User:Jw116104

Project Report for User:jw116104

For Introduction to Numerical Analysis, Fall 2010.

Introduction

For my final project, I added resources to Wikiversity concerning the bisection method for finding roots of polynomials. Here is all relevant information concerning my experiences with Wikiversity this quarter.

Initial Experience

Before engaging in the final project, I did some smaller projects as part of homework assignments.

I found the existing page on Cobweb Plots unsatisfying. Here is what is currently under "Interpretation":

"On the cobweb plot, a stable fixed point corresponds to an inward spiral, while an unstable fixed point is an outward one. A period 2 orbit is represented by a rectangle, while greater period cycles produce further, more complex closed loops. A chaotic orbit would show a 'filled out' area, indicating an infinite number of non-repeating values."

I proposed to add a bit more detail that I would have liked to have had the page hit me in the face with:

"On the cobweb plot, a stable fixed point corresponds to an inward spiral, while an unstable fixed point is an outward one. It follows from the definition of a fixed point that these spirals will occur where the diagonal y=x line crosses the function graph. A period 2 orbit is represented by a rectangle, while greater period cycles produce further, more complex closed loops. A chaotic orbit would show a 'filled out' area, indicating an infinite number of non-repeating values."

My instructor pointed out some things that would be better so I changed my proposal to:

"On the cobweb plot, a stable fixed point corresponds to an inward spiral, while an unstable fixed point is an outward one. It follows from the definition of a fixed point that these spirals will center at a point where the diagonal y=x line crosses the function graph. A period 2 orbit is represented by a rectangle, while greater period cycles produce further, more complex closed loops. A chaotic orbit would show a 'filled out' area, indicating an infinite number of non-repeating values."

I then posted my proposal to the discussion page but there were no replies. Soon after, I decided my change was not necessary.

Main Project

Motivation

The goal of the project was to add materials to Topic:Numerical analysis at Wikiversity. I chose to focus on the bisection method for finding roots of a polynomial.

MATLAB Code

My first edit was to add MATLAB code that will run the bisection method.

Worked Example

Next, I added a page that had a worked example of using the bisection method. After the problem analysis and the first iteration, all future steps are hidden to encourage the reader to work the problem out.

Quiz

Finally, I added a five question quiz on the subject. The quiz focuses on aspects of the algorithm, error, and failure.

Conclusions

In addition to that warm fuzzy feeling of contributing to the public knowledge, I appreciated the Wiki assignments this quarter as it gave me a chance to learn how to edit Wikipedia. Thanks to the assignments, I learned the Wiki Math formatting, which has helped me learn how to use LaTeX. All in all, I feel that this project has been a success.