# Homework 2 - Nonlinear Equations

## Due: Wednesday, September 19, 2001

Reading: *Gerald and Wheatley, 6th edition*, Chapter 1

##### Topics

- bisection
- linear interpolation
- Newton's method
- Muller's method
- fixed point interation
- methods for polynomials,
multiple roots, error analysis, hybrid methods

The following problems are on page 100ff of the text:

- 1, 5 - graph using Maple
- 11, also try starting at x=0
- what happens?
- 23 and then 28
- 29, 54, 59
- 70 - use Maple

##### Sample Exam Question

For homework problems (unless text gives different instructions) and exams,
you are required to use __exam precision__: chop to 4 significant digits
only when you write an intermediate or final answer down and continue the
calculations with those recorded numbers.

- Find the root of
*f(x)=exp(x)-3/x*
using the secant method for 2 iterations beyond the starting guesses, *x(1)=*1.0
and* x(2)=*2.0. Record your answers in a table of *k, x(k), x(k-1),
f(x(k)), f(x(k-1))* for each interation *k*. (final answer =
root=(4c) 1.049).

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