User:Jw116104

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Project Report for User:jw116104[edit]

For Introduction to Numerical Analysis, Fall 2010.

Introduction[edit]

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[edit]

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[edit]

Motivation[edit]

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[edit]

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

Worked Example[edit]

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[edit]

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

Conclusions[edit]

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.