Newton’s Method: Homework

1. 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: • Kenneth.Church@jhu.edu and annirvine@gmail.com • 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

2. Newton’s Methodhttp://archives.math.utk.edu/visual.calculus/3/newton.5/

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

6. Sqrt(-1)  Error (for many tools)

7. Roots (without approximations)

8. Numerical Methods:Approximations such as Newton’s Method

9. Complex Roots

10. Newton’s Methodhttp://archives.math.utk.edu/visual.calculus/3/newton.5/

11. Newton’s Methodhttp://archives.math.utk.edu/visual.calculus/3/newton.5/

12. Symbolic Alternative