History of mathematics · Maths EE idea · Solid
Newton's method then and now
A research question to start from
How did the method now called Newton–Raphson develop from Newton's original approach, and why is the modern form more powerful?
A starting point, not your question: change the case, the comparison or the limit until it is yours. The research-question builder helps you check it.
Why it works as a maths EE
A method traced through its versions and evaluated mathematically.
Mathematics you would need
- Polynomial approximation
- Iteration
- Derivatives
- Convergence analysis
Much of this goes beyond the DP course. That is expected in a maths EE, but you must understand and explain everything you use.
One possible line of attack
- Work through Newton's original approach on a cubic.
- Compare with Raphson's and the modern formulation.
- Prove convergence for the modern method.
Scope and difficulty
Solid. Solid.
Pitfalls
- Historical claims without sources.
- No convergence analysis.
Where to start reading
Search a library catalogue or a university's open lecture notes for: history Newton-Raphson method Newton original cubic; Raphson. Prefer textbooks, lecture notes and journal articles to a single website, and cite everything you use (how to reference a maths EE).