# User:Zl542711

### Things I learned

1. Introduction to Wikiversity Wikiversity is a community devoted to collaborative learning. We build up learning resources by ourselves and also link to existing internet resources. And we,as wikiversity participants, are continually updating the educational content on the pages.
2. How to edit It is very important for wikiversity participants to learn how to edit. By learning this skill, we can contribute our efforts to improve the learning resource on wikiversity's pages. On the top of the page, I can find a button named "edit this page" or "edit". After clicking it, I can edit this page and also, there is a button named "show preview" to help me avoid making any mistakes. At last, click "save page" when I am sure of my edit.
3. More about edit I can use an edit toolbar at top of the edit window to make my edit more easily and my page more beautiful. By adding a new page name after http://en.wikiversity.org/wiki/ and hit enter key, I can creat a new wikiversity page. Before creating a new page, I can use "search" to find out if this page and topic already exist.
4. The community I can create my own username to become a part of community. In the community session, I can learn about the history of Wihiversity and I can keep abreast of the latest Wikiversity news. What is more, the community portal has announcements about the Wikiversity project.
5. Help If I have any questions about Wikiversity, I can get the answer by clicking the button "Help" on the side bar. There are some important information about editor's guide or general information.

### Math formula

${\displaystyle x_{1,2}={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}}$

${\displaystyle \lim _{z\rightarrow z_{0}}f(z)=f(z_{0})}$

${\displaystyle \int _{a}^{x}\int _{a}^{s}f(y)\,dy\,ds=\int _{a}^{x}f(y)(x-y)\,dy}$

HW3, Question 1 Complementarity about Taylor's theorem

HW5, Question 1

I think I have to accept the fact that my proposal is a bad idea. Since the Statement about the theorem and the explicit formulae for the remainder have been clearly represented on the web page, my proposal confuses more than it helps. The page already says "Taylor's theorem describes the asymptotic behavior of the remainder term ${\displaystyle R_{k}(x)=f(x)-P_{k}(x)}$" thus implying that the remainder term expressed as a trivial difference is not useful. Thus, I realize that I don't totally understand the Taylor's theorem and I miss some important information. Therefore, I need to be more careful when I am reading, so I won't miss some important information again. What's more, I have a better understanding of the Taylor's theorem.

Homework 6, Question 1

What is 2*3?

## Quiz

1

 A equation with coefficients of x is 2 A second-degree polynomial equation in x A equation that has two variables None of those

2

5 is a rational number.

 TRUE. FALSE.

3

 The determinent of ${\displaystyle \left[{\begin{array}{c c}2&3\\4&2\end{array}}\right]}$ is .

4

 ${\displaystyle \displaystyle \ x_{1}=}$ 1 ${\displaystyle \displaystyle \ x_{2}=}$ 1 Next, we have Ux = y ${\displaystyle {\begin{bmatrix}2&-1\\0&4\end{bmatrix}}}$ X ${\displaystyle {\begin{bmatrix}x_{1}\\x_{2}\end{bmatrix}}}$ = ${\displaystyle {\begin{bmatrix}y_{1}\\y_{2}\end{bmatrix}}}$ So we can get: ${\displaystyle \displaystyle \ y_{1}=}$ ${\displaystyle \displaystyle \ y_{2}=}$

### Homework 7, Question 1

The topic interpolation and extrapolation in the wikiversity page introduces some important methods about polynomial interpolation including the Vandermonde Matrix, Lagrange Interpolation and Newton Interpolation. But I think this page is not very perfect because it doesn't talk about the interpolation error. So I added a section interpolation error to make this page more complete and gave the proof of the interpolation error.

### Homework 8, Question 1: Project topic

First of all, I will introduce the Adams–Bashforth methods and Adams–Moulton methods and some information about why we need to use these methods and the basic ideas of these two methods.

Do not duplicate anything already on w: Linear multistep method. What do you want to add? Mjmohio (talk) 16:38, 7 November 2012 (UTC)

Secondly, I am going to prove the two, three and four step Adams–Bashforth methods and prove the four step Adams–Moulton methods.

Prove what about them? Do you mean derive the coefficients or show their order? Deriving the coefficients would be useful; doing it four times may not be better than two or three times. Mjmohio (talk) 16:38, 7 November 2012 (UTC)

This could be useful since it seems to be missing on Wikipedia and Wikiversity. Mjmohio (talk) 16:38, 7 November 2012 (UTC)

## Final Porject

For Introduction to Numerical Analysis, Fall 2012.

### Introduction

My final project is about Adams-bashforth and Adams-moulton methods. The topic Adams-bashforth and Adams-moulton methods is a very important part in linear multistep methods. It is difficult to understand using only Wikipedia because it doesn't include the derive of the formula. To facilitate learning of this topic I give more details about Adams-bashforth and Adams-moulton methods.

### Contribution

I created this topic on the page http://en.wikiversity.org/wiki/Adams-bashforth_and_Adams-moulton_methods. which mainly contain derivation, exercise and predictor–corrector method. First I derived the two-step Adams-bashforth by using polynomial interpolation and the second order Adams-bashforth by using Taylor's theorem. Secondly, I provided two exercises about the derivation of three-step Adams-bashforth and second-order Adams-moulton including the solution. At last,I edited the predictor–corrector method by using Adams-bashforth and Adams-moulton methods as a pair.

### Future Work

I decided that although deriving the third-order Adams-moulton method and the third-order Adams-bashforth by using Taylor's theorem would be good, it was too much for this project. What's more deriving the third-order Adams-moulton method is not easy, so I just give the derivation of second-order Adams-moulton method that others can follow to work.

### Conclusions

In this project I give the derivations of Adams-bashforth and Adams-moulton methods by two methods. Also I provide some knowledge of predictor–corrector method which is not on the wikipedia. I believe this is a valuable contribution because the derivations of Adams-bashforth and Adams-moulton methods are not on the wikipedia. That is a good supplement of the topic Linear multistep method on wikipedia.