. no calculators or Maple and my survival depends on the solutions of a 19th degree polynomial equation; I surely prefer Newton's method :)

[rclakmal]

@ace2a66d20

He has a point :)

[grk2nv100]

@ace2a66d20 that is just how that works for this equation but when you have quadratic equations where there are several integers then it wont work, this is a very simple example where as you have just shown the laws of algebra work to also give the answer however for the equation f(x) =e^x-3x-5 then newtons method becomes very handy, but good find man!

[jazzangelreloaded]

@ace2a66d20 If you didn't have a calculator/had an equation where rearranging for x was impossible, this is how you might work out what x is (don't ask me about how you would do the algebra without one...).

[mytwohands]

@ace2a66d20 that makes more sense to me. I mean, you find x intercepts by solving for zero so I don't know why we have to learn this new way.

But thank you for the video. Whether or not it's useful, I still have to know it for class!

[src2043]

@ace2a66d20 you could but im pretty that there are six other non-real 7th roots of a number not sure if that ever matters tho

[illuzion30]

@ace2a66d20 The idea is that you use Newton's method when it's difficult to evaluate the roots. Simple examples like using Newton's method on x^2-2 might not be practical, but it's effective for the purposes of learning how to use Newton's method.

[Ghaiyst]

i'm a little confused. couldn't you find the x of zero to be close to the value as about 2.7, from graphing x^7-1000, Then finding x of 1 by making x of 1= 2.7(x of zero)- f(2.7 (x of zero))/f prime(2.7 (x of zero))= 2.578711? how did you approximate x of 1? i used an approxamate answer from the x intercept of the graph which is equal to 2.7?

[YukonExpatriate]

Thanks a lot for this video and others! I watched them all and they were a great study aid for my calculus exam earlier today!

[luvlaxlife]

THANK YOU. thank you thank you thank you thank you thank you thank you!!!!! ah i have a calc final tomorrow and didnt understand this ALLLLL SEMESTERRRR until NOW!!! thank you very very much

[Apolloson]

Alright you gangsta, because that's what you are, go get a job teaching for christ sake. My professor at UIUC, top 6 engineering school in the world, teaches at an efficiency level nearly half of this. He makes millions, and you deserve that money you guru gansta

[TheLivirus]

Nice, practical and clear teaching.

[twoheadsarebetter]

this is awesome! i have my end of year test on monday. this helps a lot :D

[nehochcaz]

@twoheadsarebetter How'd your test go?

[twoheadsarebetter]

@nehochcaz OMG it went reallly good!!!! :D thanks you so much, i actually recapped most of the things i needed to know :) also i recommended you to lower year levels in my highschool ;) 

[xkittyxxcatxx]

Wow... it seems so much simpler here! Thanks so much for explaining!!

But is it possible to do this without a calculator? Because my teacher's always telling us about not using calculators for problems... if we are tested on it it will have to be with calculators right??

[Himster12]

Yes thank you for this help. My math prof is very hard to understand and its nice to have a someone teaching me in my own language.

[dodds125]

What if you have to calculate multiple zeros?

[h00k3rb00ts]

well i'm not getting an A in calc, but at least i am passing thanks to these videos.

i go to the worst college EVER... i asked my prof for help and they told me to search online and ushered me out of their office... i even made an appt.

[annajayne2]

you are a total grade saver!! thank you SO much for taking the time to put stuff like this up! youre a genius! :)

[iloveyamapiii]

can you be my math teacher?

whywhywhyyyy can't my teacher explain like this??

thank you a million!

[charmartist]

if your X1 is 3, shouldn't your X2 be 2.76739173 - (2.76739173)^7 - 1000/ 7(2.76739173)^6?

Since for X1 you're essentially plugging 3 into all the XN variables.

[maiie5]

when am i going to stop computing of the values of x?

[patrickJMT]

@maiie5 whenever you want

[Plysomack]

@patrickJMT ...Or write a computer program so you can get the best possible value for x without having to continually write out each iteration.

[Cdoddsy]

@patrickJMT You stop when successive approximations of x sub n and x sub n+1 agree to the number number of deciamal places you need accurate in your aproximation.

[bombs347]

@maiie5 You stop computing the values when there's no change in the Xn's, if you know what I mean. If X5, X6, X7, and X8 are all the same, you know that you've found your solution. Try putting it into excell and you'll see what I'm talking about.

[keith8c]

@maiie5 You can stop when x(n) and x(n+1) agree to eight decimal places.

[Ced0007]

Wow !! I'm having an exam today, and there was no videos explaining this method in french.

I'm belgian and speak french but understand english, you speak and pronounce good enough for me to understand you.

I'm bad at maths and my teacher too at explaining.

I was desperate of being questionned on this method but I understood everything thanks to you and my stress has lowed down a lot. Now i'm more confident for my exam, even if this method won't be asked. TY a lot, i'll follow you on youtube.

[hossein1413]

THE only thing i dont uderstand is how do u know X1=3. U said either one of them. So we could use 2 or 3 and get the same answer?? Could someone reply please THX

[AlwaysReading2]

@hossein1413

X1 can be anything you want it to be (in this situation, not in a situation like sin or cos), the numbers you calculate will get closer and closer to the x-intercept, no matter where you start.

[mimodok]

@hossein1413 Just guess an x-value that you think is close to the actual root you are trying to find. You can make a guess by looking at the graph. In this case you could have guessed 2, 3, 2.8, etc.

[pearcea1000]

Thanks for these videos!! Helps so much!

[Yu2Kal]

raphson shud also get some credit for this to you know

[shanerobertspilot]

haha gotta love the answer: .... at, *roughly*, 2.68269580......

[mastersasori01]

do you also have tutorials for fixed-point iteration method?

[KhunanonOtori]

Hmm Cool My math Jesus.

[Hackiesacker007]

Its not possible to do this without a calculator, right?

My exam tomorrow does not allow for calculators to be used but will be testing on Newton's method.

lol by tomorrow, I mean today, and by today I mean in 2.5 hours. I stayed up all night studying lol

[patrickJMT]

@Hackiesacker007 ha, good luck on the exam! : )

and yes, i think to actually do the computations, a calculator would be very handy.

[Hackiesacker007]

@patrickJMT We weren't allowed to use calculators, but it turns out we weren't tested on Newton's method anyway! I can't thank you enough for all your help with these tutorial videos. My math professor is absolutely horrid, and after watching these videos for the past 8 hours or so(I just got back from my exam 20 min ago after pulling an all nighter), I feel like I aced my exam. Thanks again!!

[patrickJMT]

@Hackiesacker007 glad it went well (hopefully)!!!! now... go get some sleep! : )

[burningambition254]

newtons law of desire:if you run around a tree with the speed of light you can fuck yourself :-P

[winduonline]

this is what the internet was made for, for geeks to bestow their hard earned knowledge upon other geeks so that we may eventually rule this place.

[effinbored2death]

if it's Xn+1, wouldn't X2 be 2.76739173 + 1 = 3.76739173?

[effinbored2death]

nvm i got it lol. yt needs to bring back the delete option for comments

[ExcellentScore]

can you show us how to solve (lnx)(e^x)=1?

[MrBellMacleodCollege]

Thanks a lot, that really helped.

[youstink14]

IT IS THE END OF THE WORLD!!

[madhuve23]

you rock mann

[sqiuts]

thanks.

[salao000]

thanks man. I hope a lot of good things hapen to you

[rafarsimoes]

Great vid. thanks :)

[Danielkwalsh111]

This solution is not correct to 8 decimal places. The last two digits should be 79, not 80.

[Danielkwalsh111]

This solution is not correct to 8 decimal places. The last two digits should be 79, not 80.

[camf1991]

saved.

my.

ass.

Have my babies, math god friend.

[username14657]

There's a much easier way to do this on the TI-89:

Store your first x-value (your first "guess") under any letter of the alphabet, for example, a.

Store f(x) under y1(x) and f '(x) under y2(x)

Then, type in under homescreen:

a - (y1(x) / y2(x)) -> a

Using this automatic Newtonizer, hit enter until the solution repeats.

Boom. You have your root.

Saves bamboozles of time.

[username14657]

HAHA!! Named after fig newtons... pshh :)

[adrianatomo]

thanks, excelent

[ytsedreamer]

THANKS!

5/5

[paulio2293]

its actually the Newton-Raphson method. Pay some respect

[GuerraOtilio]

and a virgin

[patrickJMT]

i doubt that - he was a super star of the time

[MsJessie28]

Dam to bad your married cuz i would so marry you cuz your freaking awesome!!! thank you so much for all u do wit the math stuff!!! my professors a real dick so i use you instead thanks!!!!!

[tehseenb10]

nice ..

this method is used in Numerical methods....

which solve many problems....

[hellohello66666]

You saved my coursework dude :D

[Saeth123]

this video is fake and gay

[hellohello66666]

WANKAAAA

[moonlightkitten]

You are my math jesus

[dmphalen]

Oh man, thanks a lot, this was great for me!

[Maestroxxx1]

T_T TY!!!!!!!!!!!!!

[alphalink11]

I love you!..lol...

[nettosoul]

You are a shortcut!

[karmacomacure]

thanx, this is exactly what i needed

[tkeo]

5/5

Thanks.

[sek0123]

thanx buddy

[ElmoPansy]

I agree with the person who said you're better than a textbook. My own textbook was over $100 as well and confuses me to no end. Thank you for these videos.

[erstpierre]

you are better than a textbook, yet my textbook cost over 100 dollars, you should write textbooks

[tengichadc]

i love you man, you rock

[mhwaad]

you re marvelous it helps a lot dude

[spym92]

thank you!!!

[TwinStarMonopol]

Thanx, it help me a lot!

This was a good idea to make mathsvids!!!

[ACEofBULLYING]

how about taking the 7th root of 1000?

[BoelNielsen]

@ACEofBULLYING

thats actually the most accurate

[applelime]

WOW thanks!

it helped me a lot :D

keep posting vids!

[yearock1234567890]

what about y?

[yearock1234567890]

what does f mean?

[nohyaya]

Thank you so much!

But still can't understand what Newton's Method is good for if you can equal f(x) to zero and find the intersect x

Any explanation, please?

[Morgfang]

That only works for some equations. There are some equations you'll have to find the x-intercept to in real life that can be really nasty and require calculus to solve.

[31337Lisper]

There are problems with continous functions that are a pain in the ass to solve, or that solving them is just not affordable. Example: Intersection of two rotated ellipses.

I've been trying to give this problem an exact solution for a couple of days now, but Newton's method does the job and can be applied to anything.

[PasuTech]

Ok, and once you've written f(x)=0, what do you do next? Try working out the equation of Patrick's example analytically... Good luck! :-)

Hint: google "Abel's Impossibility Theorem"

Also, if you can write f(x)=0 then you probably don't need Newton, but machines still do because they don't know much about maths :-)

[OldplusNew]

Nohyaya, it is true that you can set any function equal to zero and find the roots of the function (provided there are any).  The problem with this approach rears it's head when dealing with complex functions, such as polynomials greater than the 3rd and 4th degree, as well as functions dealing with sin, cos, etc... It's very hard and time consuming to find the roots of these problems.

[eackpal]

i havent evn lookd at this video yet but i no its guna b worth it.. patrick = legend

[ricbella]

thank u so much!!

though i'm german and looked for this explanation in german (of course^^) I've understood it at once.

thank you!!

[abaraimido]

Again ! God bless ya ! you are inbeliveably good!!

[jerminatorzz]

thanks alot:)

[dgraves882]

i generally love you

[abodra3]

do u even know him for u to GENERALLY love him??!??!?!.....come on girls ur goin crazy!!!!!!!!

[xMrElix]

For X1 i was gonna say its easier to use fractions in this method, but i guess 14122/5103 isn't a pretty fraction lol

[Newtonianator]

its actually the newton-raphson method, it was discovered independently

[XxAvantGardexX]

Thanks for the lesson mate

[powera5]

great video man helped a lot!

[MoNoXiD3]

if you have a calculator, you can insert 3 as an answer then use ANS - ((ANS^7-1000) / (7*ANS^6)) and hit equals over and over until you get an answer

[patrickJMT]

yep, assuming newtons method works!

[BigDaNNyBoi1989]

if u had a calculator u cud jus do 1000^(1/7) lol

[patrickJMT]

yes... lol.

[xMrElix]

Wow BigDannyboi your so smart, its not like X^(1/N) = Nth root of X

Oh wait... it is...