text:
User talk:Avashnirvana

 Hello Avashnirvana, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
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 * Explore Wikiversity with the links to your left.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
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You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --mikeu talk 12:08, 24 February 2011 (UTC)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: User talk:Avashnirvana


text:
User:Abdussalam~enwikiversity

Amoo Abdussalam was born to the family of Dr. Amoo S.A. and Mrs Amoo H.O. about twenty years ago. He attended Barachel Nursery and Primary School and Al-Ilmu Nursery and Primary for his elementary education. He went further to attend Al-Hikmah College, Ipaja; WAMY International Secondary School, Ojodu and Al-Azim College for his secondary school education. Presently, he studies English and Education in the Department of Arts and Social Sciences Education, University of Lagos, Nigeria. Abdussalam enjoys reading, writing and travelling. He could be reached via abdussalam_1428@yahoo.com or amoo.abdussalam@gmail.com

title: User:Abdussalam~enwikiversity


title: File:DFT.5.B.Sampling.pdf


text:
User:Egm6936.s11

EGM 6936 Seminar, Spring 2011 Prof. Loc Vu-Quoc

University of Florida I agree to multi-license all my contributions, including my user pages, as described below (MultiLicenseWithCC-BySA-Any):

Topics

Generalized Galerkin (G2) method

= Generalized Galerkin =

Summary Generalized Galerkin method by Hoffmann

Tutorial Generalized Galerkin tutorial work in C++

Tutorial FENiCs and Python tutorial

Writing tools

Other courses

title: User:Egm6936.s11


text:
Talk:Complex socio-ecological systems/Adaptive Management and Resilience

As a member of an adaptive management (AM) doctoral program here on campus, rereading some of these texts (whole reading others for the first time), I realize how difficult it is to envision adaptive management in large-scale systems, especially in situations where the governance (traditional, nontraditional, you name it) is anemic. Walters basically argues that the cases where AM projects have been successful have been when the strength of will of individuals was enough to carry a project through. Nelson et al. says that many of the resilience-related issues in science are “fundamentally about the governance of adaptation.” True, in both these papers the empirical ecological science serves as the backdrop, but since neither of these papers is an expansion of our discussion on nature-society dualisms (false or otherwise), and indeed Nelson and Walters are both biophysical scientists, it is notable that human agency is given so much credit for evaluating and affecting complex-adaptive systems. The nonhierarchical (or nested) structures of governance and power explicit in AM apparently still need a facilitator (or handmaiden?) to see them to some end, no matter the number of stakeholders involved in democratizing the management procedures and ensuring the transparency of the science. Nelson et al. cite the importance of opinion leaders and Walters the compleat emmanuensis. Arguments against, and critiques of, AM are manifold—these come from all disciplinary fronts, and in fact are more scathing than those of socio-ecological resilience more generally probably because AM’s management implications are more direct. I believe the logic that egalitarian governance structures and multiple hypotheses driven research, focusing on complex-adaptive systems, is what will solve most management crises like overfishing and deforestation is a difficult line of reasoning to negotiate. And implicitly so do a lot of AM researchers. Very meaty discussion to be had here and a good opportunity to connect to past weeks’ topics. ~Sam -


text:
User:Darklama/History and observations

Ethics
Summery based on current observations thus far:

 * JWSchmidt has said that false claims can be retracted from Wikiversity.
 * JWSchmidt has said that legal protections can be exercised when false claims are published.
 * JWSchmidt has said that Researchers have an ethical obligation to not make unsupported claims.
 * JWSchmidt has said that challenge and clarification [of claims] are a normal part of the research process.
 * JWSchmidt claims to gladly respond when asked to support his "observations".
 * JWSchmidt has said that a normal part of human discourage [is] for an author to provide evidence that is thought to be needed.
 * JWSchmidt has said that other people can always ask for more evidence.

"Do you mean that you don't feel obligated to provide evidence for your observations, until you are asked to do so?" <-- No. I mean that it is a normal part of human discourse for an author to provide the evidence that is thought to be needed. Other people can always ask for more evidence. --JWSchmidt 13:47, 14 July 2010 (UTC)

 * Do you believe that my summary is correct?
 * Do you expect other people to provide more evidence than what they think is needed?
 * -- dark lama  14:11, 14 July 2010 (UTC)

policy
"Do you have links for the Foundation mandate and the various forums and Wikiversity projects where the research guidelines was discussed?" <-- Two good starting points are History of Wikiversity and this page about development of research policy. One of the major discussions was an IRC meeting about research, held shortly after the deadline for completing the research policy. In many cases, people who were interested in research were directed to the ongoing development of the research policy from community forums like the Colloquium by way of the research portal and related pages about research. The sitenotice and the mailing list were also used to involve the community in the process of developing research policy. What does being listed or not at "Wikiversity:Probationary custodians" have to do with anything? <-- You could ask the same thing about "Wikiversity:Candidates for Custodianship". Both "Wikiversity:Probationary custodians" and "Wikiversity:Candidates for Custodianship" are linked to from Custodianship. --JWSchmidt 23:12, 5 August 2010 (UTC)

"seems to be contrary to your claim" <-- You can ask James to explain his email, but I don't see how his email is relevant. Not many people were interested in research and even fewer were interested in doing the work of creating research policy, particularly people with no research experience. "Can you provide a link to where the Foundation mandate was made and what was said that you took for a Foundation mandate?" <-- I already provided a links to the "mandate"; see above in this section. "..... guidelines should be developped, *in particular* with regards to collaborative research. We would hope that these guidelines are as much as possible developped on the beta site (in particular collaborative research), so that all languages share a common goal and a few common non negociable rules." If you want more information, I suggest that you contact Foundation staff. "Do you know if the 6 month review that the Special Projects Committee was suppose to do ever took place?" <-- That would be a good question for someone on the Foundation staff. --JWSchmidt 07:30, 6 August 2010 (UTC)

"Did you at any point ask Anthere if his comments were a Foundation mandate?" <-- No. I saw: [http://lists.wikimedia.org/pipermail/foundation-l/2006-August/022427.html During these 6 months, guidelines should be developped, *in particular* with regards to collaborative research. We would hope that these guidelines are as much as possible developped on the beta site (in particular collaborative research), so that all languages share a common goal and a few common non negociable rules], which was a clear mandate from the Wikimedia Foundation Board. "Anthere and other members of the Special Projects Committee suggested in the same email discussion that NPOV should be a fundamental part of research at Wikiversity." <-- Darklama, please quote what the members of the Special Projects Committee wrote about NPOV. "What conclusions lead you to believe that the Foundation mandated a collaborative research policy, but that NPOV was not part of the Foundation mandate for collaborative research?" <-- Darklama, do you have evidence that I held such a belief? "Why did you ignore James Hare's call to work on resources and let policies come later?" <-- What evidence do you have that I ignored his "call"? "How do you know that the proposals you put forward as policies satisfied any Foundation mandate if you unaware of any 6 month review?" <-- Darklama, do you have evidence that I knew that? I simply did the best I could to do what the Board asked be done. --JWSchmidt 14:50, 7 August 2010 (UTC)
 * "I", "I", "I", etc. I does not equal "community". Ottava Rima (talk) 15:00, 7 August 2010 (UTC)

 * "there are also no facts to back your claim" <-- This email is a "fact" and this statement: During these 6 months, guidelines should be developped, *in particular* with regards to collaborative research. We would hope that these guidelines are as much as possible developped on the beta site (in particular collaborative research), so that all languages share a common goal and a few common non negociable rules, was a clear mandate from the Wikimedia Foundation Board. "I believe to believe so is just as reasonable" <-- Darklama, I suggest that you contact Florence Nibart-Devouard and ask her if she agrees with you. "that suggests you ignored his call" <-- Only if you make a bad faith assumption. --JWSchmidt 21:11, 7 August 2010 (UTC)

"you made policy on your own without the community's consent or consensus" <-- Darklama, please provide your favorite example of where I made policy on my own without the community's consent or consensus and then we can discuss that example. "some conflicts could have been avoided" <-- Darklama, please indicate your favorite example of such a conflict so that we can discuss it. "I provided the evidence that suggests you did." <-- It is very easy to be mistaken about one's assumptions. As a scientist I have extensive training in the identification of mistaken assumptions about what evidence can tell us. "I think a lot of people would assume the reason is due to either a guilty conscience, or because you have something to bad to hide." <-- Those are bad faith assumptions. If you wanted to assume good faith you might ask, "Are you avoiding the question?" I'm not avoiding any question. You have been asking about my reaction to a post that was made in a discussion forum almost four years ago. I have no memory of having seen that discussion forum post in 2006. I asked you for evidence that I had ignored that 2006 discussion forum post with the hope that you might direct my attention to something I wrote in 2006 about that discussion forum post. I've looked back at the Wikiversity edit history and #wikiversity-en chat logs and I suspect that I had no idea who Mr. Hare was and I simply paid more attention to Cormaggio's repeated calls for developing research guidelines. Why don't you want to answer "why did you ignore James Hare's call to let policies come later"? <-- Darklama, you have no basis for assuming that I don't want to answer that question. "Do you want to avoid people understanding your motivations?" <-- Darklama, if you are curious about my motivations then try asking a question like, "What are your motivations?" "Do you want people to avoid examining the reasons for turning proposals into policy?" <-- No. "Do you want people to speculate?" <-- Speculate about what? "Do you want people to make assumptions about you?" <-- Making assumptions about people is a normal part of human interactions. I don't wast time wanting it. "Do you care if people make assumptions?" <-- Making assumptions about people is a normal part of human interactions. I accept it as a fact that people make assumptions and I don't devote mental effort to caring about it, any more than I care that grass is green. "Do you care if people act on assumptions?" <-- I sometimes have to deal with the consequences from when people act on unwarranted assumptions. "Do you not remember your motivations?" <-- For many trivial matters, like a discussion forum post from someone I did not know four years ago, a discussion forum post that I might have read and almost instantly forgotten, for such a thing I am not likely to remember any specific motivation related to it. "Do you not remember your reasons for turning proposals into policy?" <-- What policy? "Are you unable to explain why proposals you turned into policy should be followed?" <-- No. --JWSchmidt 19:51, 9 August 2010 (UTC)

 * "You don't know that Anthere's comments were a Foundation mandate is a reasonable conclusion from your answer." <-- The email from Anthere did not fall from the sky. There were months of discussions leading up to that email and following the email. "Please identify and explain any mistaken assumptions you think I've made." <-- The main mistake you are making is assuming that you can understand the meaning of Anthere's email without knowing the historical context of that email. If you don't trust me to correctly frame the context of the email for you then you can ask other people. I've already suggested that you contact Mr. Hare, Florence Nibart-Devouard and another obvious source of information is User:Cormaggio who worked with Florence on the Special Projects Committee. This is a perfect example of where public IRC chat logs would be useful. I have chat logs of meetings held in #wikimedia-spcomm where the need for Wikiversity research policy was discussed and chat about research guideline development from #wikiversity-en. Misguided belief that such chat is "private correspondence" cripples the ability of the Wikiversity community to be informed. "You could of said that before when I asked why you ignored Mr Hare's email." <-- I only today had the time to search for and read those old chat logs. During the first week of Wikiversity there was daily IRC chat about research as well as development of wiki pages about research. There were also many other on-going concerns that had to be dealt with and nobody could give adequate time and thought and on-wiki discussion to everything. People did the best that they could do under difficult conditions, often sacrificing their real-world commitments in order to devote time to getting Wikiversity established. "Do you agree that Wikiversity participants have a duty to ensure that pages marked as policy accurately represent what the Wikiversity community wants?" <-- Darklama, I am very skeptical about the idea that anyone can ever "ensure that pages marked as policy accurately represent what the Wikiversity community wants". Most Wikiversity community members never read policies. Policies are mainly guidance for a few people who would otherwise disrupt Wikiversity if policies did not exist. Policies are mainly tools for helping keep people on track towards the Wikiversity Mission. The important thing is that a policy supports the Wikiversity Mission and helps prevent misguided people from disrupting the Wikiversity community. Wikiversity participants have a duty to make sure that policies keep people on track towards the Wikiversity Mission. --JWSchmidt 23:12, 9 August 2010 (UTC)

"you appear to be suggesting that Wikiversity policies shouldn't be questioned" <-- Policies exist as wiki pages with an edit button and a talk page. It would be absurd for anyone to suggest that policies should not be questioned. "you seem to be suggesting that only someone with historical knowledge of the context in which things happened is able to make an informed decision on whether policies like the research policy is still good for Wikiversity today" <-- Darklama, I can't imagine how it would seem to anyone that I suggested that. "one could say that the decisions for what is or is not mandatory were made in secret off-wiki discussions" <-- Darklama, what are you referring to as being "what is or is not mandatory"? "Haven't you been a strong advocate that decisions shouldn't be made off-wiki?" <-- Many decisions are made off-wiki. Wiki participants make most of their decisions about wiki participation off-wiki. Problems with off-wiki decisions can arise when decisions are purposefully made off-wiki because the people making the decisions know that what they want to do will disrupt a wiki community and would be contested were those decisions made by way of on-wiki community discussion. Such disruptive off-wiki decisions are what I object to. "Did your attitude change since than, or do you not remember?" <-- What does "since than" mean? "Please explain why you believe the block and rollback tools should continue to only be used for obvious vandalism" <-- The rollback tool was created as a tool for dealing with vandalism. If you want to revert something other than obvious vandalism then a reason should be provided. In the case of blocks, Wikiversity policy authorizes blocks in only a few situations, particularly: "Most frequently, blocking occurs in response to obvious and repeated vandalism." There are a few other uses for the block tool that are prescribed in policy, but for anything other than obvious vandalism there should be warnings and discussion and consensus before the block. --JWSchmidt 02:21, 10 August 2010 (UTC)

 * "I am referring to the Foundation mandate that you wrote was discussed off-wiki and you wrote is needed to understand the context of Anthere's email" <-- Darklama, I have described Anthere's statement, "..... guidelines should be developped, *in particular* with regards to collaborative research. We would hope that these guidelines are as much as possible developped on the beta site (in particular collaborative research), so that all languages share a common goal and a few common non negociable rules", as constituting instructions and a mandate. I would not say that research guidelines were mandatory. I do believe that in order to support research projects at Wikiversity it is useful to have research guidelines. "One could say the off-wiki discussion of the Foundation mandate was purposely decided off-wiki in secret because people knew what they wanted to do would disrupt the natural development of the Wikiversity wiki and would be contested had that discussion been made by way of on-wiki community discussion. So why didn't you object to such a off-wiki decision?" <-- Darklama, what was "purposely decided off-wiki in secret"? What I mean is "Did your attitude about decisions being made off-wiki change since the off-wiki decision that you wrote took place and that you wrote provides the context for the Foundation mandate?" <-- Darklama, I'm lost. What is "the off-wiki decision that you wrote"? "I asked you to explain why rollback and blocks should continue to only be used for obvious vandalism." <-- Darklama, I wrote, "If you want to revert something other than obvious vandalism then a reason should be provided." If you use rollback on something that is not obvious vandalism, then people are easily confused about the reason for the reversion. To avoid such confusion, rollback should only be used for its intended purpose, reverting obvious vandalism. Darklama, I never suggested that the block tool only be used to deal with obvious vandalism. Wikiversity policy explains how the block tool should be used. As I said before (above on this page), Wikiversity policy authorizes blocks in only a few situations, particularly: "Most frequently, blocking occurs in response to obvious and repeated vandalism." There are a few other uses for the block tool that are prescribed in policy, but for anything other than obvious vandalism there should be warnings and discussion and consensus before the block. The Wikiversity community long ago established consensus for imposing blocks on vandals without the need for discussion. "How is the current pages that discuss rollback and blocks important" <-- Darklama, please specify which pages you are referring to. "Quoting pages doesn't explain your reasons for believing rollback and block tools should continue to be only used for obvious vandalism." <-- I believe that the rollback tool should only be used on obvious vandalism because that was the intended purpose of the tool and when the rollback tool is used on other edits it creates confusion about why edits have been reverted. It is best to avoid that confusion and provide an edit summary that explains a reversion if the reverted edit is not obvious vandalism. In the case of using the block tool, I don't know why anyone would believe that the block tool should only be used for obvious vandalism. --JWSchmidt 16:20, 10 August 2010 (UTC)

In this case, Wikiversity participants were given a mandate (given an authoritative and official command or instruction) by the Board to develop research guidelines. "Mandatory means required" I don't view the development of research guidelines as mandatory or required. You can be instructed to do something without being required to do it. Had there been no effort to develop research guidelines, Wikiversity might have been restricted from having research projects. "what was purposely decided off-wiki in secret" <-- You should ask people who served on the Special Projects Committee how they did their work. I believe that they held public meetings. As I recall, the times for those meeting were not good for me, but sometimes I did go the the committee's IRC chat channel and log the meetings. I doubt if any decisions made by the Special Projects Committee were made in secret. I imagine that the Special Projects Committee evaluated the Wikiversity project proposal, voted to recommend that the Wikiversity project be started, issued resolution 2006-39A (calling for the development of guidelines for research), Anthere then reported to the Board on the committee's resolution, the Board then authorized Anthere to send an email to foundation-l email discussion forum as formal notification that the Board had accepted the committee's recommendations and wanted development of guidelines for research. You would have to ask Anthere if the Board's decision to launch Wikiversity was made in secret or if it was made at a public meeting of the Board. "Over the past 2 years comments by you suggest that you believe that the block tool should only be used for obvious vandalism." <-- I don't recall there ever being a very good reason for imposing a block of a Wikiversity community member. If there is some other way to deal with a problem, then a block should not be imposed. Many vandals have been blocked, so I tend to emphasize the use of blocks for vandals. I accept the existence of Wikiversity policy which prescribes blocks for a few other purposes in addition to vandalism. Even in the case of the block of User:Centaur of attention, I argued against imposing a block, preferring to let him have his say. I don't think blocks should be used to end a discussion or a debate. For blocks other than obvious vandalism there should be warnings, discussion and community consensus for the block before a block is imposed. --JWSchmidt 00:38, 11 August 2010 (UTC)

 * "Did you ask anyone at the time that the "Foundation mandate" was announced or during the discussions on the research guideline that happened before and after Anthere's email, whether Wikiversity might be restricted from having research projects if no effort was made to develop a research guideline right away?" <-- Darklama, what do you mean by "right away"? a public meeting is still "secret" because the meeting wasn't held on-wiki <-- I would not call a public meeting, such as those held by the Special Projects Committee, "secret". Nor would I call this meeting secret. Darklama, is there some other type of public meeting that you think was "secret"? "Please explain why you believe that community consensus should be required before imposing a block for reasons other than obvious vandalism." <-- Wikiversity policy says, "A Wikiversity custodian is an experienced and trusted user who can protect, delete and restore pages as well as block users from editing as prescribed by policy and community consensus." I believe that policy means that a block can be imposed if a Wikiversity policy prescribes blocking in response to a certain action and the Wikiversity community decides by consensus that a block should be imposed. Many examples from other wiki websites and from the past two years of Wikiversity show that individual sysops cannot be trusted to make wise decisions about when to use the block tool. In order to protect the Wikiversity community from the disruptive actions of rogue sysops it should be the Wikiversity community that decides on blocks. "I think requiring Custodians to discuss before blocking would prevent Custodians from preventing Wikiversity from being disrupted." <-- Darklama, please provide a specific example of a block, imposed for something other than vandalism, that prevented Wikiversity from being disrupted. "Please explain why you believe proposing a policy to obtain community consensus for additional reasons to block is unacceptable to you." <-- Can you indicate a specific example? In general, I believe that the existing policy is best because the Wikiversity community needs to be protected from sysops who vastly damage Wikiversity through their misuse the block tool. As you know, since a few rogue sysops ignore existing policy, I favor strengthening the protections against misuse of the block tool by making the consensus version of the proposed blocking policy an official Wikiversity policy. --JWSchmidt 05:04, 11 August 2010 (UTC)

title: User:Darklama/History and observations


text: File:Plan van aanpak EE4 TEam5.pdf

title: File:Plan van aanpak EE4 TEam5.pdf


text: File:Samenwerkingscontract+DEF Team 5.pdf


text:
Mandarin/Mandarin One/Lesson Two 第二课

Numbers 1-10

 * 1: yī 一 (1):

 * èr 二 (2):

 * sān 三 (3):

 * sì 四 (4):

 * wǔ 五 (5):

 * liù 六 (6):

 * qī 七 (7):

 * bā 八 (8):

 * jiǔ 九 (9):

 * shí 十 (10):

title: Mandarin/Mandarin One/Lesson Two 第二课


text: File:Cocktailnapkin design.jpg

title: File:Cocktailnapkin design.jpg


title: File:Vergadering1.pdf


title: File:Vergadering2.pdf


title: File:Vergadering3.pdf


text:
Talk:Ethics/Nonkilling/Public Health

Interesting idea - however the medical curriculum adresses most of these issues under "Preventive Medicine and Public Health". I am not sure if there is any advantage in reinventing the wheel; also "Preventive Medicine and Public Health" would better inform readers - would suggest having 'nonkilling PH" as a subsection of "Preventive Medicine"Andra Rei 20:27, 24 February 2011 (UTC)

title: Talk:Ethics/Nonkilling/Public Health


text:
Epidemiology and Biostatistics

Welcome to the Wikiversity Department of Epidemiology and Biostatistics, part of the Basic sciences Division of the School of Medicine.

The Department of Epidemiology and Biostatistics is a content development project for Wikiversity. Participants collaborate to develop learning resources for physiology.

Students
Take a look at the Epidemiology Wikibook. If you have questions or want to suggest additional areas of study, add your ideas below:

Learning projects
See: Learning Projects and the Learning model.

Learning materials and learning projects are located in the main Wikiversity namespace. Simply make a link to the name of the learning project (learning projects are independent pages in the main namespace) and start writing! We suggest the use of the learning project template, by doing on the new page.

Learning materials and learning projects can be used by multiple departments. Cooperate with other departments that use the same learning resource.
 * Preventive Medicine and Public Health
 * Evidence-Based Medicine

Remember, Wikiversity has adopted the "learning by doing" model for education. Lessons should center on learning activities for Wikiversity participants. We learn by doing.

Department news

 * February 24 2011 - Department founded!

Active participants
Active participants in this Learning Group

The histories of Wikiversity pages indicate who the active participants are. If you are an active participant in this department, you can list your name here (this can help small departments grow and the participants communicate better; for large departments a list of active participants is not needed).
 * Adrian Preda, M.D., HS Associate Professor of Psychiatry and Human Behavior, UC Irvine School of Medicine Andra Rei 20:45, 24 February 2011 (UTC)

title: Epidemiology and Biostatistics


text:
User talk:Bookworm5.99

 Hello Bookworm5.99, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.
 * Explore Wikiversity with the links to your left.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.
 * Follow Wikiversity on twitter (http://twitter.com/Wikiversity) and identi.ca (http://identi.ca/group/wikiversity).

You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! Jtneill - Talk - c 20:50, 24 February 2011 (UTC)

 Woof! My name is Jack Russell. I am a dog and a Wikiversity mascot. I am pretty new around Wikiversity. Perhaps we can learn together! Tail wag...

First course
I'd suggest a more descriptive title for this page - you can move this page to a more specific title name via the pull-down menu next to the favourite (*) button. -- Jtneill - Talk - c 20:50, 24 February 2011 (UTC)

title: User talk:Bookworm5.99


text:
Preventive Medicine and Public Health

Welcome to the Wikiversity Department of Epidemiology and Biostatistics, part of the Basic Sciences Division of the School of Medicine.

The Department of Epidemiology and Biostatistics is a content development project for Wikiversity. Participants collaborate to develop learning resources for physiology.

Students
Take a look at the Epidemiology Wikibook. If you have questions or want to suggest additional areas of study, add your ideas below:

Learning projects
See: Learning Projects and the Learning model.

Learning materials and learning projects are located in the main Wikiversity namespace. Simply make a link to the name of the learning project (learning projects are independent pages in the main namespace) and start writing! We suggest the use of the learning project template, by doing on the new page.

Learning materials and learning projects can be used by multiple departments. Cooperate with other departments that use the same learning resource.
 * Epidemiology and Biostatistics
 * Evidence-Based Medicine

Remember, Wikiversity has adopted the "learning by doing" model for education. Lessons should center on learning activities for Wikiversity participants. We learn by doing.

Department news

 * February 24 2011 - Department founded!

Active participants
Active participants in this Learning Group

The histories of Wikiversity pages indicate who the active participants are. If you are an active participant in this department, you can list your name here (this can help small departments grow and the participants communicate better; for large departments a list of active participants is not needed).
 * Adrian Preda, M.D., Professor of Clinical Psychiatry and Human Behavior, UC Irvine School of Medicine Andra Rei 20:45, 24 February 2011 (UTC)

title: Preventive Medicine and Public Health


text:
User:Egm6341.s11.team4.BM/HW4

=Using Simple Simpson's Rule to Integrate a 3rd Order Polynomial Exactly=

Problem Given on Lecture Slide 18-2

Given
Given an arbitrary 3rd degree polynomial
 * $$ \displaystyle f(x)=P_{3}(x)=c_{0}+c_{1}x^{1}+c_{2}x^{2}+c_{3}x^{3} $$

which can be expressed in sigma notation as
 * $$\displaystyle \sum_{i=0}^{3} c_{i}x^{i} $$

examine the interval
 * $$ \displaystyle [a,b]=[-2,1] $$

With the following coefficients
 * $$\displaystyle c_{0}=1, c_{1}=3, c_{2}=-9, c_{3}=12 $$

Objective
1. Evaluate the integral using simple Simpson's Rule

2. Evaluate the integral exactly

3. Compare the integral calculations to show that simple Simpson's rule exactly integrated the 3rd degree polynomial.

Solution
First, we will evaluate the integral exactly. Since this is a simple polynomial, the integral evaluation can be performed analytically with ease.

 * $$ I(f)=\displaystyle \int_{a}^{b} 12x^{3}-9x^{2}+3x+1 dx $$
 * $$ I(f)=[3x^{4}-3x^{3}+\frac{3}{2}x^{2}+x]_{a}^{b} $$
 * $$ I(f)=[3(1)^{4}-3(1)^{3}+\frac{3}{2}(1)^{2}+(1)]-[3(-2)^{4}-3(-2)^{3}+\frac{3}{2}(-2)^{2}+(-2)] $$
 * $$ I(f)=[3-3+\frac{3}{2}+1]-[48+24+\frac{3}{2}4-2] $$
 * $$ I(f)=\displaystyle [2.5]-[76] $$
 * $$ I(f)= \displaystyle -73.5 $$

So, if simple Simpson's rule exactly integrates a 3rd degree polynomial as expected we expect that it will produce a value of -73.5 through quadrature.

Simple Simpson's is expressed below

 * $$ I_{n}(f)=\frac{b-a}{6}[f(a)+4f(\frac{a+b}{2})+f(b)] $$

Substituting in for a and b, we get
 * $$ I_{n}(f)=\frac{1+2}{6}[f(-2)+4f(\frac{-2+1}{2})+f(1)] $$

Evaluating our function at the given points, we have
 * $$ I_{n}(f)=\frac{1}{2}[-137+4(-4.25)+7] $$
 * $$ I_{n}(f)=\frac{1}{2}[-137-17+7] $$
 * $$ I_{n}(f)=\frac{-147}{2} $$

Now we have a final answer through quadrature, comparing it to our exact integral, we see
 * $$ I_{n}(f)=I(f)=\frac{-147}{2}=-73.5 $$

Thus simple Simpson's rule, though it approximates the function as a simple 2nd order parabola, can exactly integrate a polynomial of degree 3. Though the quadrature rule does not exactly approximate the function it exactly integrates the function through cancellation of areas. This principle is shown in the graph below.

Simpson's rule underestimates the area under the curve initially and then overestimates the curve. These errors in the approximation exactly cancel each other out for a 3rd order polynomial and the simple Simpson's rule exactly integrates the function.

Given

 * $$ e^{(1)}(t)= [F(-t)+F(t)]-\frac{1}{3}[F(-t)+4F(0)+F(t)]-\frac{t}{3}[-F^{(1)}(-t)+F^{(1)}(t)] $$

Objective
Show that
 * $$ e^{(3)}(t)=-\frac{t}{3}[-F^{(3)}(-t)+F^{(3)}(t)] $$

Solution
Starting with our given equation for $$ e^{(1)} $$ which was given in class on lecture slide 20-2 and is proven in homework problem 4.2.

 * $$ e^{(1)}(t)= [F(-t)+F(t)]-\frac{1}{3}[F(-t)+4F(0)+F(t)]-\frac{t}{3}[-F^{(1)}(-t)+F^{(1)}(t)] $$

We take the derivative with respect to t and obtain.

 * $$ e^{(2)}(t)=[-F^{(1)}(-t)+F^{(1)}(t)]   -     \frac{1}{3}[-F^{(1)}(-t)+F^{(1)}(t)]    -    \frac{1}{3}[-F^{(1)}(-t)+F^{(1)}(t)] -\frac{t}{3}[F^{(2)}(-t)+F^{(2)}(t)]] $$

This function can be simplified to

 * $$ e^{(2)}(t)=\frac{1}{3}[-F^{(1)}(-t)+F^{(1)}(t)] - \frac{t}{3}[F^{(2)}(-t)+F^{(2)}(t)] $$

Now, if we take the derivative again, we obtain

 * $$ e^{(3)}(t)=\frac{1}{3}[F^{(2)}(-t)+F^{(2)}(t)] -\frac{1}{3}[F^{(2)}(-t)+F^{(2)}(t)] -\frac{t}{3}[-F^{(3)}(-t)+F^{(3)}(t)] $$

Simplifying again, we obtain

 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * style="width:92%; padding:10px; border:2px solid #8888aa" |

e^{(3)}(t)= -\frac{t}{3}[-F^{(3)}(-t)+F^{(3)}(t)]

$$
 *
 * }

Which is the desired equation.

title: User:Egm6341.s11.team4.BM/HW4


text:
Human Behavior

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title: Human Behavior


title: File:Egm6341.s11.team4.bm.1.jpg


text: File:Layered Channel Flow2.png

title: File:Layered Channel Flow2.png


text:
User:Egm6341.s11.team4/HW4

Homework 4

=Problem 4.1 Using Simple Simpson's Rule to Integrate the 3rd Order Polynomial Exactly=

Problem Given on Lecture Slide 18-2

Given
Given an arbitrary 3rd degree polynomial
 * $$ \displaystyle f(x)=P_{3}(x)=c_{0}+c_{1}x^{1}+c_{2}x^{2}+c_{3}x^{3} $$

which can be expressed in sigma notation as
 * $$\displaystyle \sum_{i=0}^{3} c_{i}x^{i} $$

examine the interval
 * $$ \displaystyle [a,b]=[-2,1] $$

With the following coefficients
 * $$\displaystyle c_{0}=1, c_{1}=3, c_{2}=-9, c_{3}=12 $$

Objective
1. Evaluate the integral using simple Simpson's Rule

2. Evaluate the integral exactly

3. Compare the two integral calculations to show that simple Simpson's rule exactly integrates the 3rd order polynomial.

Exact Integral
First, we will evaluate the integral exactly. Since this is a simple polynomial, the integral evaluation can be performed analytically with ease.

 * $$ I(f)=\displaystyle \int_{a}^{b} f(x) dx $$

Substituting in our function

 * $$ I(f)=\displaystyle \int_{a}^{b} 12x^{3}-9x^{2}+3x+1 dx $$

Performing the integration

 * $$ I(f)=[3x^{4}-3x^{3}+\frac{3}{2}x^{2}+x]_{a}^{b} $$

 * $$ \begin{align} I(f)&=[3(1)^{4}-3(1)^{3}+\frac{3}{2}(1)^{2}+(1)] \\

& {} \qquad {}  -[3(-2)^{4}-3(-2)^{3}+\frac{3}{2}(-2)^{2}+(-2)] \end{align} $$

 * $$ I(f)=[3-3+\frac{3}{2}+1]-[48+24+\frac{3}{2}4-2] $$

 * $$ I(f)=\displaystyle [2.5]-[76] $$

 * $$ I(f)= \displaystyle -73.5 $$

So, if simple Simpson's rule exactly integrates a 3rd degree polynomial as expected we expect that it will produce a value of -73.5 through quadrature.

Simple Simpson's Rule Quadrature
Simple Simpson's is expressed below

 * $$ I_{n}(f)=\frac{b-a}{6}[f(a)+4f(\frac{a+b}{2})+f(b)] $$

Substituting in for a and b, we get

 * $$ I_{n}(f)=\frac{1+2}{6}[f(-2)+4f(\frac{-2+1}{2})+f(1)] $$

Evaluating our function at the given points, we have

 * $$ I_{n}(f)=\frac{1}{2}[-137+4(-4.25)+7] $$

 * $$ I_{n}(f)=\frac{1}{2}[-137-17+7] $$

 * $$ I_{n}(f)=\frac{-147}{2} $$

Now we have a final answer through quadrature, comparing it to our exact integral, we see

 * $$ I_{n}(f)=I(f)=\frac{-147}{2}=-73.5 $$

Thus simple Simpson's rule, though it approximates the function as a simple 2nd order parabola, can exactly integrate a polynomial of degree 3.

Error Cancellation
Though the quadrature rule does not exactly approximate the function it exactly integrates the function through cancellation of areas. This principle is shown in the graph below.

Simpson's rule underestimates the area under the curve initially and then overestimates the area. These errors in the approximation exactly cancel each other out for a 3rd order polynomial and the simple Simpson's rule exactly integrates the function.

This problem was solved by Brendan Mahon

Given
Given that:
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

A(t)=\int\limits_{-t}^{+t}{F(x)dx=}\int\limits_{-t}^{k}{F(x)dx+}\int\limits_{k}^{+t}{F(x)dx}

$$ Prove:
 *
 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

{{A}^{(1)}}(t)=F(-t)+F(t)

$$
 *
 * }

Answer:
Take a derivative on this equation,
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

A(t)=\int\limits_{-t}^{+t}{F(x)dx=}\int\limits_{-t}^{k}{F(x)dx+}\int\limits_{k}^{+t}{F(x)dx}

$$ We assume that $$\displaystyle \begin{align} & G(t)=\int{F(t)dt},\frac{dG(t)}{dt}=F(t) \\ & \\ \end{align}$$
 *
 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\int\limits_{-t}^{k}{F(x)dx}=G(k)-G(-t)

$$
 *
 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\int\limits_{k}^{+t}{F(x)dx}=G(t)-G(k)

$$ Where k is constant value,
 *
 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\begin{align} & \frac{dA(t)}{dt}=\frac{d\left( G(k)-G(-t) \right)}{dt}+\frac{d\left( G(t)-G(k) \right)}{dt} \\ & =-\frac{d\left( G(-t) \right)}{dt}\frac{d\left( -t \right)}{dt}+\frac{d\left( G(t) \right)}{dt}=F(-t)+F(t) \\ \end{align}

$$ So,
 *
 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * style="width:92%; padding:10px; border:2px solid #8888aa" |

{{A}^{(1)}}(t)=F(-t)+F(t)

$$
 *
 * }

=Problem 4.3 Show that the second derivative of G(0) equals to zero=

Given
To prove Simple Simpson Error Theorem. Let, where,

Objectives
Show that

Solution
From given equation, the first derivative of e(t) is below.

Differentiate once more from eq(3.1) we get eq(3.2).

Substitute 0 into the eq(3.2), we get eq(3.3).

From the given equation about G(t). Calculate the first derivatives.

Calculate the first derivatives from eq(3.4).

Substitute 0 into the eq(3.5).

Given

 * $$ \begin{align} e^{(1)}(t)&= [F(-t)+F(t)]-\frac{1}{3}[F(-t)+4F(0)+F(t)] \\

& {} \qquad {}                     -\frac{t}{3}[-F^{(1)}(-t)+F^{(1)}(t)]    \end{align} $$

Objective
Show that
 * $$ e^{(3)}(t)=-\frac{t}{3}[-F^{(3)}(-t)+F^{(3)}(t)] $$

First Derivative
Starting with our given equation for $$ e^{(1)} $$ which was given in class on lecture slide 20-2 and is proven in homework problem 4.2.

 * $$ \begin{align} e^{(1)}(t)&= [F(-t)+F(t)]-\frac{1}{3}[F(-t)+4F(0)+F(t)] \\

& {} \qquad {} -\frac{t}{3}[-F^{(1)}(-t)+F^{(1)}(t)] \end{align} $$

Second Derivative
We take the derivative with respect to t and obtain.

 * $$ \begin{align} e^{(2)}(t) &=[-F^{(1)}(-t)+F^{(1)}(t)]-\frac{1}{3}[-F^{(1)}(-t)+F^{(1)}(t)]\\

& {} \qquad {} -\frac{1}{3}[-F^{(1)}(-t)+F^{(1)}(t)] -\frac{t}{3}[F^{(2)}(-t)+F^{(2)}(t)] \end{align} $$

This function can be simplified to

 * $$ \begin{align} e^{(2)}(t) &= \frac{1}{3}[-F^{(1)}(-t)+F^{(1)}(t)] -\frac{t}{3}[F^{(2)}(-t)+F^{(2)}(t)] \end{align}$$

Third Derivative
Now, if we take the derivative again, we obtain

 * $$ \begin{align} e^{(3)}(t) &=\frac{1}{3}[F^{(2)}(-t)+F^{(2)}(t)] -\frac{1}{3}[F^{(2)}(-t)+F^{(2)}(t)] \\

& {} \qquad {} -\frac{t}{3}[-F^{(3)}(-t)+F^{(3)}(t)] \end{align} $$

Simplifying again, we obtain

 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * style="width:92%; padding:10px; border:2px solid #8888aa" |

e^{(3)}(t)= -\frac{t}{3}[-F^{(3)}(-t)+F^{(3)}(t)]

$$
 * }
 * }

Which is the desired equation.

This problem was solved by Brendan Mahon

Given
From the equation of SSET.

Objectives
Find the relationship between $$ \zeta $$ and $$ \xi $$.

Solution
In the proof of SSET, we used transformation of variable.

Let

Substitute 1,-1 into the eq(2.2), we get eq(5.3) and eq(5.4).

From eq(5.3) and eq(5.4), we can get eq(5.5) and eq(5.6).

From addition of eq(5.5) and eq(5.6), we get eq(5.7)

From subtraction of eq(5.5) and eq(5.6), we get eq(5.8)

Substitute eq(5.7) and eq(5.8) into eq(5.2), we get eq(5.9).

Given
Refer to lecture notes [[media:nm1.s11.mtg21.djvu|21-1]] for more details.

Objective
1. Use roots of Legendre Polynomial to the accuracy of $$10^{-6}$$. Plot $$f _n^L(x)$$ and $$f(x)$$.

2. Use roots of Chebyshev Polynomial, to the accuracy of $$10^{-6}$$ by Newton-cotes methods. Plot $$f _n^L(x)$$ and $$f(x)$$.

3. Comparison of Lagrangian Interpolation using three different types of nodes.

Using nodes of Legendre Polynomial

Using nodes of Chebyshev Polynomial

Since there the difference in above figure is not much clear, we plot above picture using $$n=6$$ again.

Comment
From above results, we see that:

Among three different types of interpolation nodes, using roots of Chebyshev Polynomial is much accurate and can best fix Runge phenomenon, although using roots of Legendre Polynomial can also settle it.

In this problem, Runge phenomenon happens only when we use odd number of nodes to do Lagrangian interpolation.

Reference
1.	Lagrange_polynomial 2.	Legendre_polynomials 3.     Chebyshev_polynomials 4.     Gauss-Legendre_quadrature

=Problem 4.7: Composite Simpson Rule Error Boundary=

Refer to lecture slide [[media:Nm1.s11.mtg22.djvu|22-2]] for problem assignment.

Objective
Prove that the error when using the composite Simpson rule to approximate the integral of a function, $$\displaystyle f$$, from a to b is bound by

where

Solution
From equation [[media:Nm1.s11.mtg7.djvu|(4)p.7-4]]

Breaking (7.2) into discrete intervals yields

Now applying the simple Simpon's error theorem presented on lecture slide [[media:Nm1.s11.mtg18.djvu|18-2]] to each interval:

Next, define $$\displaystyle \overline{M_4}$$

(7.7) becomes

Since

Substituting (7.11) into (7.9)

 * {| style="width:95%" border="0" align="center"

$$\displaystyle $$ $$
 * style="width:35%" |
 * style="width:20%; padding:10px; border:2px solid #8888aa" |
 * style="width:20%; padding:10px; border:2px solid #8888aa" |
 * E_n^S| \leq \frac{(b-a)h^4}{180}M_4 = \frac{(b-a)^5}{180n^4}M_4
 * $$\displaystyle
 * style= |
 * }
 * }

Note: This solution differs from the problem statement but is confirmed by Atkinson pp.257&258

Solved by William Kurth.

=Problem 4.8: Taylor, Trapezoidal and Simpson's Error Estimate Comparisons=

Refer to lecture slide [[media:nm1.s11.mtg22.djvu|22-2]] for the problem statement.

Given

 * {| style="width:70%" border="0" align="center"

(8.1)
 * $$\displaystyle I:=\int_{a}^{b}\underbrace{\frac{e^x-1}{x}}_{f(x)}dx$$
 *
 * }
 * }

For the Taylor Series Expansion, the max error in the integral is limited by the following from lecture [[media:nm1.s11.mtg7.djvu|7-2]]

 * {| style="width:70%" border="0" align="center"

(8.2)
 * $$\displaystyle E_n \le \frac{e}{(n+1)!(n+1)}$$
 *
 * }
 * }

For the composite Trapezoidal rule, the max error is limited by the following from lecture [[media:nm1.s11.mtg22.djvu|22-1]]

 * {| style="width:70%" border="0" align="center"

(8.3)
 * $$\displaystyle \vert E_n \vert \le \frac{(b-a)h^2}{12}M_2$$
 *
 * }
 * }

For the composite Simpson's rule, the max error is limited by the following from lecture [[media:nm1.s11.mtg22.djvu|22-2]]

 * {| style="width:70%" border="0" align="center"

(8.4)
 * $$\displaystyle \vert E_n \vert \le \frac{(b-a)h^4}{2880}M_4$$
 *
 * }
 * }

Where

 * {| style="width:70%" border="0" align="center"

 * $$\displaystyle a = -1$$

 * }
 * }

 * {| style="width:70%" border="0" align="center"

 * $$\displaystyle b = 1$$

 * }
 * }

and,

 * {| style="width:70%" border="0" align="center"

 * $$\displaystyle h = \frac{(b-a)}{n}$$

 * }
 * }

Objective
1.a.) Find n such that En = O(10^-6) and compare to numerical results in HW2.4 using Taylor Series error.

1.b.) Find n such that En = O(10^-6) and compare to numerical results in HW2.4 using Composite Trapezoidal rule error.

1.c.) Find n such that En = O(10^-6) and compare to numerical results in HW2.4 using Composite Simpson's rule error.

2.a.) Numerically find the power of h in the Composite Trapezoidal rule error.

2.b.) Numerically find the power of h in the Composite Simpson's rule error.

Solution
Using Wolfram Alpha we find that the exact value of the integral to 12 significant digits is:

I = 2.11450175075

1.a.) Taylor Series Error Comparison
From equation (8.1) we can easily show that when n = 7 the error will be less than or equal to 8.4272 x 10^-6.

To compare the predicted value of the integral with the actual value of the integral we will use the following:

I = 2.11450175075

And from HW2.4:

 * {| style="width:70%" border="0" align="center"

(8.5)
 * $$\displaystyle I_7 = \left[\sum_{i=1}^{7}\frac{x^{i}}{i!i}\right]_{x=-1}^{x=1} = 2.11450113379$$
 *
 * }
 * }

Now,

 * {| style="width:70%" border="0" align="center"

 * $$\displaystyle E_{7} = |I - I_{7}| = |2.11450175075 - 2.11450113379| = 6.1696 \times 10^{-7}$$

 * }
 * }

In this case the actual error is approximately one order of magnitude less than the maximum possible error.

1.b.) Composite Trapezoidal Rule Error Comparison
From equation (8.3) with

 * {| style="width:70%" border="0" align="center"

 * $$\displaystyle M_2 = max |f^{(2)}(x)| = e - 2 \approx 0.718281828459$$

 * }
 * }

We get

 * {| style="width:70%" border="0" align="center"

 * $$\displaystyle En \le 7.3067 \times 10^{-6} \quad at \quad n = 256$$

 * }
 * }

From equation (1) on lecture slide [[media:nm1.s11.mtg7.djvu|7-4]] we get:

 * {| style="width:70%" border="0" align="center"

(8.6)
 * $$\displaystyle I_{256} = h \left[\frac{1}{2}f_0 + f_1 + \cdots + f_{n-1} + \frac{1}{2}f_n\right] = 2.11450549301$$
 *
 * }
 * }

This compares well with

 * {| style="width:70%" border="0" align="center"

(8.7)
 * $$\displaystyle E_{256} = |I - I_{256}| = |2.11450175075 - 2.11450549301| = 3.7423 \times 10^{-6}$$
 *
 * }
 * }

1.c.) Composite Simpson's Rule Error Comparison
From equation (8.4) with

 * {| style="width:70%" border="0" align="center"

 * $$\displaystyle M_4 = max |f^{(4)}(x)| = 9e - 24 \approx 0.464536456131$$

 * }
 * }

We get

 * {| style="width:70%" border="0" align="center"

 * $$\displaystyle En \le 1.2601 \times 10^{-6} \quad at \quad n = 8$$

 * }
 * }

From equation (4) on lecture slide [[media:nm1.s11.mtg7.djvu|7-4]] we get:

 * {| style="width:70%" border="0" align="center"

(8.8)
 * $$\displaystyle I_8 = \frac{h}{3} \left[f_0 + 4f_1 + 2f_2 + \cdots + 4f_{n-2} + 2f_{n-1} + f_n\right] = 2.11451145359$$
 *
 * }
 * }

However when we compare I8 with I we get an actual E8 that is greater than what the error equation tells us we should get. See below:

 * {| style="width:70%" border="0" align="center"

(8.9)
 * $$\displaystyle E_{8} = |I - I_{8}| = |2.11450175075 - 2.11451145359| = 9.70284 \times 10^{-6}$$
 *

 * }
 * }

2.a.) Composite Trapezoidal Rule Error Power of h Determination
Using equations (8.6) and (8.7) we construct the following two tables:

By graphing the above table with log(h) on the x-axis and log(En) on the y-axis with MS Excel and fitting a linear regression line across the points we get the graph below. As can be seen on the graph the slope of the line is approximately two which corresponds to the power of h in the composite Trapezoidal rule error equation.

2.b.) Composite Simpson's Rule Error Power of h Determination
Using equations (8.8) and (8.9) we construct the following two tables:

By graphing the above table with log(h) on the x-axis and log(En) on the y-axis with MS Excel and fitting a linear regression line across the points we get the graph below. As can be seen on the graph the slope of the line is approximately four which corresponds to the power of h in the composite Simpson's rule error equation.

This problem was solved by Erle Fields

=Problem 4.9 proof of SSET in different cases= Refer to lecture slide [[media:nm1.s11.mtg22.djvu|mtg-22]] for the problem statement.

Objectives
A). Redo the proof for two cases:

1).
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

G(t):=e(t)-{{t}^{4}}e(1)

$$ 2). :{| style="width:100%" border="0" $$ \displaystyle
 *

 * }
 * style="width:95%" |
 * style="width:95%" |

G(t):=e(t)-{{t}^{6}}e(1)

$$ Point out where proof breaks down.
 *

 * }

B). for G(t) as in (1) p.19-1(w/t5), find G(3)(0) and follow same steps in proof to see what happen.

Solutions
A). Redo the proof for two cases: 1). $$\displaystyle G(t):=e(t)-{{t}^{4}}e(1)$$
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

e(t)=\int\limits_{-t}^{+t}{F(t)dt}-\frac{t}{3}[F(-t)+4F(0)+F(t)]

$$ Where $$\displaystyle F(t)=f(x(t))$$
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\text{G}\left( 0 \right)=e(0)-{{0}^{4}}e(1)=\int\limits_{-0}^{+0}{F(t)dt}-\frac{0}{3}[F(-0)+4F(0)+F(0)]=0

$$
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\text{G}\left( 1 \right)=e(1)-{{1}^{4}}e(1)=0

$$ Apply Rolle ‘ s theorem, it yields:
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\exists {{\xi }_{1}}\in \left( 0,1 \right)\begin{matrix} {} & st. \\ \end{matrix}{{G}^{\left( 1 \right)}}({{\xi }_{1}})=0

$$
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\begin{align} & {{\text{G}}^{(1)}}\left( t \right)={{e}^{(1)}}(t)-4{{t}^{3}}e(1)={{A}^{(1)}}(t)-A{{_{2}^{L}}^{(1)}}(t)-4{{t}^{3}}e(1) \\ & \begin{matrix} \begin{matrix} {} & {} \\ \end{matrix} & {}  \\ \end{matrix}=F(-t)+F(t)-\{\frac{1}{3}[F(-t)+4F(0)+F(t)]+\frac{t}{3}[-{{F}^{(1)}}(-t)+{{F}^{(1)}}(t)]\}-4{{t}^{3}}e(1) \\ \end{align}

$$ So,
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\begin{align} & {{\text{G}}^{(1)}}\left( 0 \right)=F(-0)+F(0)-\{\frac{1}{3}[F(-0)+4F(0)+F(0)]+\frac{0}{3}[-{{F}^{(1)}}(-t)+{{F}^{(1)}}(t)]\}-4\centerdot {{0}^{3}}e(1) \\ & \begin{matrix} {} & {} & {} \\ \end{matrix}=0 \\ \end{align}

$$ Apply Rolle ‘ s theorem, it yields:
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\exists {{\xi }_{2}}\in \left( 0,{{\xi }_{1}} \right)\begin{matrix} {} & st. \\ \end{matrix}{{G}^{\left( 2 \right)}}({{\xi }_{2}})=0

$$
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\begin{align} & {{\text{G}}^{(2)}}\left( t \right)={{e}^{(2)}}(t)-12{{t}^{2}}e(1)={{A}^{(2)}}(t)-A{{_{2}^{L}}^{(2)}}(t)-12{{t}^{2}}e(1) \\ & \begin{matrix} \begin{matrix} {} & {} \\ \end{matrix} & {}  \\ \end{matrix}=-{{F}^{(1)}}(-t)+{{F}^{(1)}}(t)-\{\frac{1}{3}[-{{F}^{(1)}}(-t)+{{F}^{(1)}}(t)] \\ & \begin{matrix} {} & {} & {} & {} \\ \end{matrix}+\frac{1}{3}[-{{F}^{(1)}}(-t)+{{F}^{(1)}}(t)]+\frac{t}{3}[{{F}^{(2)}}(-t)+{{F}^{(2)}}(t)]\}-12{{t}^{2}}e(1) \\ & \begin{matrix} \begin{matrix} {} & {} \\ \end{matrix} & {}  \\ \end{matrix}=\frac{1}{3}[-{{F}^{(1)}}(-t)+{{F}^{(1)}}(t)]-\frac{t}{3}[{{F}^{(2)}}(-t)+{{F}^{(2)}}(t)]\}-12{{t}^{2}}e(1) \\ \end{align}

$$ So,
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\begin{align} & {{\text{G}}^{(2)}}\left( 0 \right)=\frac{1}{3}[-{{F}^{(1)}}(-0)+{{F}^{(1)}}(0)]-\frac{0}{3}[{{F}^{(2)}}(-0)+{{F}^{(2)}}(0)]\}-12\centerdot {{0}^{2}}e(1) \\ & \begin{matrix} {} & {} & = \\ \end{matrix}0 \\ \end{align}

$$ Apply Rolle ‘ s theorem, it yields:
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\exists {{\xi }_{3}}\in \left( 0,{{\xi }_{2}} \right)\begin{matrix} {} & st. \\ \end{matrix}{{G}^{\left( 3 \right)}}({{\xi }_{3}})=0

$$
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\begin{align} & {{\text{G}}^{(3)}}\left( t \right)=\frac{1}{3}[-{{F}^{(1)}}(-t)+{{F}^{(1)}}(t)]-\frac{t}{3}[{{F}^{(2)}}(-t)+{{F}^{(2)}}(t)]-24te(1) \\ & \begin{matrix} {} & {} & = \\ \end{matrix}\frac{1}{3}[{{F}^{(2)}}(-t)+{{F}^{(2)}}(t)]-\frac{1}{3}[{{F}^{(2)}}(-t)+{{F}^{(2)}}(t)]-\frac{t}{3}[-{{F}^{(3)}}(-t)+{{F}^{(3)}}(t)]-24te(1) \\ & \begin{matrix} {} & {} & = \\ \end{matrix}-\frac{t}{3}[-{{F}^{(3)}}(-t)+{{F}^{(3)}}(t)]-24te(1) \\ \end{align}

$$ So, $$\displaystyle {{\text{G}}^{(3)}}\left( {{\xi }_{3}} \right)=\frac{3}[{{F}^{(3)}}(-{{\xi }_{3}})-{{F}^{(3)}}({{\xi }_{3}})]-24\left( {{\xi }_{3}} \right)e(1)=0$$, then using DMVT:
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

e(1)=\frac{\frac{3}[{{F}^{(3)}}(-{{\xi }_{3}})-{{F}^{(3)}}({{\xi }_{3}})]}{24\left( {{\xi }_{3}} \right)}=\frac{\frac{3}[-2{{\xi }_{3}}{{F}^{(4)}}({{\xi }_{4}})]}{24\left( {{\xi }_{3}} \right)}=\frac{-{{\xi }_{3}}{{F}^{(4)}}({{\xi }_{4}})}{36}

$$ Where, $$\displaystyle {{\xi }_{4}}\in \left( -{{\xi }_{3}},{{\xi }_{3}} \right)$$
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * style="width:92%; padding:10px; border:2px solid #8888aa" |

{{\text{E}}_{2}}=h\centerdot e(1)=h\frac{-{{\xi }_{3}}{{F}^{(4)}}({{\xi }_{4}})}{36}

$$     (Eq ) The proof will break down here because the magnitude of error is related to $$\displaystyle {{\xi }_{3}}$$in the above equation.
 *

 * }

2)

$$\displaystyle G(t):=e(t)-{{t}^{6}}e(1)$$
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

e(t)=\int\limits_{-t}^{+t}{F(t)dt}-\frac{t}{3}[F(-t)+4F(0)+F(t)]

$$ Where $$\displaystyle F(t)=f(x(t))$$
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\text{G}\left( 0 \right)=e(0)-{{0}^{6}}e(1)=\int\limits_{-0}^{+0}{F(t)dt}-\frac{0}{3}[F(-0)+4F(0)+F(0)]=0

$$
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\text{G}\left( 1 \right)=e(1)-{{1}^{6}}e(1)=0

$$ Apply Rolle ‘ s theorem, it yields:
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\exists {{\xi }_{1}}\in \left( 0,1 \right)\begin{matrix} {} & st. \\ \end{matrix}{{G}^{\left( 1 \right)}}({{\xi }_{1}})=0

$$
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\begin{align} & {{\text{G}}^{(1)}}\left( t \right)={{e}^{(1)}}(t)-6{{t}^{5}}e(1)={{A}^{(1)}}(t)-A{{_{2}^{L}}^{(1)}}(t)-6{{t}^{5}}e(1) \\ & \begin{matrix} \begin{matrix} {} & {} \\ \end{matrix} & {}  \\ \end{matrix}=F(-t)+F(t)-\{\frac{1}{3}[F(-t)+4F(0)+F(t)]+\frac{t}{3}[-{{F}^{(1)}}(-t)+{{F}^{(1)}}(t)]\}-6{{t}^{5}}e(1) \\ \end{align}

$$ So,
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\begin{align} & {{\text{G}}^{(1)}}\left( 0 \right)=F(-0)+F(0)-\{\frac{1}{3}[F(-0)+4F(0)+F(0)]+\frac{0}{3}[-{{F}^{(1)}}(-t)+{{F}^{(1)}}(t)]\}-6\centerdot {{0}^{5}}e(1) \\ & \begin{matrix} {} & {} & {} \\ \end{matrix}=0 \\ \end{align}

$$ Apply Rolle ‘ s theorem, it yields:
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\exists {{\xi }_{2}}\in \left( 0,{{\xi }_{1}} \right)\begin{matrix} {} & st. \\ \end{matrix}{{G}^{\left( 2 \right)}}({{\xi }_{2}})=0

$$
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\begin{align} & {{\text{G}}^{(2)}}\left( t \right)={{e}^{(2)}}(t)-30{{t}^{4}}e(1)={{A}^{(2)}}(t)-A{{_{2}^{L}}^{(2)}}(t)-30{{t}^{4}}e(1) \\ & \begin{matrix} \begin{matrix} {} & {} \\ \end{matrix} & {}  \\ \end{matrix}=-{{F}^{(1)}}(-t)+{{F}^{(1)}}(t)-\{\frac{1}{3}[-{{F}^{(1)}}(-t)+{{F}^{(1)}}(t)] \\ & \begin{matrix} {} & {} & {} & {} \\ \end{matrix}+\frac{1}{3}[-{{F}^{(1)}}(-t)+{{F}^{(1)}}(t)]+\frac{t}{3}[{{F}^{(2)}}(-t)+{{F}^{(2)}}(t)]\}-30{{t}^{4}}e(1) \\ & \begin{matrix} \begin{matrix} {} & {} \\ \end{matrix} & {}  \\ \end{matrix}=\frac{1}{3}[-{{F}^{(1)}}(-t)+{{F}^{(1)}}(t)]-\frac{t}{3}[{{F}^{(2)}}(-t)+{{F}^{(2)}}(t)]\}-30{{t}^{4}}e(1) \\ \end{align}

$$ So,
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\begin{align} & {{\text{G}}^{(2)}}\left( 0 \right)=\frac{1}{3}[-{{F}^{(1)}}(-0)+{{F}^{(1)}}(0)]-\frac{0}{3}[{{F}^{(2)}}(-0)+{{F}^{(2)}}(0)]\}-30\centerdot {{0}^{4}}e(1) \\ & \begin{matrix} {} & {} & = \\ \end{matrix}0 \\ \end{align}

$$ Apply Rolle ‘ s theorem, it yields:
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\exists {{\xi }_{3}}\in \left( 0,{{\xi }_{2}} \right)\begin{matrix} {} & st. \\ \end{matrix}{{G}^{\left( 3 \right)}}({{\xi }_{3}})=0

$$
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\begin{align} & {{\text{G}}^{(3)}}\left( t \right)=\frac{1}{3}[-{{F}^{(1)}}(-t)+{{F}^{(1)}}(t)]-\frac{t}{3}[{{F}^{(2)}}(-t)+{{F}^{(2)}}(t)]-120{{t}^{3}}e(1) \\ & \begin{matrix} {} & {} & = \\ \end{matrix}\frac{1}{3}[{{F}^{(2)}}(-t)+{{F}^{(2)}}(t)]-\frac{1}{3}[{{F}^{(2)}}(-t)+{{F}^{(2)}}(t)]-\frac{t}{3}[-{{F}^{(3)}}(-t)+{{F}^{(3)}}(t)]-120{{t}^{3}}e(1) \\ & \begin{matrix} {} & {} & = \\ \end{matrix}-\frac{t}{3}[-{{F}^{(3)}}(-t)+{{F}^{(3)}}(t)]-120{{t}^{3}}e(1) \\ \end{align}

$$ So, $$\displaystyle {{\text{G}}^{(3)}}\left( {{\xi }_{3}} \right)=\frac{3}[{{F}^{(3)}}(-{{\xi }_{3}})-{{F}^{(3)}}({{\xi }_{3}})]-120{{\left( {{\xi }_{3}} \right)}^{3}}e(1)=0$$, then using DMVT:
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

e(1)=\frac{\frac{3}[{{F}^{(3)}}(-{{\xi }_{3}})-{{F}^{(3)}}({{\xi }_{3}})]}{120{{\left( {{\xi }_{3}} \right)}^{3}}}=\frac{\frac{3}[-2{{\xi }_{3}}{{F}^{(4)}}({{\xi }_{4}})]}{120{{\left( {{\xi }_{3}} \right)}^{3}}}=\frac{-{{F}^{(4)}}({{\xi }_{4}})}{180{{\xi }_{3}}}

$$ Where, $$\displaystyle {{\xi }_{4}}\in \left( -{{\xi }_{3}},{{\xi }_{3}} \right)$$
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * style="width:92%; padding:10px; border:2px solid #8888aa" |

{{\text{E}}_{2}}=h\centerdot e(1)=h\frac{-{{F}^{(4)}}({{\xi }_{4}})}{180{{\xi }_{3}}}

$$
 *

 * }The proof will break down here because the magnitude of error is related to $$\displaystyle {{\xi }_{3}}$$in the above equation.

B)
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

G(t):=e(t)-{{t}^{5}}e(1)

$$
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

e(t)=\int\limits_{-t}^{+t}{F(t)dt}-\frac{t}{3}[F(-t)+4F(0)+F(t)]

$$ Where $$\displaystyle F(t)=f(x(t))$$
 *

 * }

 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\text{G}\left( 0 \right)=e(0)-{{0}^{5}}e(1)=\int\limits_{-0}^{+0}{F(t)dt}-\frac{0}{3}[F(-0)+4F(0)+F(0)]=0

$$
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\text{G}\left( 1 \right)=e(1)-{{1}^{5}}e(1)=0

$$ Apply Rolle ‘ s theorem, it yields:
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\exists {{\xi }_{1}}\in \left( 0,1 \right)\begin{matrix} {} & st. \\ \end{matrix}{{G}^{\left( 1 \right)}}({{\xi }_{1}})=0

$$
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\begin{align} & {{\text{G}}^{(1)}}\left( t \right)={{e}^{(1)}}(t)-5{{t}^{4}}e(1)={{A}^{(1)}}(t)-A{{_{2}^{L}}^{(1)}}(t)-5{{t}^{4}}e(1) \\ & \begin{matrix} \begin{matrix} {} & {} \\ \end{matrix} & {}  \\ \end{matrix}=F(-t)+F(t)-\{\frac{1}{3}[F(-t)+4F(0)+F(t)]+\frac{t}{3}[-{{F}^{(1)}}(-t)+{{F}^{(1)}}(t)]\}-5{{t}^{4}}e(1) \\ \end{align}

$$ So,
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\begin{align} & {{\text{G}}^{(1)}}\left( 0 \right)=F(-0)+F(0)-\{\frac{1}{3}[F(-0)+4F(0)+F(0)]+\frac{0}{3}[-{{F}^{(1)}}(-t)+{{F}^{(1)}}(t)]\}-5\centerdot {{0}^{4}}e(1) \\ & \begin{matrix} {} & {} & {} \\ \end{matrix}=0 \\ \end{align}

$$ Apply Rolle ‘ s theorem, it yields:
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\exists {{\xi }_{2}}\in \left( 0,{{\xi }_{1}} \right)\begin{matrix} {} & st. \\ \end{matrix}{{G}^{\left( 2 \right)}}({{\xi }_{2}})=0

$$
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\begin{align} & {{\text{G}}^{(2)}}\left( t \right)={{e}^{(2)}}(t)-20{{t}^{3}}e(1)={{A}^{(2)}}(t)-A{{_{2}^{L}}^{(2)}}(t)-20{{t}^{3}}e(1) \\ & \begin{matrix} \begin{matrix} {} & {} \\ \end{matrix} & {}  \\ \end{matrix}=-{{F}^{(1)}}(-t)+{{F}^{(1)}}(t)-\{\frac{1}{3}[-{{F}^{(1)}}(-t)+{{F}^{(1)}}(t)] \\ & \begin{matrix} {} & {} & {} & {} \\ \end{matrix}+\frac{1}{3}[-{{F}^{(1)}}(-t)+{{F}^{(1)}}(t)]+\frac{t}{3}[{{F}^{(2)}}(-t)+{{F}^{(2)}}(t)]\}-20{{t}^{3}}e(1) \\ & \begin{matrix} \begin{matrix} {} & {} \\ \end{matrix} & {}  \\ \end{matrix}=\frac{1}{3}[-{{F}^{(1)}}(-t)+{{F}^{(1)}}(t)]-\frac{t}{3}[{{F}^{(2)}}(-t)+{{F}^{(2)}}(t)]\}-20{{t}^{3}}e(1) \\ \end{align}

$$ So,
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\begin{align} & {{\text{G}}^{(2)}}\left( 0 \right)=\frac{1}{3}[-{{F}^{(1)}}(-0)+{{F}^{(1)}}(0)]-\frac{0}{3}[{{F}^{(2)}}(-0)+{{F}^{(2)}}(0)]\}-20\centerdot {{0}^{3}}e(1) \\ & \begin{matrix} {} & {} & = \\ \end{matrix}0 \\ \end{align}

$$ Apply Rolle ‘ s theorem, it yields:
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\exists {{\xi }_{3}}\in \left( 0,{{\xi }_{2}} \right)\begin{matrix} {} & st. \\ \end{matrix}{{G}^{\left( 3 \right)}}({{\xi }_{3}})=0

$$
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\begin{align} & {{\text{G}}^{(3)}}\left( t \right)=\frac{1}{3}[-{{F}^{(1)}}(-t)+{{F}^{(1)}}(t)]-\frac{t}{3}[{{F}^{(2)}}(-t)+{{F}^{(2)}}(t)]-60{{t}^{2}}e(1) \\ & \begin{matrix} {} & {} & = \\ \end{matrix}\frac{1}{3}[{{F}^{(2)}}(-t)+{{F}^{(2)}}(t)]-\frac{1}{3}[{{F}^{(2)}}(-t)+{{F}^{(2)}}(t)]-\frac{t}{3}[-{{F}^{(3)}}(-t)+{{F}^{(3)}}(t)]-60{{t}^{2}}e(1) \\ & \begin{matrix} {} & {} & = \\ \end{matrix}-\frac{t}{3}[-{{F}^{(3)}}(-t)+{{F}^{(3)}}(t)]-60{{t}^{2}}e(1) \\ \end{align}

$$ So,
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

{{\text{G}}^{(3)}}\left( 0 \right)=-\frac{0}{3}[-{{F}^{(3)}}(-t)+{{F}^{(3)}}(t)]-60\centerdot {{0}^{2}}e(1)=0

$$ Apply Rolle ‘ s theorem, it yields:
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\exists {{\xi }_{4}}\in \left( 0,{{\xi }_{3}} \right)\begin{matrix} {} & st. \\ \end{matrix}{{G}^{\left( 4 \right)}}({{\xi }_{4}})=0

$$
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

{{\text{G}}^{(4)}}\left( t \right)=\frac{1}{3}[{{F}^{(3)}}(-t)-{{F}^{(3)}}(t)]-\frac{t}{3}[{{F}^{(4)}}(-t)+{{F}^{(4)}}(t)]-120te(1)

$$ So,
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

{{\text{G}}^{(4)}}\left( {{\xi }_{4}} \right)=\frac{1}{3}[{{F}^{(3)}}(-{{\xi }_{4}})-{{F}^{(3)}}({{\xi }_{4}})]-\frac{3}[{{F}^{(4)}}(-{{\xi }_{4}})+{{F}^{(4)}}({{\xi }_{4}})]-120{{\xi }_{4}}e(1)=0

$$ Using DMVT:
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

e(1)=\frac{\frac{1}{3}[-2{{\xi }_{4}}{{F}^{(4)}}({{\xi }_{5}})]-\frac{3}[{{F}^{(4)}}(-{{\xi }_{4}})+{{F}^{(4)}}({{\xi }_{4}})]}{120{{\xi }_{4}}}=\frac{-[2{{F}^{(4)}}({{\xi }_{5}})+{{F}^{(4)}}(-{{\xi }_{4}})+{{F}^{(4)}}({{\xi }_{4}})]}{360}

$$ Where, $$\displaystyle {{\xi }_{5}}\in \left( -{{\xi }_{4}},{{\xi }_{4}} \right)$$
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * style="width:92%; padding:10px; border:2px solid #8888aa" |

{{\text{E}}_{2}}=h\centerdot e(1)=h\frac{-[2{{F}^{(4)}}({{\xi }_{5}})+{{F}^{(4)}}(-{{\xi }_{4}})+{{F}^{(4)}}({{\xi }_{4}})]}{360}

$$ Here, it is observed that the magnitude of error is related to the value of function at these two points$$\displaystyle {{\xi }_{4}},{{\xi }_{5}}$$in the above equation.
 *

 * }

=Problem 4.10: Error Convergence for the Trapezoidal and Simpon's Rules=

Refer to lecture slides [[media:Nm1.s11.mtg22.djvu|22-3 through 22-5]] for problem assignment.

Given
Consider the exact integrals

and

Objectives

 * 1.) Create a table showing the approximations of (10.1) by using the Trapezoidal rule with successively doubling values of n, as well as the corresponding error involved in the approximation. Also, the table should include the ratio of successive errors to show the effect of doubling the value of n on the error.

 * 2.) Create a table showing the approximations of (10.1) by using Simpson's rule with successively doubling values of n, as well as the corresponding error involved in the approximation. Also, the table should include the ratio of successive errors to show the effect of doubling the value of n on the error.

 * 3.) Create a table showing the errors of approximating (10.2) by using both the Trapezoidal and Simpon's rules, as well as the ratio of successive errors to show the effect of doubling the value of n on the error.

Calculation of the True Values of the Integrals
Wolfram Alpha was used to compute the exact values of (10.1) and (10.2):

Approximation of the Integral of $$f(x) = e^x sin(x)$$ by Trapezoidal Rule
The following MATLAB code was used to calculate the approximation of (10.1) for increasing values of n using the Trapezoidal rule, as well as the associated approximation errors and the ratios of successive approximation errors.

As can be seen in this table the error is quartered when the interval size is halved, indicating that the error indeed scales with $$ O(h^2)$$.

Approximation of the Integral of $$f(x) = e^x sin(x)$$ by Simpon's Rule
The following MATLAB code was used to calculate the approximation of (10.1) for increasing values of n using Simpson's rule, as well as the associated approximation errors and the ratios of successive approximation errors.

As can be seen in this table that as the interval size is halved the error is reduced by a factor of sixteen, indicating that the error indeed scales with $$ O(h^4)$$.

Error of Approximating the Integral of $$ f(x) = x^{3.7}$$ Using Both Trapezoidal and Simpon's Rules
The following MATLAB code was used to calculate the approximation of (10.2) for increasing values of n using both the Trapezoidal and Simpson's rules, as well as the associated approximation errors and the ratios of successive approximation errors for each method.

As can be seen in this table that as the interval size is halved the error associated with the Trapezoidal rule is quartered and the error associated with Simpson's rule is reduced by a factor of sixteen, indicating that the errors indeed scale with $$ O(h^2)$$ and $$ O(h^4)$$, respectively.

Solved by William Kurth.

=Contributing Members & Referenced Lecture=

= Signatures =

 * Brendan Mahon 04:45, 2 March 2011 (UTC)

 * Erle Fields 04:53, 2 March 2011 (UTC)

 * William Kurth 04:58, 2 March 2011 (UTC)

 * Hailong Chen 1:30PM, 1 March 2011 (EST)

 * Taeho Kim 12:35, 3 March 2011 (UTC)

 * shengfeng yang 9:30AM, 2 March 2011 (EST)

title: User:Egm6341.s11.team4/HW4


text:
User:Bcosio

Use of modal verbs

title: User:Bcosio


text:
Talk:Psycholinguistics/Reading

Psycholinguistics peer review: letter grade A Research:  •	You provide a very thorough review of literature and excellent supporting articles to illustrate your points. •	You could include a figure illustrating brain area implicated in reading. •	Excellent variety of sources (books, articles etc.) •	Could provide more current viewpoints and contrasting ideas •	Excellent support of arguments, though it doesn’t hurt sometimes to include multiple sources for some of the more key points even just to emphasize how widely accepted or refuted their point is •	It might be good to also include different viewpoints about “ways to read” and not just Erhis point of view •	It might be interesting to include a small chunk or concluding paragraph touching on ways of teaching reading logic / Organization: •	It would be a nice to add a section on the psychological consequences of reading on language production and perception and development, but perhaps not in the “what is reading” chunk, it could be its own chunk. Your chapter however is not lacking in content or length, so do not feel pressured to include this section though if you have already done or found some research on it, including it wouldn’t hurt. •	Instead of having a separate section about what reading is, I would just continue the intro paragraph as your “what is reading” component. You seemed to define it well already in the intro, it seems redundant to do it again. I would just delete this subheading •	It might be good to quickly describe who Ehri is (early reading researcher or something). Often in textbooks, when someone is so heavily cited, there is some mention of who they are and what their contribution to the field was. •	It would not hurt to provide an introductory paragraph to the section on ways to read, to clarify that it was included at that point delibartely because as it is it just sort of seems like it was thrown in there. This section could be its own major subheading. •	Excellent layout and flow of ideas: I would not change much if at all about the way you have ordered the subheadings. •	Probably do not need to include section on reading sign could just mention in overall concluding paragraph, as this online book of ours already has sections on production and perception of sign languages so you could delete the section on “other models”. •	Under models of reading, though you chose focus on the main one, are there others and why might they be dismissed while the DRC is so widely accepted? This would show that there is a lot of research in the area and that despite other models, this one is still the best. •	It would not hurt to include some transition statement or ideas to further the flow even more. Such statements/ideas would also show the reader that your choice of order of arguments and topics is deliberately chosen and necessary. Analysis/integration: •	Excellent comprehensive discussion of models of reading. It is great that you did include the strengths and fallbacks of each model. •	It might be helpful to take a closer look at the way that you described the models: that was the only chunk that really slowed me down while reading it. Perhaps try describing the models to a friend who is not in our class and doesn’t really have much background knowledge about cognitive models of reading. It was a little bit confusing ( such a willing friend might be hard to come by I understand) Answers Questions/ Makes arguments: •	Great choice of literature support of main ideas, lots of applicable evidence. •	Make sure that it is clear why you chose to include each piece of literature cited and how it directly applies to that subheading. There were some sections about previous literature/findings/specific studies that lacked transition statements, which made it unclear as to how they directly apply to that subheading. Writing style:  •	When citing authors in your sentence it is typical to include the year of publication in brackets at the end of the sentence •	Be careful with long sentences. It is often helpful to break long sentences for clarity (my short term memory is way too short for long sentences and I truly appreciate textbooks that just break it down) •	Double-check your use of colons and semi-colons, though I think you were spot on for the most part. There are good rules for using each outlined in the following website http://www.libraryonline.com/default.asp?pID=32 •	Very clear and concise, excellent choice of words. •	Writing style very appropriate for target audience, the level of information and explanation was spot for the most part, however there were a few spots where more explanation or definitions of what might seem like common knowledge to us, because we are taking a class on it, would be very convenient and appreciated by readers who are new to the subject. These spots are highlighted in the attached corrected copy of your chapter. •	Be consistent with which words you italicize or put in quotations •	Everything was very esthetically pleasing and easy to read. All of it was very clear except for chunk on models, could use a bit of tweaking to make it more clear. •	Reference section is awesome. I am not sure that you need to include where things are cited (i.e. cite in blah blah blah) but it never hurts, great job. •	I have attached a PDF with some specific suggestions about writing style and areas that could use more explanation. Structure: •	You probably don’t nee to include the fun facts part as fun as it is. Instead you could just include the fun facts as they apply to each topic (embedded within each subheading) •	Well-organized and easy to follow. As mentioned above it might be helpful to include an image about the brain areas. •	You could include a concluding paragraph, it might tie things up nicely. •	As mentioned above it would be good to double check that you have intro and concluding statements between subheadings. If you message me i would like to send you a marked up word file with suggestions, but i cannot currently figure out how to post it. I am working on it. I will keep you posted.

(Moraghjang 22:55, 24 February 2011 (UTC))

Thanks for the very thorough editing job! I appreciated all of the suggestions and it looks like your advice is going to be really helpful. I definitely needed a pair of outside eyes to show me what needs to be worked on the most. jnvincent 01:59, 25 February 2011 (UTC)

title: Talk:Psycholinguistics/Reading


text:
User talk:Choconancy

 Hello Choconancy, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
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 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
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You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Moulton 22:54, 24 February 2011 (UTC)

Greetings
Hi Nancy!

It's been ages.

Welcome to Wikiversity.

Moulton 23:01, 24 February 2011 (UTC)

title: User talk:Choconancy


text:
User:Egm6341.s11.team2.franklin/hwk4

Problem 5: Show relationship in Simple Simpson's Error Theorem
''' This problem was solved without referring to S10 homework. '''

From the lecture slide Mtg 21-1

Problem Statement
Given

find relation between $$ \xi\ \ $$ and $$ \zeta_4\ \ $$.

Solution
Let

Transforming coordinates $$\displaystyle \left( t=\zeta_4, x=\xi\right) $$ gives:

With Eqn 5.1-7, the proof is as follows:

The fourth derivative of $$\displaystyle F \left(\zeta_4\right) $$ is

Substituting $$\displaystyle \frac{dx}{h} $$ for $$\displaystyle  dt $$ and $$\displaystyle  f\left(\xi\right) $$ for $$\displaystyle  F\left(\zeta_4\right) $$ in Eqn 5.8 gives:

Substitute Eqn 5.11 into Eqn 5.1 gives:

By transforming $$\displaystyle t=\zeta_4 $$ and $$\displaystyle x=\xi $$, Eqn 5.4 becomes

Problem 10: Comparisons of Comp. Trapezoidal and Comp. Simpson's Rules
''' This problem was solved without referring to S10 homework. '''

From the lecture slide Mtg 22-3

Problem Statement
a) Produce a table similar to table 5.1, page 255, Atkinson text book using the composite Trapezoidal rule (Atkinson is cos(x) instead of sin(x)).

b) Produce a table similar to table 5.3, page 258, Atkinson text book using the composite Simpson's rule (Atkinson is cos(x) instead of sin(x)).

Solution
 Part (a):  The given integral is: $$I=\int_{0}^{\pi} e^{x} \sin \left ( x \right )\cdot dx$$ where $$f\left ( x \right )=e^{x} \sin \left ( x \right )$$ is the integrand and $$\;x\in \left [ 0,\pi \right ]$$. We will use the composite trapezoidal rule to obtain the following tabulated results:

 MATLAB Code:

 Part (b):  The given integral is: $$I=\int_{0}^{\pi} e^{x} \sin \left ( x \right )\cdot dx$$ where $$f\left ( x \right )=e^{x} \sin \left ( x \right )$$ is the integrand and $$\;x\in \left [ 0,\pi \right ]$$. We will use composite simpson's rule to generate the following tabulated results:

 MATLAB Code:

title: User:Egm6341.s11.team2.franklin/hwk4


text:
User:Altes2011

Qualifications: MD degree, specialty Internal Medicine, fellowship in Immunotherapy (Northwestern University, non ACGME accredited) PhD in Molecular Biology

main achievements: First Stem cell Transplant for Devic's Disease in the world; first non-myeloablative allogeneic stem cell transplant for Leukocyte Adhesion Deficiency and Chron's disease utilizing cord blood stem cells in the world.

Goals: Create the world's first web-based MULTIVERSITY aiming to the synthesis of the learning and research knowledge accumulated by various universities and disseminating it in the forms of textbooks, lectures, videos and multimedia. Essentially the Multiveristy is a repository of knowledge which eveolves and updates with the times. It is also a degree awarding institution, awarding degrees such as the Doctorate of technology and aiming to transform basic science into applied science, transforming science into usable technologies.

title: User:Altes2011


text:
Countries of the World

Wikiversity welcomes most types of learning materials that are not encyclopedia or textbook  articles. Please note that Wikiversity is not a place for duplication of other Wikimedia projects.

Wikiversity has adopted a "learn by doing" model for online education and encourages the creation of learning activities for Wikiversity participants. Everyone is invited to help add useful content to Wikiversity. If you need help learning how to add content, see the editing tutorial and Welcome, newcomers.

title: Countries of the World


text:
User:Yongtao-Li/NM.HW4.2

=Problem 4.2 "One step in the proof of Simple Simpson's Error Theorem"=

Given
In order to prove Simple Simpson's Error Theorem, we define

Find
Find the first derivative of the first term of (4.2.1) since it is needed to compute the first derivative of (4.2.2).

Solution
Suppose there is a constant $$ k \in \left] { - t,t} \right[ $$ and then the first term can be written as

Then we can find out the first derivative of (4.2.3) is

Therefore the first derivative of the first term of (4.2.1) is

title: User:Yongtao-Li/NM.HW4.2


text:
User:Yongtao-Li/NM.HW4.4

=Problem 4.4 "Another step in the proof of Simple Simpson's Error Theorem"=

Given
In order to prove Simple Simpson's Error Theorem, we define

Find
The third derivative of (4.4.1)

Solution
From Problem 4.2, we have the first derivative of (4.4.1):

Then we can compute the second derivative of (4.4.1) use the above equation (4.4.2)

At last we can get the third derivative of (4.4.1) use the above equation (4.4.3)

title: User:Yongtao-Li/NM.HW4.4


text:
User talk:Ottava Rima/archives/2011/feb

when the real world starts to release you
Please come back soon...maybe you can bring in some good collaborators for your areas of expertise...folks who will help you have fun building some interesting learning projects. --JWSchmidt 01:14, 24 February 2011 (UTC)

Avoidance vs Engagement with Adversarial Antagonists

 * After Jeff finishes his Ph.D. Thesis, perhaps he will return and engage with his adversaries in a gracious and sincere Truth and Reconciliation process. —Moulton 12:28, 24 February 2011 (UTC)

title: User talk:Ottava Rima/archives/2011/feb


text:
Talk:Complex socioecological systems/Adaptive Management and Resilience

Schultz et al. (2011):

This article is important for it challenges the idea that participation can lead to less desirable outcomes, such as less conservation. I was glad to see that the authors sought to examine the relationship between the participation of different stakeholders and the outcomes of adaptive management. What caught my attention is that the authors examine the relationship between scientist participation and specific outcomes. In my readings on participation, I have found that community members, representatives of civil society organizations, and government representatives are usually expected to participate and their social roles in co-management schemes are more problematized. Scientists are usually given only the supportive role of providers of data and research findings. In adaptive co-management scientists gain a more central role because scientific knowledge is considered the/a guide to provide information as regards ecosystem conditions. Therefore, evaluations of (adaptive) co-management schemes need to consider the active role of scientists, as well the interactions between scientists and other groups. Not considering the active role of scientists in adaptive co-managemnet schemes is problematic because it means ignoring an important social actor, who has resources and influence to push towards specific outcomes. flaleite 06:01, 25 February 2011 (UTC)

Here is one of the questions of my qualifying exams: What is the adaptive co-management approach and how does it differ from other approaches to sustainable land management such as community- or market-based approaches? What are the characteristic strengths and weaknesses of each?

Can you answer it? flaleite 15:48, 25 February 2011 (UTC)


text:
User:Moulton/Mimnetics

Wild Mind Mimnetic Mirroring
 Ultimate Journey by Robert A. Monroe  There is no beginning, there is no end, There is only change.  There is no teacher, there is no student, There is only remembering.  There is no good, there is no evil, There is only expression.  There is no union, there is no sharing, There is only one.  There is no joy, there is no sadness, There is only love.
 There is no greater, there is no lesser,
 There is only balance.

 There is no stasis, there is no entropy,
 There is only motion.

 There is no wakefulness, there is no sleep,
 There is only being.

 There is no limit, there is no chance,
 There is only a plan.
 (—Monroe Institute)

 ˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜
 There is no babbling, there is no soliloquy,
 There is only conversation.

 There is no conversation, there is no dialogue,
 There is only insight.

 There is no insight, there is no common ground,
 There is only theory.

 There is no theory, there is no practice,
 There is only perfection.

 There is no perfection, there is no honor,
 There is only love.

 There is no love, there is no suffering,
 There is only divinity.

 There is no divinity, there is no holiness,
 There is only becoming.

 (—Moultonic Mimnetic Wild Mind Continuation, Jan 10, 2003)

 * [Source: Moultonic Musings, Sunday, May 20, 2007]

title: User:Moulton/Mimnetics


text: File:Similarity considerations2 2.png

title: File:Similarity considerations2 2.png


text: File:Losses energie11 2.png

title: File:Losses energie11 2.png


text:
User:Opriter/Math

I. Algebra 1

1. Introduction to Real Numbers

1.1 Where do numbers come from?

http://cnx.org/content/m31203/latest/

1.2 Real number line

http://siyavula.cnx.org/content/m21895/latest/

2. Properties of Real Numbers

http://siyavula.cnx.org/content/m21894/latest/

3. Exponents

Preliminary Notions

Rules of Exponents

The Power Rules of Exponents

4. Operations with Real Numbers

Signed Numbers

Absolute Value

Addition of Signed Numbers

Subtraction of Signed Numbers

Multiplication and Division of Signed Numbers Negative Exponents

Scientific Notation

5. Operations with Polynomials

Algebraic Expressions

Classification of Polynomials

Addition and Subtraction of Polynomials

Multiplication of Polynomials

Special Binomial Products

6. Factorization of Polynomials

Finding the factors of a monomial

Factoring a monomial from polynomial

The Greatest Common Factor

Factoring by grouping

Factoring two special products

Factoring trinomials with leading coefficient 1

Factoring trinomials with lesding coefficient other than 1

7. linear Function

8. Equations and Inequalities

Resolution of Equations and Inequalities with absolute value

9. Radicals

10. Quadratic equations

Solution by factorization and quadratic formula

11. Systems of linear equations and inequalities

12. Word Problems

13. Additional Resources

Mathematics Grade 9 by Syavula Uploaders: [http://siyavula.cnx.org/content/m31203/1.1/ http://siyavula.cnx.org/content/m31203/1.1/ ] Ninth Grade Content (k-12 math info) http://wikieducator.org/Ninth_Grade_Content_%28k-12math.info%29 Multiplication and Division of Signed Numbers

'''II. Algebra 2'''

1. Complex Numbers

2. Euler and Moivre identities. Pascal's triangle

3. Arithmetic and Geometric sequences

4. Finite Arithmetic and Geometric series

5. Binomial theorem

6. Equation and Inequalities

7. Matrices

8. System of linear equations

9. Function: maximum and minimum values

10. Translation and scale changes of a given function

11. Operation on function. Inverse of function

12. Quadratic Equations

13. Logarithmic and exponential functions. System of equations and inequalities involving algebraic exponential and logarithmic expressions

III. Calculus Resources 1. The Calculus trap

2. Calculus course

3. Wikiversity Topic: Calculus

4. Wikiversity Category: Calculus

5. Wikiversity Calculus topics

6. AP Calculus AB: Revolving Solids Known Cross Sections

7. How to help and video for dummies

8. Evaluating integrals using area interpretation

9. Differential and Integral Calculus Lect i Math 31 A UCLA

10. courses University of Washington online Open course library

11. Calculus II Open course library

12. Differential Calculus

Math Resources

1. Math Sites

Algebra Help

Art of Problem Solving

Open High School of Utah

2. Videos

title: User:Opriter/Math


text:
Engineering Experience 4: Design a Small Solar Vehicle/Nl/Team AM6

RATON
‘Raton’ is een opkomend ingenieursbureau dat door bedrijven of particulieren gecontacteerd kan worden om prototypes te ontwerpen en te bouwen. Deze prototypes kunnen zeer uiteenlopend zijn, van “Computer Based Controls” tot zonnewagens. Op een tijdsduur van maximum vier maanden bezorgen zij een prototype, een gedetailleerde handleiding, eventueel een besturingsprogramma en nog veel meer. Deze kunnen later door het bedrijf of particulier zelf worden gebruikt om bijvoorbeeld verbeteringen aan te brengen aan hun product alvorens het op de markt te brengen.

De naam is afkomstig van twee Zonnegoden van Egypte, Ra en Aton. Hoewel ze allebei Zonnegoden zijn, werden ze niet samen aanbeden. Ra werd samen met de andere Egyptische Goden afgeschaft bij de opkomst van Farao Echnaton en werden vervangen door de God Aton. Na de dood van Echnaton werden de oude Egyptische Goden weer aanbeden.

Het logo bestaat dan ook uit de voorstelling van de twee Goden, de zonneschijf van Aton (Aton betekend letterlijk zon of zonneschijf) en het hiëroglief van Ra, het oog.

Week 1
De teams zijn gevormd, er is samengekomen voor het plan van aanpak, het samenwerkingscontract en de gantt chart te maken. Verder is er in die tijd ook de groepsnaam 'Raton' gekozen en een hierbij passend logo gecreëerd.

Week 2
Deze week zijn we begonnen met een seminarie van het Solar Challenge team van GroepT. Zij hebben uitleg gegeven over de verschillende aspecten van de SSV en waar we precies op moeten letten. Vervolgens was er een engelstalig seminarie over de werking van de elektromotor en berekeningen in verband met de Gear ratio. Na deze seminaries heeft elk team een zonnepaneel gekregen dat de nodige stroom en spanning aan de elektromotor moet leveren zodat deze voldoende vermogen kan opwekken om de SSV voort te drijven. Om onze stroomspanningskarakteristiek op te stellen hebben we ons zonnepaneel getest onder een lamp. Om af te sluiten hebben we nog een seminarie gehad over FabLab.

Week 3
We zijn deze week op zoek gegaan naar de juiste materialen en waar we deze kunnen kopen. Hier hebben we besloten om met plexiglas te werken (en dit in het FabLab te bewerken) en kogellagers en assen op maat te kopen. Verder zijn de eerste berekeningen van de weerstand die het autootje zal ondervinden theoretisch berekend. Deze zullen door de weken heen aangepast worden aan de juiste materialen en grootte van de SSV. Ook hebben we deze week bespreking gehad van onze WBS,Gantt chart en samenwerkingscontract. Over het algemeen waren deze in orde. Enkel bij de Gantt Chart moesten er nog wat aanpassingen gebeuren. Deze zal ook gedurende het verloop van het project aangepast worden.

Week 4
Deze week hebben we een bespreking gekregen over Simulink, een wiskundig modelleerprogramma dat we gebruiken om de gear-ratio te berekenen. Hier werd mee begonnen en de theoretische berekening werd ook verder gezet. Verder zijn we gestart met een houten model van de uiteindelijke SSV en is er een marktonderzoek in gang geschoten om te bepalen hoe ons SSV op de markt moet gebracht worden.

Week 5
In week 5 is het team verdergegaan op het werk dat in week 4 gestart en/of hervat werd: de theoretische en simulink berekening van de gear-ratio, het marktonderzoek en het verzamelen van materiaal voor de SSV.Verder werd er in het algemeen naar de eerste deadline toegewerkt.

Week 6
Deze week hebben we de definitieve berekeningen gemaakt, verder zijn we naar het fablab geweest om onze wielen & tandwielen uit te zagen. Hierdoor kunnen we ons prototype in MDF ontwikkelen. Bij onze berekeningen in simulink duiken nog steeds fouten op maar hier wordt verder aan gewerkt in de loop van de week. Hopelijk halen we de deadline.

Week 7
Deze week hebben we feedback gehad over SSV case part 1. Ons werk bleek maar net voldoende. Doordat we vrijdag nog steeds vastzaten met de berekeningen in Simulink is al onze tijd hieraan verloren gegaan. En hebben we het tussentijdse procesrapport te haastig moeten afwerken. De volgende week gaan we de fouten uit ons simulink programma halen. Verder hebben we ons prototype afgewerkt, hier zullen we eventuele obstakels tegen komen die we dan bij ons definitief model kunnen aanpassen. Zo zijn er al verschillende problemen opgetreden waar we hier niet op kunnen verder ingaan wegens privacy redenen. Verder gaan deze week de krachten op de as berekend worden. Hiervoor gebruiken we onze vers opgedane kennis uit de cursus sterkteleer.

Week 8
Vorige week zijn de uiteindelijke onderdelen uitgesneden in het fablab. Hierdoor kunnen we deze week ons autootje in elkaar steken en beginnen met de testen. Verder is er deze week nog gekozen voor een lichtere as, en wordt er getracht zoveel mogelijk gewicht te besparen om naar de 750gr te streven. De laatste loodjes worden ook aan simulink gelegd.

Week 9
Deze week konden we ons wagentje testen op de baan. Hier hebben we gretig gebruik van gemaakt om eventuele mankementen aan ons ontwerp te ontdekken en aan te passen. We waren zeer tevreden over onze tests, het wagentje deed er zelfs een paar tienden van een seconde sneller over dan wat ons model in simulink voorspelde.

Week 10
Maandagavond 2 mei kwam op Toledo te staan dat de race dinsdag ging doorgaan. Dinsdag ochtend werden er nog een paar aanpassingen gedaan en werden er ledjes ter afwerking van de wagen gemonteerd op de wagen. In de namiddag was de race, hier won team Raton hun eerste 2 races moeiteloos waardoor we in de kwartfinales kwamen. Ook deze kwartfinales wonnen we, jammer genoeg kregen we in de halve finales te maken met materiaalpech (Een gebroken tandwiel), waardoor we zonder overbrenging kwamen te zitten en genoege moesten nemen met een mooie 4de plaats van de 17 teams.

Week 11
Deze week moet het eindverslag afgewerkt worden, hiervoor zijn alle taken verdeeld en is iedereen bezig met de laatste loodjes aan het rapport te leggen.


text: File:Losses energy.png

title: File:Losses energy.png


text: File:WikipediaDisease.png

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