# User:Gc953496

Five things I have learned about Wikiversity:

1. "Wiki" means that one can edit the pages.
3. A new Wikiversity page is created by adding the name of the page to http://en.wikiversity.org/wiki/
4. Wikiversity was launched at Wikimania 2006.
5. Whereas Wikipedia has articles (single page entities), Wikiversity has learning projects, which are multi-page entities devoted to learning, based on a particular topic.

A complicated math formula(Taylor's Theorem):

${\displaystyle f(x)=f'(x)+f'(a)(x-a)+(f''(a)/2!)(x-a)^{2}+\cdots +(f^{(k)}(a)/k!)(x-a)^{k}}$

where ${\displaystyle k\geq 1}$ is an integer and ${\displaystyle f}$ is a function differentiable ${\displaystyle k}$ times.

What is the convergence rate of the Newton Fixed Point Iteration?

1

Which of the following root-finding algorithms converges the fastest?

 Secant Method. Regula Falsi Method Newton's Method. Eeny Meeny Miny Moe Method.

2

Which numerical integration method has an error of O(Δx^4)?

 Trapezoid Rule. Midpoint Rule. Simpson's Rule. Murphy's Law.

On 10/17/2012 I edited the Numerical Analysis ODE Exercises page and added an exercise using the Runge-Kutta 4 method. The page is at http://en.wikiversity.org/wiki/Topic:Numerical_Analysis/ODE_Exercises .

### Project

For my Math 5600 Final Project, I plan to improve the proof of quadratic convergence of Newton's Method on Wikiversity.

The proof you refer to is on Wikipedia, not Wikiversity, so it is not appropriate for a Wikiversity project. If you want to work on Newton's method, you could
1. Move the content of The Newton's method to a page under Topic:Numerical analysis where it belongs and fix it up.
2. Move the content of Exercises_and_quiz to two pages under Topic:Numerical analysis where it belongs and fix them up.
3. Find something else new to add to Wikiversity about Newton's method.
Mjmohio (talk) 18:22, 7 November 2012 (UTC)
The more I consider this, the more I think you would be better off chosing a fresh topic. Mjmohio (talk) 18:43, 7 November 2012 (UTC)

Final Project Report:

For my final project, I created a Loss of Significance topic page for Wikiversity. Specifically, I created a number of exercises that illustrate the use of the formula

${\displaystyle 2^{-q}\leq 1-{y \over x}\leq 2^{-p}}$

for determining a bound on the loss of significance. I feel that concepts and theorems are always clarified by examples, and thought it would be worthwhile to present some examples of this theorem. I presented several specific examples of subtraction problems that can result in loss of significance, and a generalized example using

${\displaystyle f(x+h)-f(x)}$.

The Wikipedia Loss of Significance page is at w:Loss of significance and the Wikiversity page I made is at http://en.wikiversity.org/wiki/Topic:Numerical_Analysis/Loss_of_Significance .

Another thing I think is lacking on the Wikipedia page is reducing loss of significance by posing the problem differently. I tried to address that in my exercises as well.

I hope to add more exercises and improvements to this Wikiversity topic in the future. Gc953496 (talk) 23:07, 24 November 2012 (UTC)