Newton Raphson Method: Derivation

Learn how to derive the Newton Raphson method of solving a nonlinear equation of the form f(x)=0. For more videos and resources on this topic, please visit nm.mathforcolle...

[@appeleper4436]

welcome to 13 years from when this method was posted... this video helped me ace my presentation on newton's raphson method

[@marcosmartinez4037]

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[@sarahsaleh4661]

Marcos Martinez agree👍

[@sutanugantait9429]

Agree with you

[@numericalmethodsguy]

Thanks for your comments. We will have about 200 videos by end of June 2009.

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[@user-mt9un2dn5s]

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[@numericalmethodsguy]

@@randyrockranaq Thank you. Please subscribe and ask your friends to subscribe - our goal is to get to 100,000 subscribers by the end of 2021. To get even more help, subscribe to the numericalmethodsguy channel kzbin.info, and go to MathForCollege.com/nm and MathForCollege.com/ma for more resources. Follow the numerical methods blog at AutarKaw.org. You can also take a free massive open online course (MOOC) at canvas.instructure.com/enroll/KYGTJR Please share these links with your friends and fellow students through social media and email.

[@numericalmethodsguy]

@@user-mt9un2dn5s Thank you. Please subscribe and ask your friends to subscribe - our goal is to get to 100,000 subscribers by the end of 2021. To get even more help, subscribe to the numericalmethodsguy channel kzbin.info, and go to MathForCollege.com/nm and MathForCollege.com/ma for more resources. Follow the numerical methods blog at AutarKaw.org. You can also take a free massive open online course (MOOC) at canvas.instructure.com/enroll/KYGTJR Please share these links with your friends and fellow students through social media and email. Support the channel if you able to do so at kzbin.info/store

[@numericalmethodsguy]

@@user-mt9un2dn5s Thank you. Please subscribe and ask your friends to subscribe - our goal is to get to 100,000 subscribers by the end of 2021. To get even more help, subscribe to the numericalmethodsguy channel kzbin.info, and go to MathForCollege.com/nm and MathForCollege.com/ma for more resources. Follow the numerical methods blog at AutarKaw.org. You can also take a free massive open online course (MOOC) at canvas.instructure.com/enroll/KYGTJR Please share these links with your friends and fellow students through social media and email. Support the channel if you able to do so at kzbin.info/store

[@hellostranger2709]

This video was published 12 years ago but still very helpful! Thank you!

[@Tigeress8482]

You're the best. Seriously, thank you for sharing your gift of teaching with those who are not able to have a professor like you. :) Your videos have helped me a lot, and I know I'm not alone! Way to help build the future!

[@punkfluff64]

Thanks so much for this. This derivation has been bothering me for ages as it hadn't been explained to me in the context of tan. Really clear.

[@numericalmethodsguy]

Thank you. To get even more help, go to MathForCollege.com/nm for more resources. Follow my numerical methods blog at AutarKaw.org. You can also take a free online course at www.canvas.net/?query=numerical%20methods

[@amdperacha]

Wow! Thank you very much for this! Your explanation is clear and concise. Very easy to understand. Thank you very much, indeed. From Pakistan

[@chad8707]

best video for numerical analysis..

[@MrNuigit]

Surprisingly clear and thorough :)

[@dmitriypetrovykh8763]

80 seconds in, and I already got what I needed. Excellent explanation

[@29jimmy980]

Sir, you are a legend. Many thanks to you for making life a lot easier.

[@marcusrosales3344]

My computational physics teacher told me the Newton-Raphson method is this formula... That was my lesson.

[@numericalmethodsguy]

Sorry to hear that. Go here for all resources. nm.mathforcollege.com/ Tell your classmates.

[@kyeongs_c]

Thanks for the clear and wonderful explanation!

[@eleeson4169]

You have very neat board writing. Thanks for the video.

[@IfeanyiEKalu]

Really enjoyed your teaching...one of my most favorites youtube teacher. Thanks Prof!

[@numericalmethodsguy]

Thank you. To get even more help, subscribe to the numericalmethodsguy channel, and go to MathForCollege.com/nm and MathForCollege.com/ma for more resources and share the link with your friends through social media and email. Support the site by buying the textbooks at www.lulu.com/shop/search.ep?keyWords=autar+kaw&type= Follow my numerical methods blog at AutarKaw.org. You can also take a free online course at www.canvas.net/?query=numerical%20methods Best of Learning Autar Kaw AutarKaw.com

[@maxguichard4337]

That's a very neat and intuitive explanation, thank you for sharing :)

[@numericalmethodsguy]

To get even more help, subscribe to the numericalmethodsguy channel, and go to MathForCollege.com/nm and MathForCollege.com/ma for more resources and share the link with your friends through social media and email. Support the site by buying the textbooks at www.lulu.com/shop/search.ep?keyWords=autar+kaw&type= Follow my numerical methods blog at AutarKaw.org.

[@johnk1973]

Thank You for your explanations! Great job! I needed to refresh quickly numerical methods. With your videos I did it in couple of evenings! Thank You very much

[@ingloeski]

ty, great teacher and simple explanation

[@sandeepgabhale]

simple and nice explanation

[@numericalmethodsguy]

@MachiP0p0 Es means pre-specified tolerance. It is a stopping criteria to stop iterations. When the absolute relative approximate error is less than pre-specified tolerance, then we can stop the iterations. How do we choose Es? Go to numericalmethods(.)eng(.)usf(.)edu and click on Measuring Errors under Introduction. See pages 5-7 of the pdf file of the texbook chapter.

[@9dubb9]

Thanks agian....another ace on exam in a few hours...u are a great teacher

[@nsartigo]

@NancyEng It is the second guess or a better guess than xi . It is closer to the root. Hence it is called xi+1.

[@esakkithirugnanam6626]

Nice explanation...

[@rahulsharma-cb7kk]

GREAT VIDEO,VERY HELPFUL

[@eden9808]

Really helpful. Thanks sir 👍

[@trantamphuong]

Hi there, I love your videos, every single one. Your explainations are really clear, your lecture ignites my passion in numerical method. Hope that you could construct a youtube curricular for the course

[@numericalmethodsguy]

nm.mathforcollege.com

[@07dalle]

great videos

[@basimkhajwal2896]

Great, really helped me to understand why it works

[@numericalmethodsguy]

@fullheavy Just follow the example given in the Newton-Raphson playlist. It is not a difficult problem to do. Be sure that your calculator is set to the radians mode. Once the 5 decimal places do not change in the answer, you have your answer.

[@phobia6661]

Brilliant sir, thanks to you I'll pass.!

[@numericalmethodsguy]

I do not know of a general technique to do so. If the problem is connected to a physical phenomenon, you can use the knowledge of the physical problem to choose a good initial guess.

[@romance177]

thank you for this nice explanation :) actually I'm doing my master thesis and I'm taking computational methods course so you just helped me a lot>>> BY THE WAY, i just subscribed! :)

[@numericalmethodsguy]

x(i+1) is the next iterative value of the root after x(i). There is no restriction that x(i+1) has to be greater than x(i).

[@numericalmethodsguy]

Thank you. Please subscribe and ask your friends to subscribe - our goal is to get to 100,000 subscribers by the end of 2021. To get even more help, subscribe to the numericalmethodsguy channel kzbin.info, and go to MathForCollege.com/nm and MathForCollege.com/ma for more resources. Follow the numerical methods blog at AutarKaw.org. You can also take a free massive open online course (MOOC) at canvas.instructure.com/enroll/KYGTJR Please share these links with your friends and fellow students through social media and email. Support the channel if you able to do so at kzbin.info/store

[@numericalmethodsguy]

@xTabbyCat I do not know of a general technique to do so. If the problem is connected to a physical phenomenon, you can use the knowledge of the physical problem to choose a good initial guess. Go to numericalmethods(.)eng(.)usf(.­)edu and click on Newton Raphson Method. Click on the textbook chapter to see a physical problem.

[@johnroberts7529]

In my humble opinion you are an excellent teacher. Many thanks. Regards, John Roberts.

[@karanbhatia6712]

Great explanation. Thank you very much!

[@johnjv24]

Awesome video!!!!

[@sarahhope8516]

Thank you so so so much!!!

[@johnydesuza8644]

thank you very much sir

[@yassiraladdin5886]

Thank you so much!! YOU ARE THE BEST

[@fikret8422]

that was amazing thank you

[@xTabbyCat]

How do I find use the tangent to find the initial estimate? I have a graph of two curves; (y=e^x) and (y=4/x) And it says I have to find the initial estimate for the root of the equation: x e^x - 4 = 0 The answer is that the solution is the intersection of f(x) - e^x and f(x) = 4/x but that doesn't help me find the actual NUMBER for the initial estimate. How would I go about finding the initial estimate NUMBER?

[@fullheavy]

Sir, could you help me with this question? Use the Newton-Raphson process to determine a value of x near x1 = 0 for which f(x) = 0, where f(x) = 9 x+0.4−8 sin( x ) giving your answer (and the interim results we ask for) correct to 5 decimal places. What are the values of x and f(x) at the second iteration? What are the values of x and f(x) at the third iteration? The value of x (correct to 5 decimal places) such that f(x) = 0.

[@gustavomarcelo7250]

Why does the error = ( xi-x0)/xi and not (xi-x0)/x0? Why does roots are define at f(x) = 0?

[@numericalmethodsguy]

You always compare with current approximation. Second question needs more clarification.

[@hedgehog1962]

Thank you very helpful

[@viratpavan1336]

Amazing

[@nancyeng6250]

Can i just ask why Xi+1 is behind the point Xi ? in the graph ?

[@numericalmethodsguy]

Yes, if that is what it turns out to be.

[@davisbrown3342]

who is this legend

[@jdlopez131]

why is the tangent of theta the same as the derivative of the function at x sub i? I mean, shouldn't it be that the theta is the slope of the line in any case? But he is talking about tangent of theta, and that's where it doesn't make sense

[@numericalmethodsguy]

If you remember the slope of the tangent line is given by tan(theta)=rise/run. Now think about derivative is (f(x+dx)-f(x))/dx as dx ->0. What is the numerator dy (difference between y values at x+dx and x).

[@jdlopez131]

@@numericalmethodsguy yes, it suddenly dawned on me what you were saying. Thank you

[@dhananjoypal1949]

thank you sir..

[@tessemagetebo8655]

O! NICE

[@MachiP0p0]

What mean by Es?

[@numericalmethodsguy]

The whole curriculum with videos will be done by June 2009. Just visit numericalmethods(dot)eng(dot)usf(dot)edu

[@MexterO123]

Why is this called an open method?

[@autarkaw1826]

Because it is not bracketed. We have only one initial guess. Two initial guesses do not make a method bracketed as is the case in secant method. Why? Because the two initial guesses do not have to bracket a root. Bisection method is a bracketing method.

[@nutankumari5548]

Could anybody please clarify how to calculate (E)s that is ebslons s?

[@numericalmethodsguy]

+Nutan Kumari Epsilon-s is prespecified tolerance. That is an input. You can however relate epsilon-s to how many significant digits do you want at least correct in your answer. If you want m significant digits to be correct,then epsilon-s is 0.5*10^(2-m) percent. Check nm.mathforcollege.com/topics/measuring_errors.html for more info.

[@nutankumari5548]

Thanks for the answer.could you please explain how to guess the value initially in this method.?

[@numericalmethodsguy]

+Nutan Kumari I do not know of a general technique to do so. If the problem is connected to a physical phenomenon, you can use the knowledge of the physical problem to choose a good initial guess. Go to nm.mathforcollege.com/topics/newton_raphson.html and look at the examples from other majors.

[@akarsh.saxena]

+Nutan Kumari Just put x=0,1,2... in f(x). The two consecutive values for which the f(x) changes its sign (-ve to +ve or vica-versa) (say 2 and 3), then you can take initial approximation between those two points (between 2 and 3 i.e. 2.5). For trigonometric functions, just put the values (0,pi/4,pi/2....) and for the values say pi/4 and pi/2, the f(x) changes its sign, then the initial approximation can be taken as (3*pi/4). This works in all the questions I've done.

[@muhammadroshan7315]

Nicely done but a little too slow

[@ahmedmohamed-yx1ln]

great video

[@Arvindchoudhary_]

Legends who watching 2022. Like it

[@yourdeadmother]

dat derivation doe

[@wangb13]

hi.

[@arassen19]

boy, indians are excellent at math for some reason XD..

[@muhammadroshan7315]

You mean in cramming math. Yeah I can agree on that. But definitely not on creativity

[@numericalmethodsguy]

@@muhammadroshan7315 Indians are not generally excellent in math. We got 1.3 billion people and we better have many people who are excellent in math. The cramming you talk about is a good start in being creative. How would one get a creative thought without having a base knowledge?

[@sohaginfinity]

dhon bujlam na kisu

[@PavanKumar-yx8ss]

thank you sir

[@numericalmethodsguy]

Thank you. To get even more help, go to MathForCollege.com/nm and MathForCollege.com/ma for more resources and share the link with your friends. Follow my numerical methods blog at AutarKaw.org. You can also take a free online course at www.canvas.net/?query=numerical%20methods