Newton's Method: Theory

[@dineshrajuthangavel6328]

Best lecture on newton's method all of KZbin. Got that intuitive understanding I was looking for... A great fan of your lectures btw.

[@mysterry2000]

I legit felt the same way. I was looking for solid intuition, and this dude is always the right person for the job

[@adwaitaroy1786]

Just loved how you explained it in such a simple manner, thanks a lot. Keep posting such great videos!

[@LOLxUnique]

This is an absolute ingenious method of approximating roots.

[@evyatarchaimoff7007]

Amazing! Thank you very much!

[@danielc.martin]

Great explanation.

[@a.man38]

my goat

[@sakshishukla41]

What is the mathematical logic behind tangent getting us close to the zeroes? I have sometimes encountered situations where the tangent does not get us closer to the zero? So is there a principle that goes behind this (tangent being being so special at times)?

[@soupy5890]

I was wondering the same thing, I believe the general idea involves that as the limit as f(x) approaches 0, the equation approaches x or something to the like, and idk when this doesn't break down

[@carultch]

@@soupy5890 As long as you don't have problem points between your initial guess, and the point you are trying to find, this method will converge to the solution. By problem points, I mean any of the following: 1. Stationary points of any kind 2. Vertical asymptotes 3. Jump discontinuities 4. Jump discontinuities in the derivative, that show up as kinks or cusps in the function

[@soupy5890]

@@carultch Thanks for the information, I still wasn't confident on what counted as a problem point

[@carultch]

@@soupy5890 No prob. I've made a Geogebra resource for this concept, solving the equation 10*x*e^(-x) - 1 = 0. I can't think of a good way to generalize how far away from the problem point you have to be, for it to converge on the solution. For this example, the stationary point is at x=1, and the lowest guess I found for convergence is x=1.21, to the solution of 3.577. The highest guess I found for proper convergence is 5.52. There's also the issue, of, what if your stationary point turns out to also be your solution?

[@Aliaskar98]

Awesome 👌

[@carlosdominguez9420]

So wonderful

[@mohamedusama4526]

really great I have got it easily

[@GovindKumar-mu6jq]

Thanks 🙏

[@classic8054]

I wished my highschool math class were like this fun

[@Amine-gz7gq]

teachers like eddie woo are very very rare

[@tuongdihoc]

OMG!!!!

[@langwane8038]

I CAN'T SEE...

[@kaadshah7737]

hehe tadda