Newton’s Method: Homework Create a Google Spreadsheet – that uses Newton’s Method – to find roots of x^2 + x = 1 Link to this page from your homepage Send link(s) to: – and Extra credit: – Multiple roots: There are two roots to this equation. You will get one root or the other depending on the initial value. Show that this is the case. That is, produce two spreadsheets with two initial values that converge on different roots. Which initial values converge on which root? – What happens if you try to use Newton’s Method to solve: x^2 + x = -1

Newton’s Method

nx[n]x[n+1]sqrt(5)

Symbolic Features (Bet you can’t do this with your favorite statistics package) Complex Numbers: Sqrt(-1) Roots (without approximations) Differentiation (without approximations) Integration (without approximations) The On-Line Encyclopedia of Integer Sequences Eval Symbolic Methods ≠ Numeric Methods – Newton’s Method: Approximation for Reals

Sqrt(-1)  Error (for many tools)

Roots (without approximations)

Numerical Methods: Approximations such as Newton’s Method

Complex Roots

Newton’s Method

Newton’s Method

Symbolic Alternative