I’ve written several blog posts about equation solving recently. This post will summarize how in hindsight they fit together.
How to solve trig equations in general, and specifically how to solve equations involving quadratic polynomials in sine and cosine.
This weekend I wrote about a change of variables to “depress” a cubic equation, eliminating the quadratic term. This is a key step in solving a cubic equation. The idea can be extended to higher degree polynomials, and applied to differential equations.
Before that I wrote about how to tell whether a cubic or quartic equation has a double root. That post is also an introduction to resultants.
Numerically solving equations
First of all, there was a post on solving Kepler’s equation with Newton’s method, and especially with John Machin’s clever starting point.
Another post, also solving Kepler’s equation, showing how Newton’s method can be good, bad, or ugly.
And out there by itself, Weierstrass’ method for simultaneously searching for all roots of a polynomial.