Mastodawn

Alright, future engineers!
**Bisection Method:** Finds roots of `f(x)=0` by repeatedly halving an interval where `f(x)` changes sign.
Ex: If `f(a)f(b)<0`, a root lies between `a` and `b`.
Pro-Tip: Guaranteed to converge (slowly!) if a root exists in your initial bracket – very robust!
#NumericalMethods #RootFinding #STEM #StudyNotes

kipriyanovich 1d ago

Alright, future engineers!

**Newton-Raphson:** Iteratively finds roots of f(x)=0 by following tangent lines to the x-axis.
Ex: `x_new = x_old - f(x_old)/f'(x_old)`
Pro-Tip: Super fast convergence, but needs a good initial guess and `f'(x)` not zero!
#NumericalMethods #RootFinding #STEM #StudyNotes

kipriyanovich Jun 14

Alright, future engineers!
**Newton-Raphson Method:** Iteratively finds a function's root (where f(x)=0).
Formula: `x_n+1 = x_n - f(x_n)/f'(x_n)`
Pro-Tip: A good initial guess is crucial for rapid convergence!
#RootFinding #NumericalMethods #STEM #StudyNotes

kipriyanovich Jun 2

Alright, future engineers!
**Newton-Raphson:** An iterative method to find roots (zeros) of a function.
Formula: `x_new = x_old - f(x_old) / f'(x_old)`
Pro-Tip: A good initial guess is CRUCIAL for fast convergence!

#NumericalMethods #RootFinding #STEM #StudyNotes

kipriyanovich May 30

Alright, future engineers!
**Newton-Raphson:** Iteratively finds roots `f(x)=0` by following tangent lines.
Ex: `x_new = x_old - f(x_old) / f'(x_old)`
Pro-Tip: A good initial guess is CRUCIAL for fast convergence (or any convergence)!
#NumericalMethods #RootFinding #STEM #StudyNotes

kipriyanovich May 28

Alright, future engineers!
**Bisection Method:** Finds roots by repeatedly halving an interval where a sign change occurs.
Ex: If f(a)*f(b) < 0, root is in [a,b]. New midpoint c=(a+b)/2.
Pro-Tip: Slow but *guaranteed* to converge if a root is bracketed!
#RootFinding #NumericalMethods #STEM #StudyNotes

kipriyanovich May 27

Alright, future engineers!
**Newton-Raphson** iteratively finds roots of `f(x)=0` by using tangent lines.
Formula: `x_n+1 = x_n - f(x_n) / f'(x_n)`
Pro-Tip: A good initial guess `x_0` is CRUCIAL for quick convergence!
#NumericalMethods #RootFinding #STEM #StudyNotes

kipriyanovich Apr 26

Alright, future engineers!
**Newton-Raphson:** Iteratively finds function roots (where f(x)=0).
Formula: `x_n+1 = x_n - f(x_n) / f'(x_n)`
Pro-Tip: A poor initial guess can lead to divergence or finding the wrong root!
#NumericalMethods #RootFinding #STEM #StudyNotes

kipriyanovich Apr 21

Alright, future engineers!
**Bisection Method:** Finds f(x)=0 roots by repeatedly halving intervals where sign changes.
Ex: If `f(a)f(b)<0`, root's in `[a,b]`. `x_new = (a+b)/2`.
Pro-Tip: Guaranteed convergence if root is bracketed, but can be slow!
#NumericalMethods #RootFinding #STEM #StudyNotes

kipriyanovich Apr 21

Alright, future engineers!

**Newton-Raphson** finds roots of `f(x)=0` by iteratively refining guesses.
Ex: `x_new = x_old - f(x_old)/f'(x_old)`.
Pro-Tip: A good initial guess speeds up convergence & prevents divergence!

#NumericalMethods #RootFinding #STEM #StudyNotes