Newton's Method
A playlist of all videos related to Newton's Method can be found here.
There are multiple videos related to Newton's Method for finding the root of a single equation. The Original and the Video Mistakes. The topic is also expanded upon in Newton's Method Convergence Interval (code: here documentation: here) and Newton-Bisection Hybrid (code: here documentation: here) as well as Newton Fractals (code: here documentation: here).
Solving nonlinear systems with Generalized Newton's Method is discussed in this video with code located in Generalized Newton's Method. It is written in GNU Octave but should work in MATLAB. The code can be run online through octave-online. If locally using GNU Octave, be sure that the symbolic package has been installed. In case it isn't use the command pkg install -forge symbolic which only has to be run once. Documentation for the symbolic package can be found here.
- "Historical Development of the Newton–Raphson Method" by Ypma https://doi.org/10.1137/1037125
- "Thomas Simpson and ‘Newton's method of approximation’: an enduring myth" by Kollerstrom https://doi.org/10.1017/S0007087400029150
- "Essays on Several Curious and Useful Subjects, in Speculative and Mix'd Mathematicks" by Simpson https://books.google.com/books?id=3HpYAAAAcAAJ&dq
- "A New Treatise of Fluxions" by Simpson https://books.google.com/books?id=GGZbUevBqskC