Newton's Method

This calculus video tutorial provides a basic introduction into newton's method. It explains how to use newton's method to find the zero of a function which is the same as the x-intercept.
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[@TheOrganicChemistryTutor]

Derivative Applications - Free Formula Sheet: bit.ly/4eV6r1b Derivative Applications - Video Lessons: www.video-tutor.net/derivative-applications.html

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If you are studying thermodynamics, you should know about Newton's method.

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One thing you didn't mention is that this is used for fast square root algorithms. The famous Quake 3 Fast Inverse Square root algorithm uses only 2 iterations for 7 decimals of precision. It can even be optimized by using a "magic number" to get close to most guesses on the first try. Dave's Garage went over it and described the error as very minimal while the calculation time is only a few cycles as compared to traditional square root finders that test certain numbers to find the root. (i.e. looping from 0 or binary search). Basically this method is very useful for guessing things when you can't spare the energy to find out the whole answer. Wonder if it works with pi as well.

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-Take the first three odd integers: 1,3,5 -Double them thusly: 113355 -Divide the last three by the first three thusly: 355/113 There ya go, Pi accurate to 6 decimal places!

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you stop when you feel like you've got enough accuracy.

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Hi sir, thanks for everything but could you please do videos about bisection method and secant method as well??

[@OzilHohuk]

we can also use the dichotomie method to find a smaller interval of the approximate solution

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Great video! You would think Newton would have come up with something easier than this to find a zero

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I'll stick with synthetic division for now or use this when my college teaches me. The process is too long for me. In which scenarios is this method useful? I would love to know that to appreciate this method.

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This works for all continuously differential equations, not just polynomials. For example, f(x) = cos(x)sin(x) - e^x + 4x^2.

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Please no video on fixed point iteration method?

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I’ve been thought to divide the function by x-(something I have to guess) until there is no remainder and then I’ll get (x-(the number))(answer). X=the number I guessed. I think it’s called the factor theorem

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[@SolutionInnHub]

Newton's Method is a fascinating numerical technique for finding approximations to the roots of a real-valued function. Starting with an initial guess, the formula iteratively refines the estimate using the function and its derivative. While the concept may seem straightforward, applying it requires a solid understanding of derivatives and function behavior. For anyone exploring numerical methods like this, tools like the AI Study Tool on SolutionInn can be a game-changer. It provides step-by-step explanations and tailored guidance to help you tackle calculus problems efficiently. Make solving complex equations less intimidating and more approachable.