1. Greg Kelly, Hanford High School, Richland, Washington

2. Newton’s Method Finding a root for: We will use Newton’s Method to find the root between 2 and 3.

3. Guess: (not drawn to scale) (new guess)

4. Guess: (new guess)

5. Guess: (new guess)

6. Guess: Amazingly close to zero! This is Newton’s Method of finding roots. It is an example of an algorithm (a specific set of computational steps.) It is also called the Newton-Raphson method This is a recursive algorithm because a set of steps are repeated with the previous answer put in the next repetition. Each repetition is called is called an iteration.

7. This is Newton’s Method of finding roots. It is an example of an algorithm (a specific set of computational steps.) It is sometimes called the Newton-Raphson method Guess: Amazingly close to zero! Newton’s Method: This is a recursive algorithm because a set of steps are repeated with the previous answer put in the next repetition. Each repetition is called an iteration.

8. Find where crosses.

9. There are some limitations to Newton’s method: Wrong root found Looking for this root. Bad guess. Failure to converge

10. Acknowledgement I wish to thank Greg Kelly from Hanford High School, in Richland, Washington, USA for his hard work in contributing towards this PowerPoint. http://online.math.uh.edu/ Greg has kindly given permission for this resource to be downloaded from www.mathxtc.com and for it to be modified to suit the Western Australian Mathematics Curriculum. www.mathxtc.com Stephen Corcoran Head of Mathematics St Stephen’s School – Carramar www.ststephens.wa.edu.au