text:
User talk:Rukmini~enwikiversity

 Hello Rukmini, 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. To get started, you may

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The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

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Renamed
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title: User talk:Rukmini~enwikiversity


text:
User talk:Obadiah~enwikiversity

 Hello Obadiah, 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. To get started, you may

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Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Obadiah. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Obadiah~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

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

title: User talk:Obadiah~enwikiversity


text:
User talk:Alinai65

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title: User talk:Alinai65


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User talk:Guts r mine

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title: User talk:Guts r mine


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User talk:Blox0rz26526

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title: User talk:Blox0rz26526


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User talk:HellBelle

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title: User talk:HellBelle


text:
User talk:Thabonch~enwikiversity

 Hello Thabonch, 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. To get started, you may

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Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Thabonch. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Thabonch~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

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Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:45, 17 March 2015 (UTC)

Renamed
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title: User talk:Thabonch~enwikiversity


text:
User talk:Nuibb38

 Hello Nuibb38, 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. To get started, you may

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title: User talk:Nuibb38


text:
Motivation and emotion/Textbook/Motivation/Exercise

History
It was as early as 1890 when one of the forerunners in empirical psychology, William James, introduced discussion of the many aspects of motivation (Deci & Ryan, 1985). When intrinsically motivated, James theorised that an individual’s attention was drawn to a particular activity, therefore affecting the behaviour related with that activity. Although according to Deci and Ryan (1985), it was Woodworth in 1918 that discovered that an individual’s engagement in a particular activity can also be extrinsically motivated. Woodworth’s theory of extrinsic motivation appeared around the same time as non-motivational theorists Thorndike (1913) and Watson (1913) and therefore did not receive the attention it deserved. As a result of this there was limited research carried out in the following decades, and the research that was taking place was focussed on drive theory, which laid the foundations of Hull’s drive theory in 1943.

What is motivation?
Motivation is an instinctive characteristic displayed within every human. It makes us act upon our instincts to satisfy any need which is being felt at that particular time, whether it is getting a sandwich due to being hungry or by going for a run to satisfy your need to exercise. Motivation initiates our instincts and is a characteristic which allows us to undertake various tasks throughout life (Velez, 2008). Generally speaking, the term motivation describes the reason why a person does something, though it is much more complex than that as it involves many forces which affect our behaviour daily. These include aspects such as the cognitive, biological, social and emotional forces. According to Velez (2008) motivation may act as a fuel which inspirers us to set, compete in and achieve our goals to which we desire.

Motivation is what helps us achieve our goals to our fullest desires (Velez, 2008). There are many different components of motivation, though we can focus on three main points: foundation, determination and passion (Cherry, 2010). When talking about the foundation of motivation we are talking about a considered decision to initiate certain behaviours, such as playing for a sporting team and going to pre-season training. Determination at this task would be making your way to as many pre-season trainings as you are able and completing them. Attending these would further not only your fitness but also skills in your desired area of exercise, even though in doing this you are investing a considerable amount of time, effort and possibly money. Whilst passion can be seen as the concentration and effort that you are constantly putting into your training to better yourself in preparation for the season ahead. An example of this could be one member of the team casually appears at pre-season training when they desire, whilst on the other hand another member of the team does not miss a training, puts in his/her best efforts each and every time and therefore is one of the first picked for the team each week during the proper season.

Driving forces

There are two driving forces behind motivation, these being intrinsic motivation and extrinsic motivation. These two motivators are the reasons all tasks are completed by human beings. An intrinsically motivated task is one in which an individual performs for his/her own self satisfaction. It is an internal reward from engaging in that particular activity (Ryan, Frederick, Lepes, Rubio, & Sheldon, 1997). According to Deci and Ryan (1985) this type of behaviour is undertaken as a part of enjoyment, exploration and personal interest within which it does not require the use of a reinforcer to complete the behaviour/ activity.

Extrinsic motivation relies on reinforcers to be present as a direct result of participating in that activity or behaviour. These motivating forces arise outside of the individual and usually require a reward such as a trophy, money, stickers, and food, being praised and possibly socially recognition which is separate from the behaviour itself (Deci & Ryan, 1985). For example a person might go to a job they highly dislike and work for five hours, then at the end of their shift they are rewarded with a monetary amount that has previously been agreed upon.

What is exercise?
Regular exercise is extremely good for the human body contributing to many health and psychological benefits. These types of benefits include such things as a reduced risk of obesity, certain cancers, adult onset of diabetes, heart diseases, and most recent findings include it being linked to a reduced risk of metabolic syndrome (Wilson, Mack, & Grattan, 2008). Considering these facts it is astounding that in America alone it is found that over 50% of the adult population does not regularly exercise (Stevenson & Lochbaum, 2008).

In modern times exercise is also referred to as physical activity, and when one is engaging in this for a certain purpose it may be called physical fitness. Exercise itself is variable for each individual as some may only exercise to stay fit and healthy at a desired level, whilst others may need to exercise so that they are able to compete during physically taxing events (for example, elderly people may walk to stay physically active, whilst a younger person in training for the 100m at the Olympics would need to be much fitter and completing running/sprint training). Simply speaking, exercise is the movement of your body in a way that increases your intensity to a level you normally would not reach during your usual daily activity. The general aim of exercise is to achieve physical fitness as it raises your heart rate and works your muscles at a more intense rate (Glanville, 2009).

There are many different ways to exercise in today’s society, with all the gym equipment that is now ready available to all individuals. A few of the more common physical activities that people often engage in are walking, running, playing sports and dancing just to name a few. Although when you are thinking about exercising you should choose something that you enjoy and are likely to keep doing, therefore engaging in physical activity more often. If you choose to be physically active the activities you participate in must be considered challenging otherwise it just isn’t exercise.

Theories and research
There are many theories and common perceptions as to why people exercise and what motivates them to exercise. These theories cover both an intrinsic view of motivation, looking at the self-determination theory which was developed by Edward Deci and Richard Ryan at the University of Rochester and the incentive theory, which is based more upon the external rewards you may receive from exercise.

Self-determination theory
Self-determination theory (SDT) has been comprehensively researched and widely used by psychologists around the world. This theory was initially developed by Deci and Ryan during continuing research at the University of Rochester. The theory which was developed by Deci and Ryan mainly focuses on the importance that intrinsic motivation has on the driving forces of human behaviour. Self-determination theory shows a natural tendency towards the growth and development of individuals; however this does not automatically mean that these individuals will achieve (Deci & Ryan, 1985). When an individual is physically active, they show an increased psychological well being and sense of physical health, therefore living a healthy full life (Ryan, Williams, Patrick, & Deci, 2009). It is important to note that when being linked to physical activity or exercise, the most basic principles of SDT can be either intrinsically or extrinsically motivated. It is important to note that amotivation also has its role in SDT, as motivation has different subtypes which will be explained briefly below (Ryan et al.).

The term amotivation means ‘without motivation’ and therefore would generally not apply to SDT. Although when an individual takes part in physical activity there are many cases within which an individual may have absolutely no intention to act upon what is happening around him/her (Ryan et al., 2009). There may be many reasons for this as the person may lack the confidence to take part in the activity due to personal issues, prior experience or lack of skill to take part. Amotivation goes hand in hand with a sincere lack of self-determination by the individual (Wininger, 2006). Extrinsic motivation can be defined as taking part in an action or behaviour in order to gain a desired outcome which is completely separate from the activity itself (Deci & Ryan 1985). Extrinsic motivation is broken up into four subtypes of behavioural regulation: external, introjected, identified and integrated. External regulation is most commonly linked to operant conditioning within which it is stated that it is the least self-determined form of extrinsic motivation (Wininger, 2006). Introjected regulation refers to behaviours that are partially internalised, yet are not fully self-determined. Identified regulation refers to tasks which are performed under no pressure due to the fact that they are personally valued and relatively self-determined. Whilst finally, identified regulation is the most self-determined for of extrinsic motivation as the behaviour or action is taking effect as a personal choice (Thogersen-Ntoumani & Ntoumani, 2006). As a perspective of SDT, intrinsic motivation involves an individual’s ability to deeply understand and engage in activity using a variety of skills that one possesses (Ryan, Williams, Patrick, & Deci, 2009). Intrinsic motivation is a more common factor in SDT as it is associated with the individual who is engaging in the activity. Individuals may be participating for internal reasons such as enjoyment rather than focussing on the outcome that may take effect as a result of the exercise being done (Thogersen-Ntoumani & Ntoumani, 2006). Self-determination theory plays a large part in human beings engaging, continuing and achieving during physical activity. This has been found to be a very effective theory and tool when looking at what motivates people to exercise. Self-determination is a driving force behind all exercise or physical activity that individuals engage in, whether it is on a regular basis or not. It has the ability to help us sustain physical fitness and to compete at elite levels or to the level in which an individual so desires. To be intrinsically motivated and self-determined to further engage and participate in exercise or physical activity helps us gain greater self satisfaction and healthy well-being.

Incentive theory
The incentive theory of motivation is more focussed upon the external rewards offered to individuals upon completion of a task. In today’s society there are many reasons why incentives are offered to people. For example, an individual has no interest in exercising, though when offered a chocolate bar upon completion of the exercise they decide this is good enough incentive to engage in the phsy6ical activity. This is considered to be a primary reinforcer (Stevenson & Lochbaum, 2008). Although there are also secondary reinforcers, as the individual may be participating in the activity as a burning desire to fulfil an internal drive for that activity. Although the ultimate goal for this activity is to receive a medal or trophy of some description. An example may be a person that trains for eleven months of the year and plays in the AFL, the ultimate goal here is to be successful in winning the AFL (or local league) grand final and receive a trophy.

Summary
What motives each individual plays a large role in the reasons behind why we exercise or why we do not exercise. There are many theories that discuss this topic, though the theories of self-determination and incentive theory seem to be the most effective. An individual can be extrinsically motivated to take part in exercise or physical activity, although it is linked with a lower self satisfaction level upon the completion of that activity (Ryan et al., 2009). Self-determination theory shows the link between intrinsic motivation and the need for self satisfaction, displaying that intrinsic motives for exercise or physical activity are more beneficial in terms of health and well-being for an individual (Ryan et al., 2009). Self determination requires an individual to be free from all pressures and future rewards, therefore having the ability to be free from all control and therefore being intrinsically motivated creating a greater sense of self satisfaction. When talking about physical activity or exercise the link between intrinsic and extrinsic motivation is extremely relevant. In either motivational case an individual is involved in exercise; however, their reasons for this engagement may be completely different. For example an individual may be extrinsically motivated to engage in physical activity looking at the incentive or reward at the end of the day, therefore, it is possible that they are focussing on simply wanting to look good for others. Whilst on the other hand an individual can also be intrinsically motivated and it is their internal forces that are driving them to engage in physical activity, showing and focussing on their own individual will and need to stay physically fit and healthy (Ryan, Williams, Patrick, & Deci, 2009). {{Hide in print|


text:
User:Egm6321.f10.team3.roark/HW1

This is my HW1 sandbox. Thanks!

$$\sqrt{b^{2}-4ac}$$

$$f(x)=\dot{Q}\left( z \right)$$

title: User:Egm6321.f10.team3.roark/HW1


text:
User:Patmcgervey~enwikiversity

Patrick Joseph McGervey, M.A., M.Ed. Avon Lake, Ohio USA

title: User:Patmcgervey~enwikiversity


text:
User talk:Patmcgervey~enwikiversity

 Hello Patmcgervey, 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. To get started, you may

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The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Patmcgervey. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Patmcgervey~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

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title: User talk:Patmcgervey~enwikiversity


text:
Talk:International Relations/The Gulf War

Discussion
This conflict makes me angry.
 * What is the scope of this page? The gulf war of the early 90s or events since 2003?


text:
User talk:Robinjos~enwikiversity

 Hello Robinjos, 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. To get started, you may

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Biographies
If you want to write a personal biography, please keep it to User:Robinjos and not in mainspace. Ottava Rima (talk) 17:47, 6 September 2010 (UTC)

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The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

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 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 06:20, 19 April 2015 (UTC)

title: User talk:Robinjos~enwikiversity


text:
User talk:Youngjinmoon

 Hello Youngjinmoon, 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. To get started, you may

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title: User talk:Youngjinmoon


text:
User:Egm6321.f10.team2.zou

Xiangyu "Louis" Zou

HW1

HW2

Problem with Mtg14

HW3

HW4

HW5

title: User:Egm6321.f10.team2.zou


text:
User talk:EGM6321.f10.team6.cook

 Hello EGM6321.f10.team6.cook, 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. 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.

 * 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.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Ottava Rima (talk) 21:25, 6 September 2010 (UTC)

title: User talk:EGM6321.f10.team6.cook


text:
University of Canberra/Wikis for research

Here logs the workshops on using Wikiversity for research at the University of Canberra

7 September 2010
Time: 10am, 7 September 2010 Location: University of Canberra, Building 10, level A, Room 10A24 Sponsor: University of Canberra Research Office

This is a handout to support an introductory workshop on using wikis for research. The workshop runs for 1 hour, and has 3 parts:

 * 1) 20 minute show and tell. Looking at Wikispaces and MediaWiki as used by the Wikimedia Foundation projects. Focus will be on Wikipedia, Wikibooks and Wikiversity, including the governance and etiquette of those projects.
 * 2) 20 minute how to. Creating a user page on Wikiversity. Creating a sub page to a user page. Adding links. . Talk pages. Exporting
 * 3) 20 Minute discussion

Participants

 * 1) Guifang Shang 01:07, 7 September 2010 (UTC)
 * 2) Ahmed10 01:09, 7 September 2010 (UTC)
 * 3) Carolyn Page 01:10, 7 September 2010 (UTC)
 * 4) Jackychen 01:11, 7 September 2010 (UTC)
 * 5) Hoangpham 01:12, 7 September 2010 (UTC)
 * 6) Joelle Vandermensbrugghe 01:13, 7 September 2010 (UTC)
 * 7) Franky manumpil 01:15, 7 September 2010 (UTC)
 * 8) Felicityrai 02:12, 8 September 2010 (UTC)

Recent activity on participant User pages
category=University of Canberra/Wikis for research order=descending ordermethod=lastedit mode=unordered shownamespace=true

See also: Special:Recentchangeslinked/University of Canberra/Wikis for research


text:
User:Egm6321.f10.team5.steinberg

Given
The vehicle component equation of motion for a Maglev train is represented by a second-order nonlinear partial differential equation (Eq. 2.5e).

The coefficient for the second-order term is defined as follows (assuming $$ I_w = 0 $$):

$$ C_3(Y^1,t) := M \left [ 1 - \bar{R} u,_{SS}^2 (Y^1,t) \right ]^2 $$

Find
Show that $$ C_3 \! $$ is non-linear with respect to $$ Y_1 \! $$.

Solution
If the coefficient $$ C_3 \! $$ is linear, it must satisfy both properties of homogeneity and additivity.

Homogeneity $$ \Rightarrow C_3(\alpha Y^1,t) = \alpha C_3(Y^1,t) $$, where $$ \alpha \! $$ is an arbitrary constant.

$$ C_3(\alpha Y^1,t) = M \left [ 1 - \bar{R} u,_{SS}^2 (\alpha Y^1,t) \right ]^2 = M \left [ 1 - \alpha \bar{R} u,_{SS}^2 (Y^1,t) \right ]^2 \not= \alpha M \left [ 1 - \bar{R} u,_{SS}^2 (Y^1,t) \right ]^2 $$

$$ C_3(\alpha Y^1,t) \not= \alpha C_3(Y^1,t) $$

Since $$ C_3 \! $$ is not homogeneous, it is therefore nonlinear with respect to $$ Y_1 \! $$.

title: User:Egm6321.f10.team5.steinberg


text:
User:Guifang Shang

Hello, do you want to know more about Ross River virus pathogenesis? Now try to use Wikitalk to communicate. Now I am 10A24 to learn how to use wiki. =introduction= University of Canberra

GUI

Mtg 5

Bloom Clock/Keys/Global/Temperate/Late Spring/Brown Flowers/DPL

Technical writing AlistairRomeoExercise

=project=
 * /Learning to learn a wiki way/

=interest= http://en.wikipedia.org/wiki/Cheat_sheet

=methods= =conclusions= =participants= Carolyn Page

title: User:Guifang Shang


text:
User:Hoangpham

Hoang is a PhD student at University of Canberra, Australia. He teaches at Ho Chi Minh City University of Pedagogy, Vietnam.

=Interests=
 * English Basics 101 q1 clicked2

 * Bloom Clock/Keys/Southeastern Pennsylvania/June/Yellow Flowers

 * Leigh Blackall

 * /The use of humour in EFL teaching/

=Wishes=

For others
=Likes=

=Dislikes=

title: User:Hoangpham


text:
User:Joelle Vandermensbrugghe

Joelle Vandermensbrugghe works at the University of Yangon, supporting academics and researchers. Previously she worked at University of Canberra, supporting research students to acquire skills to do and present research.

=interests= Research design, research methodologies

Communicating research

Media representations

Cross cultural communication

title: User:Joelle Vandermensbrugghe


text:
User:Carolyn Page

Carolyn lives at The Angle in New South Wales, Australia. She is a retired teacher and education policy analyst. She is completing a PhD at the University of Canberra

=Interests=

Online learning
Current work by Leigh Blackall on online learning is interesting. His research is saved in his Wikiversity site and others can comment on it or correct it.

At the University of Canberra, Joelle Vandermensbrugghe has provided a variety of ways for the research student community to participate in an online learning community.

=Projects= /Talking about change/

Useful links
Wikipedia Cheat Sheet

title: User:Carolyn Page


text:
User:Ahmed10

This is Ahmed Ullah, a Ph.d student at the faculty of Business and Government, university of canberra =Introduction= University of Canberra =World Poverty= Research Proposal In Quest of Pro-Poor Public Spending Multiplier: A Case Study of Bangladesh

Submitted To Dr. Muni Perukmal School of Business and Government University of Canberra

Submitted By Ahmed Ullah ID # u3033710

Introduction Poverty is a global phenomenon. No matter where we go, individuals living in absolute poverty will never be far away. Although the number of people living in extreme poverty fell from 1.9 billion in 1981 to about 1.4 billion in 2005, this significant reduction in poverty disguises large regional differences. Millions of people still trapped in poverty and most of them are from Sub-Saharan Africa and South Asia. Governments of these countries, along with the international community, have made poverty alleviation a top priority in their development strategies. The United Nations set the first target of Millennium Development Goals (MDGs) to halve the proportion of people in extreme poverty, between 1990 and 2015 (WorldBank, 2010b). Agenor (2005 p-370) comments that, based on current trends, sub-Saharan Africa and Asia as a whole will not be able to reduce poverty by half between 1990 and 2015. Bringing relief to the poorest part of the world therefore remains one of the central policy issues of the new millennium, he added. Economic theory and different studies (discussed in the next part) suggest that government spending has a seminal effect on growth as well as poverty reduction. The concept of public spending/purchase multiplier in particular, suggest that how much income rises in response to a one dollar increase in government spending. According to the Keynesian cross, the government-spending multiplier is larger than one that means if government increase its spending by one dollar, citizens’ income will raise more than one dollar (Mankiw, 2003 p-262). But if inequality increased along with per capita income growth, it is possible for the world to have witnessed both positive per capita GDP growth and an increasing number of people below the poverty line. So the concept of pro-poor growth is introduced by different academics (like sala-i-martin, agenor) and development institutions (like World Bank, Asian Development Bank etc.) The Poverty Reduction Strategy (ADB 1999, 6) proposes that “growth is pro-poor when it is lobor absorbing and accompanied by policies and programs that mitigate inequalities and facilitates income as well as employment generation for the poor, particularly women and other traditionally excluded groups”. The government of developing nations is spending a huge amount of local as well as foreign currency every year (sourced as loans and grants and from developed country and donor agencies) in the name of development or poverty reduction. But as discussed earlier, this spending does little to the poor from getting out of poverty. So this research project broadly tries to study the nature of public spending and its impact on poverty reduction in developing countries. In particular, the case of Bangladesh will be examined with a objective to find out the pro-poor public spending multiplier (public spending benefited the poor section of the society to a larger extent). The reason for selecting Bangladesh as a sample of developing countries is explained in the methodology part of this proposal. Literature Review Sala-i-martin (2004) claims that economic growth is the single most important factor affecting individual levels of income. He further states that, greater understanding of how to increase the standards of living of individuals in the world and, thereby, lessen world poverty is of high importance. But Sala-i-martin (2004) also cautions that, although the average person on the planet has been getting richer over time, this does not mean that the income of all citizens has increased. In particular, it does not mean that the incomes of the poorest people have grown or that the number of people whose incomes are below a certain poverty line (for example, 1.25 dollars a day) has declined. Gasparini et al., (2007) support this comment as follows “the concern for pro-poor growth is in part the consequence of evidence showing that in some countries the fruits of economic growth were not equally shared by all the population, and, more worrisome, evidence that in some growth episodes the well-being of the poor actually decrease”. Mody and Pattillo (2006) argues that, in principle, poverty reduction occurs through two channels: first, growth raises average incomes and, hence, reduces poverty; second, poverty is reduced even more when the rise in incomes especially benefits the poor. The second channel can be marked as pro-poor. Theoretically the poverty reduction can be achieved either by increasing the average income or through redistribution mechanism via taxation and transfer payment. However, Lopez Groth (2004) thinks that, it is difficult to reduce poverty only by the redistribution policies in the absence of economic growth (or rise of per capita income). Poverty reduction through redistribution is also politically unpopular and administratively difficult. So for every government it is comparatively easier and practical to set some poor specific program aimed at poverty reduction. To make the economic growth pro-poor, principal responsibility borne by government. Because of the characteristics of non-rivalness and non-exclusiveness, ‘Poverty reduction’ can be tagged as a public good and usually private sector is not interested to do anything in this area. Aart kraay (2004) argues that, “ in the medium run, most of the variation in changes in poverty is due to growth, suggesting that policies and institutions that promote broad-based growth should be central to pro-poor growth”. Agenor (2002) explains that the policy changes in tax structure, spending, transfers, or subsidies, increases in prices of publicly provided services or reductions in public sector employment or real wages (fiscal policy)– can have both direct and indirect effect on income distribution. But Rosen (2005 p-165) remarks ‘Although there is a strong consensus among the economists and policy makers all over the world that government should help the poor, there is also enormous controversy over what form such help should take’.

In the ‘Poverty Reduction Strategy for Bangladesh’ Barakat et al., (2009) comments that ‘Quality rate of growth is one that creates demand for the labor supplied by the poor and expands demand for the products and services produced by the poor people. …. government efforts need to focus on increasing the availability education, training facilities and healthcare to all poverty stricken groups. Another way to enhance market access for the poor, specially, those who are unable to participate in the local market is to develop infrastructures such as roads and communication’.

From a theoretical standpoint, the issue of the impact of government activity on economic performance has been a controversial one. There is no uniformly accepted theory that predicts a clear-cut relationship between the size of government (in terms of spending) and economic activity. A voluminous literature has developed over the years in search for empirical linkages between economic performance and a variety of fiscal policy variables, including government spending.

The recent interest in the impact of public investment on economic activity has stimulated by Aschauer's (1989a, b) provocative empirical work revealing a large positive impact of the stock of public capital on private sector total factor productivity. If Aschauer's estimates are accurate, the policy implication is obvious: governments can stimulate productivity by investing in infrastructure. Easterly (1993) finds public investment in transport and communication to be positively related to growth. But, Devarjan (1996) finds the result is speculative and depends, among other things, the sample used. While Bose (2003) finds that total and investment expenditure on education raise growth in developing countries. In one of the seminal contributions to endogenous growth theory, Borro (1990) awarded fiscal policy a central place. Other authors (Romer, 1990, Lucas, 1988, Azariadis, 1990) have stressed the importance of externalities to argue the government has an important role to fulfill in the growth process. In a generic model, Zagler (2003) has shown that the various engines of growth in the endogenous growth literature are closely connected with different categories of the government budget. Mankiw (2003) comments that, when the government changes its spending or the level of taxes, it affects the demand for the economy’s output of goods and services and alters national saving, investment, and the equilibrium interest rate

In sum, a vast literature, has been developed to trace the empirical linkages between government expenditures and economic performance. The studies mentioned above are only a sample from this literature. However, the diverse results obtained in these studies suggest that, at present, the empirical record is mixed and inconclusive. Moreover, these studies do not tell us anything about whether the achieved growth is pro-poor or not. This research project will seek to find out the sectors which are pro-poor, that means, spending which benefited the poor section of the society more than the rich.

Objective of the Research The relationship between economic growth and poverty alleviation is not automatic. To achieve the Millennium Development Goals (MDGs) robust economic growth is essential but not sufficient. The financial allocation of resources among the sectors is the crucial role of the government to achieve simultaneous goal of economic growth and poverty reduction. Public spending in some sectors will generate substantial economic growth while spending to other contributes of poverty reduction. Again, there are some sectors which can affect both economic growth as well as poverty reduction (Barakat et al., 2009). So, the overall objective of the study is to investigate more effective ways of resource allocation for improved economic performance and attaining the Millennium Development Goal (MDGs) of poverty reduction in developing countries. Research Question Is growth really pro-poor in developing countries like Bangladesh? If so then how robust the affect of public spending in physical infrastructure like roads, bridges and social infrastructure like health, education on poverty rate in Bangladesh? Methodology Guba and Lincoln (2004) comment that, the ontological, epistemological and methodological questions must be addressed in order to determine whether research should follow a qualitative or quantitative methodology. They suggest developing and inquiry a research paradigm by asking ontological question of what ‘reality’ is and what can be known about “reality’. They propose ‘Positivism’ in the first place, where a simply reality is assumed governed by natural laws; knowledge is context free and controlled by cause and effect laws (p-112). Guba and Lincoln (2004) continues, an objectivist or positivist ontological position requires an objective form of knowledge, to measure relationships precisely using a quantitative methodology of research (p-117). Under Guba and Lincolon (2004) positivist paradigm of ‘reality’ the researcher can research the object of inquiry without impact and set research procedures are followed to eliminate bias; repetition produces the same result. They argue, the research methodology for positivist paradigm involves empirical analysis to test stated hypothesis. The conditions of the experiment are controlled to prevent bias. But Carter and Little (2007) remark, ‘researchers might object that they are not, or do not wish to be, methodologists or epistemologists. They do research. They generate useful findings. Nothing further is necessary’. Although they also argue, the researcher’s epistemological position and the methodology are shaped by the discipline in which she or he is trained or has read and the formal theories of knowledge the researcher has read. Guba and Lincoln (2004) express their view that scientific research in the field of mathematics, physics and chemistry has been dominated by a need to quantify hypotheses using mathematical formulas in order to predict and control natural phenomena. They added, this quantification is widely believed necessary for the validity and legitimacy of findings. Although economics is marked as a discipline as social science, it is frequently using the mathematical and statistical tool to prove or disprove theories. So it can be believed that the comments from Guba and Linclon (2004) is equally applicable for the discipline of economics too. As economists are regularly interested in relationships between different quantities and traditionally econometrics has focused upon aggregate economic relationships, Verbeek (2008, p 1-2) claims that the most important job of econometrics is to quantify these relationships on the basis  of available data and using statistical techniques, and to  interpret, use or exploit. In particular, Haughton and Khandker (2009) explain, when anyone want to monitor and evaluate the effects of specific policies (like public spending) on poverty, it is necessary to measure how poverty changes over time. They go on with: changes in poverty rates are typically based on comparisons of cross-sectional data. Although panel data has the advantage of paired test ( analysis the same person or household over time), it has also the drawback of attrition bias, as respondents gradually drop out of the panel; they may become less representative over time of the population they are supposed to reflect and they require considerable managerial skills and expense. On the other hand, a single cross-sectional survey can provide a snapshot of poverty at one point of time. It does not allow one to track the evolution of a household’s poverty over time (Haughton and Khandker, 2009). Thus, information on the “dynamics of poverty” is needed to monitoring and evaluating the effect of a specific policy on poverty, for example, public spending on infrastructure (Haughton and Khandker, 2009). They added, ‘The most common way that poverty is tracked is by using the results from two or more household surveys over time. To allow for comparisons over time, the questions need to be comparable in each wave of the survey’. Accordingly to examine the effect of public spending on poverty, the secondary data of two Household Income and Expenditure Survey (HIES) of 1995 and 2005 of Bangladesh Bureau of Statistics (BBS) and public spending data of Bangladesh from the Asian Development Bank (ADB, 2010) statistics website which will provide central government expenditure by function like education, health, infrastructure (transport and communications), and electricity, gas and water can be used. To be free from the estimation bias all time series public spending figure will be adjusted with the then inflation. The reason to select Bangladesh as my research field is that it represents a success story in poverty alleviation among developing countries. Poverty incidence, which was as high as 57 percent at the beginning of the 1990s, had declined to 49 percent in 2000. This trend accelerated subsequently, reducing the poverty headcount rate to 40 percent in 2005. However, nearly half of the population remains poor and per capita GDP (PPP) remains extremely low at $1400 in 2009 (IMF). The inequality is quite high; the lowest quintile of households has only 0.92 per cent of the income, the Gini coefficient being 31 per cent in 2008. So, Bangladesh simultaneously represents a success as well as not a success story in poverty alleviation among developing countries. Second reason for selecting Bangladesh is that as a Bangladeshi citizen as well as civil servant of Bangladesh Government, I have some special access to the government and different development institutions. Moreover I have good knowledge of my own country’s social and political culture, administrative structure, development program implementation process etc. Chen and Ravallion (2008, p-2) think that, in assessing the extent of poverty in a given country one naturally uses a poverty line which is considered appropriate for that country. But before thinking about the poverty line it is necessary to fix the measure of well being. There are two competing variable, one is income and other is consumption/expenditure. According to Deaton & Zaidi (2002), consumption is not closely tied to short-term fluctuations in income, and that consumption is smoother and less variable than income. They added, especially in developing countries, where the rural agriculture sector is large, it is difficult to gather accurate income data. Bangladesh Bureau of Statistics (BBS) uses consumption variable, specifically Cost of Basic Need (CBN) method to derive the poverty line and subsequently the headcount ratio of poverty. With the CBN method, poverty lines represent per capita consumption expenditure at which the members of a household can be expected to meet their basic needs (food and non-food consumption). A household with per capita consumption expenditure falling below a given poverty line will be considered poor. So, with the first set of regression, the relationship of average income of the people and consumption of the poor people (i.e consumption of the people below the poverty line) will be examined. If this regression proves a strong relationship between the independent and dependent variables it can be said that the growth is pro-poor. This is almost the same methodology used by Dollar and Kraay (2002) and  Wodon (1997), but here the variable poverty headcount ratio is used as a dependent variable ( they use the average income of the lowest quintile of the population). If the relationship between the independent and the dependent variable found to be statistically significant it can be concluded that growth is pro-poor. In their study Dollar and Kraay (2002,4) concludes, ‘policies that raise average incomes are likely to be central to successful poverty reduction strategies’. Haughton and Khandker (2009) comments, these might include improvements in education, health, infrastructure, and the like. But Dollar and Kraay (2002, 27) also comment that, ‘existing cross-country evidence….provides disappointingly little guidance as to what mix of growth-oriented policies might especially benefit the poorest in society’. So in the second set of regressions, poverty headcount ratio will be used as a dependent variable and the independent variables are public spending in the four sectors namely: health, education, transport & communication and electricity, gas, and water. But this is not the definitive set of calculations; as the research project goes on it might  exclude some variables, include others or change the model, putting some dummy variable (for example to differentiate the poverty rate between the urban and rural areas or poverty between male and female) etc. The most common criticisms regarding regression analyses involve the choice of econometric method, the problem of unit roots (non-stationarity) usually found in economic series, the problem of omitted variables and, most importantly, the possibility of reverse causation”; the latter refers to the possibility that it may be strong output and productivity growth that lead to higher public investment in infrastructure, rather than the other way around". Overall, in the words of Ford & Poret (1991) "the regression results suggest that the numerical estimates of the effect of infrastructure on productivity are not robust enough to support a policy recommendation of a sharp acceleration of infrastructure investment".

Prospective Outcome of the Research As Bangladesh has the Vision-2021 to a substantial reduction of poverty to 14 per cent from about 36 per cent (in 2008-09), this study will help the Government of Bangladesh to achieve the target by discovering the path of quality economic growth that ultimately help to reduce the rate of poverty at a faster rate. It is expected that the study will also generate useful knowledge on public spending policy/strategy which accelerate the poverty reduction in the developing countries. Important findings also help the development partner like different development nations and World Bank, IMF. ADB etc

Bibilography

AART, K. (2004) "When Is Growth Pro-Poor? Cross-Country Evidence.". IMF Working Paper, 4. ADB, A. D. B.-. (1999) Fighting poverty in Asia and the Pacific: The Poverty Reduction Strategy. ADB, A. D. B. (2010). AGENOR, P.-R. (2002) Maxroeconomic Adjustment and the Poor: Analytical Issues and Cross-Country Evidence

AGENOR, P.-R. (2005) The Macroeconomics of Poverty Reduction. Centre for Growth and Business Cycle, University of Manchester, 73. AZARIADIS, C. A. D., A. (1990) Threshold externalities in economic development. Quarterly Journal of Economics. AZARIADIS, C. A. D. & GASPARINI, L. BARAKAT, A., AHMED, A. K. M.-W. U. & KHAN, S. (2009) Financing Growth and Poverty Reduction: Policy Challenges and Options in Bangladesh. General Economic Division, Planning Commission, Ministry of Planning. BARRO, R. J. & SALA-I-MARTIN, X. (2004) Economic Growth, Cambridge, Massachusetts, The MIT press. BORRO, R. (1990) Government spending in a simple model of endogenous growth. Journal of Political Economy, 98

BOSE, N., HAQUE,M. AND OSBORN, D. (2003) Public expenditure and economic growth: a disaggregated analysis for developing countries. Discussion Paper, 30. CARTER, S. M. & LITTLE, M. (2007) Justifying Knowledge, Justifying Method, Taking Action: Epistemolgies, Methodologies and Methods in Qualitative Research. Qualitative Health Research, 17. CHEN, S. & RAVALLION, M. (2008) The Developing Wourld Is Poorer Than We Thought, But No Less Successful in the Fight aganinst Poverty. Policy Research Working Paper. DEATON, A. & ZAIDI, S. (2002) Guidelines for Constructing Consumption Aggregates for Welfare Analysis. LSMS Working Paper, World Bank. DEVARAJAN, S., SWAROOP, V AND ZOU, H. (1996) The composition of public expenditure and economic growth. Journal of Monetary Economics, 37. DOLLAR, D. & KRAAY, A. (2002) Growth Is Good for the Poor. Jouranal of Economic Growth. EASTERLY, W. A. R., S. (1993) Fiscal policy and economic growth: an empirical investigation. Journal of Monetary Economics. GASPARINI, L., GUTIERREZ, F. & TORNAROLLI, L. (2007) GROWTH AND INCOME POVERTY IN LATIN AMERICA AND THE CARIBBEAN: EVIDENCE FROM HOUSEHOLD SURVEYS. GUBA, E. G. & LINCOLN, Y. S. (1994a) Competing Paradigm in Qualitative Research. GUBA, E. G. & LINCOLN, Y. S. (1994b) Competiting Paradigm in Qualitative Research. GUBA, E. G. & LINCOLN, Y. S. (2004) Competing Paradigms in Qualitative Research. Handbook of Qualitative Research. Thousand Oaks, CA: Sage. HALCOUSSIS, D. (2005) Understanding Econometrics, Mason, Ohio, USA, South-Western, Thomson. HAUGHTON, J. & KHANDKER, S. R. (2009) Handbook on Poverty+Inequality, The World Bank. LOPEZ GROTH, C. (2004) Some derivations in the Alesina & Rodrik(1994) Model. . Department of Economics, University of Copenhagen

LUCAS, R. (1988) On the mechanics of economic development. Journal of Monetary Economics. MANKIW, N. G. (2003) Macroeconomics, New York, Worth Publishers. MODY, A. & PATTILLO, C. (2006) Macroeconomic Policies and Poverty Reduction, New York, Routledge. ROMER, P. (1990) Endogenous technological changes. Journal of Political Economy, 98. ROSEN, H. S. (2005) Public Finance, NewYork, McGraw-Hill. SALA-I-MARTIN (2003) The World Distribution of Income, 1970-2000. The University of Columbia. SALA-I-MARTIN, R. J. B. X. (2004) Economic Growth, Cambridge, Massachusetts, The MIT press. VERBEEK, M. (2008) Modern Econometrics, West Sussex, England, John Wiley & sons Ltd. W.L.NEUMAN (2003) Social Research Methods: Qualitative and Quantitative Approaches. Boston, Pearson Education. WORLDBANK (2010b) http://devdata.worldbank.org/atlas-mdg/. ZAGLER, M. A. S., G. (2003) Fiscal policy and economic growth. Journal of Economic Survey.

=Poverty in Bangladesh= Education Media Current page by Leigh Blackall
 * /Research Methodology/

title: User:Ahmed10


text:
User:Jackychen

I am jacky, interested in wiki-kongfu.

This workshop is lead by leighblackall.

=Introduction= University of Canberra

User:Guifang Shang Guifang

Wiki Campus Radio

=Interests=

=Projects=

Past
=Research= There will be many exciting projects coming up soon. Keep in tune!
 * /Wiki-Taichi/

title: User:Jackychen


text:
User:Rolandgoecke

Roland is an Assistant Professor of Software Engineering at the Faculty of Information Sciences and Engineering at the University of Canberra. I am also the head of the Vision and Sensing Group.

=Research Interests= My research interests are at the intersection of affective computing, computer vision, pattern recognition, human-computer interaction, image processing, multimodal signal processing and eResearch. See my personal homepage for further details.

title: User:Rolandgoecke


text:
User talk:Rolandgoecke

Wikis for research

 Hello Rolandgoecke, 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. 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.

 * 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.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Ottava Rima (talk) 00:54, 7 September 2010 (UTC)

title: User talk:Rolandgoecke


text:
User talk:Jackychen

Wikis for research

 Hello Jackychen, 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. 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.

 * 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.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Ottava Rima (talk) 00:54, 7 September 2010 (UTC)

title: User talk:Jackychen


text:
User talk:Ahmed10

Wikis for research

 Hello Ahmed10, 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. 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.

 * 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.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Ottava Rima (talk) 00:54, 7 September 2010 (UTC)

title: User talk:Ahmed10


text:
User talk:Carolyn Page

Wikis for research

 Hello Carolyn Page, 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. To get started, you may

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title: User talk:Carolyn Page


text:
User talk:Joelle Vandermensbrugghe

Hello from Felicity
Thanks for all your help Joelle. With the assistance of Leigh Blackall I have now caught up with the other Wikis for Research group. Best, Felicity--Felicityrai 02:19, 8 September 2010 (UTC)

Wikis for research

 Hello Joelle Vandermensbrugghe, 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. To get started, you may

 * Take a guided tour and learn to edit.
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 * 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.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Ottava Rima (talk) 00:54, 7 September 2010 (UTC)

title: User talk:Joelle Vandermensbrugghe


text:
User talk:Hoangpham

Wikis for research

 Hello Hoangpham, 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. To get started, you may

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And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Ottava Rima (talk) 00:54, 7 September 2010 (UTC)

title: User talk:Hoangpham


text:
User talk:Guifang Shang

Wikis for research

 Hello Guifang Shang, 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. To get started, you may

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 * 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.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Ottava Rima (talk) 00:54, 7 September 2010 (UTC)

title: User talk:Guifang Shang


text:
User:Franky manumpil

=Interests=

=Projects= University of Canberra Gui

Current
Current work by Guifang Shang I am working.

Past
I worked.

=Research= /Wikis for research/

title: User:Franky manumpil


text:
User:Egm6321.f10.team3.franklin/Hwk1

= Problem 3 - Linearity Test of Maglev Train EOM Coefficient =

Given
$$\displaystyle C_3$$ from the Maglev Train EOM is defined as

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

C_3(Y^1,t) \triangleq M\left [\left( 1-\bar Ru^2,_{ss}\left(Y^1,t\right)\right)\right]^2 $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 1)
 * }
 * }

Find
Using the definition of linearity of a function, show that $$\displaystyle C_3$$ is nonlinear, with respect to $$\displaystyle Y^1$$.

Solution
A linear function is a function which obeys the two functions below. $$\displaystyle H$$ is an arbitrary function while $$\displaystyle c$$ is an arbitrary constant.

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

H(cx) = cH(x) $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 2)
 * style= |
 * }

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

H(x+y) = H(x) + H(y) $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 3)
 * style= |
 * }

In order for $$\displaystyle C_3(Y^1,t)$$ to be linear, the following equation must be true.

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

$$
 * $$\displaystyle C_3(cx,t) = cC_3(x,t)$$
 * $$\displaystyle (Eq. 4)
 * $$\displaystyle (Eq. 4)
 * style= |
 * }

Applying the cumulative property to (Eq. 1) gives us

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

$$
 * $$\displaystyle C_3(cx,t) = M\left [\left( 1-\bar Ru^2,_{ss}\left(cx,t\right)\right)\right]^2.$$
 * $$\displaystyle (Eq. 5)
 * $$\displaystyle (Eq. 5)
 * style= |
 * }

Let us assume the function $$\displaystyle u^2,_{ss}$$ is linear, (Eq. 5) becomes

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

$$
 * $$\displaystyle C_3(cx,t) = M\left [\left( 1-c\bar Ru^2,_{ss}\left(x,t\right)\right)\right]^2.$$
 * $$\displaystyle (Eq. 6)
 * $$\displaystyle (Eq. 6)
 * style= |
 * }

Now we evaluate the right half of (Eq. 4)

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

$$
 * $$\displaystyle cC_3(x,t) = cM\left [\left( 1-\bar Ru^2,_{ss}\left(x,t\right)\right)\right]^2.$$
 * $$\displaystyle (Eq. 7)
 * $$\displaystyle (Eq. 7)
 * style= |
 * }

Since

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

$$
 * $$\displaystyle C_3(cx,t) \not= cC_3(x,t),$$
 * $$\displaystyle (Eq. 8)
 * $$\displaystyle (Eq. 8)
 * style= |
 * }

$$\displaystyle C_3(Y^1,t)$$ is nonlinear because it did not meet the linearity test of a function.

=Problem 4=

Hello, I am Hong SJ.. First of all, I am so sorry, gentlemen.. Please, be tolerant the fact that I post this on the wiki page. I am supposed to take problem 4 & 5.. My solution for #5 is almost same with Sudheesh's. However, my solution for #4 is different from the solution posted this wiki page... (I am sorry, I just found it...)

As you know, we do not have time to hold a meeting for this because the deadline for HW1 is tomorrow. That's why I should post my solution for #4 on this page in haste before the deadline. I think we should recheck this problem (#4), even if I am not sure whether my solution is correct, or not..

Here is my solution...

Given

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

$$ y \left( a\right) =  \alpha $$
 * style="width:95%" |
 * style="width:95%" |
 * }
 * }

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

$$ y \left( b\right) =  \beta $$
 * style="width:95%" |
 * style="width:95%" |
 * }
 * }

Find
Find $$c,d$$ in terms of $$\alpha$$ and $$\beta$$

Solution
y(x) was defined as the following.

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

$$ y \left( x\right) =  c {y}^{1}_{H}\left( x\right) + d {y}^{2}_{H} \left( x\right) + {y}_{p} \left( x\right) $$ $$
 * style="width:95%" |
 * style="width:95%" |
 * $$\displaystyle
 * }

Apply given factors, y(a) & y(b) to y(x)

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

$$ y \left( a\right) =  c {y}^{1}_{h}\left( a\right) + d {y}^{2}_{h} \left( a\right) + {y}_{p} \left( a\right) $$ $$
 * style="width:95%" |
 * style="width:95%" |
 * $$\displaystyle
 * }

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

$$ y \left( b\right) =  c {y}^{1}_{h}\left( b\right) + d {y}^{2}_{h} \left( b\right) + {y}_{p} \left( b\right) $$ $$
 * style="width:95%" |
 * style="width:95%" |
 * $$\displaystyle
 * }

If we multiply {y}^{1}_{b}\left( b\right) to y(a), we can find the equation below.

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

$$ c{y}_{h}^1(a){y}_{h}^2(b)+d{y}_{h}^2(a){y}_{h}^2(b)+{y}_{p}(a){y}_{h}^2(b)=\alpha{y}_{h}^2(b) $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
$$\displaystyle
 * }

Also, let's multiply {y}^{2}_{a}\left( b\right) to y(b).

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

$$ c{y}_{h}^1(b){y}_{h}^2(a)+d{y}_{h}^2(b){y}_{h}^2(a)+{y}_{p}(b){y}_{h}^2(a)=\beta{y}_{h}^2(a) $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
$$\displaystyle
 * }

By solving simultaneous equations above, we can detemine the equation with respect to c

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

$$ c{y}_{h}^1(a){y}_{h}^2(b) - c{y}_{h}^1(b){y}_{h}^2(a) + {y}_{p}(a){y}_{h}^2(b) - {y}_{p}(b){y}_{h}^2(a) =  \alpha{y}_{h}^2(b) - \beta{y}_{h}^2(a) $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
$$\displaystyle
 * }

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

$$ c = \frac{\alpha{y}_{h}^2(b)-\beta{y}_{h}^2(a) -{y}_{p}(a){y}_{h}^2(b))+{y}_{p}(b){y}_{h}^2(a)}{{y}_{h}^1(a){y}_{h}^2(b)-{y}_{h}^2(a){y}_{h}^1(b)} $$ $$
 * style="width:25%; padding:1px; border:2px solid #0000FF" |
 * style="width:25%; padding:1px; border:2px solid #0000FF" |
 *
$$\displaystyle
 * }

In the same way, we can determine the equation with respect with d.

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

$$ c{y}_{h}^1(a){y}_{h}^1(b)+d{y}_{h}^2(a){y}_{h}^1(b)+{y}_{p}(a){y}_{h}^1(b)=\alpha{y}_{h}^1(b) $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
$$\displaystyle
 * }

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

$$ c{y}_{h}^1(b){y}_{h}^1(a)+d{y}_{h}^2(b){y}_{h}^1(a)+{y}_{p}(b){y}_{h}^1(a)=\beta{y}_{h}^1(a) $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
$$\displaystyle
 * }

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

$$ d = \frac{\alpha{y}_{h}^1(b)-\beta{y}_{h}^1(a) -{y}_{p}(a){y}_{h}^1(b))+{y}_{p}(b){y}_{h}^1(a)}{{y}_{h}^1(a){y}_{h}^2(a)-{y}_{h}^1(a){y}_{h}^2(b)} $$ $$
 * style="width:25%; padding:1px; border:2px solid #0000FF" |
 * style="width:25%; padding:1px; border:2px solid #0000FF" |
 *
$$\displaystyle
 * }

Hong SJ Egm6321.f10.team3.Hong SJ 11:12, 14 September 2010 (UTC)

=Notes and references=

title: User:Egm6321.f10.team3.franklin/Hwk1


text:
User talk:Franky manumpil

 Hello Franky manumpil, 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. 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.

 * 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.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Ottava Rima (talk) 01:37, 7 September 2010 (UTC)

title: User talk:Franky manumpil


text:
User:Hoangpham/The use of humour in EFL teaching

= What is humour? =

= Benefits of humour =

Social
= Why humour in education? =

= Why humour in EFL teaching? =


text:
User:Franky manumpil/Wikis for research

Research Methods 1

title: User:Franky manumpil/Wikis for research


text:
User:Joelle Vandermensbrugghe/thesis writing

This notes will guide students......

2011


text:
User:Carolyn Page/Talking about change

One of the most interesting areas is the way school leaders talk about change. 7/9/10

title: User:Carolyn Page/Talking about change


text:
User:Guifang Shang/Learning to learn a wiki way

hello


text:
User:Jackychen/Wiki-Taichi

The first stage on Digital Taichi will be completed by 31 December 2010.

title: User:Jackychen/Wiki-Taichi


text:
User talk:Jackychen/Wiki-Taichi

Powerful yet smoothy.

title: User talk:Jackychen/Wiki-Taichi


text:
User:Egm6321.f10.team3.Sudheesh/Homeworks/Homework2

= Problem 1 =

Solution
= Problem 2 =

Solution
= Problem 3 =

Solution
= Problem 4 - Create Exact Nonlinear First Order Ordinary Differential Equation (N1-ODE) =

Given
Conditions of Exactness:

 * For function $$F\left( . \right)$$ to be exact:

 * $$\left( 1 \right)$$ $$F\left( . \right)$$ must be in the form:

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

$$
 * $$F\left( x,y,{{y}^{1}} \right)=M\left( x,y \right)+N\left( x,y \right){{y}^{'}}$$
 * $$\displaystyle (Eq. 4.1)
 * $$\displaystyle (Eq. 4.1)
 * }
 * {| style="width:100%" border="0"
 * {| style="width:100%" border="0"

 * Where $$M\left( x,y \right)$$, and $$N\left( x,y \right)$$, are functions of $$x$$, and $$y$$, $$=\frac{dy}{dx}$$
 * }
 * }
 * }

 * $$\left( 2 \right)$$ $$M\left( x,y \right)$$, and $$N\left( x,y \right)$$ must satisfy:

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

$$
 * $$\frac{\partial M}{\partial y}=\frac{\partial N}{\partial x}$$
 * $$\displaystyle (Eq. 4.2)
 * $$\displaystyle (Eq. 4.2)
 * }
 * }

Given function:

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

$$
 * $$\phi \left( x,y \right)={{x}^{2}}{{y}^{{}^{3}\!\!\diagup\!\!{}_{2}\;}}+\log \left( {{x}^{3}}{{y}^{2}} \right)=k$$
 * $$\displaystyle (Eq. 4.3)
 * $$\displaystyle (Eq. 4.3)
 * }
 * }

Find

 * $$\left( 1 \right)$$ Find function $$F\left( . \right)$$ such that $$F\left( x,y,{{y}^{1}} \right)=\frac{d\phi }{dx}$$

 * $$\left( 2 \right)$$ Verify that $$F\left( x,y,{{y}^{1}} \right)$$ is an Exact N1-ODE

 * $$\left( 3 \right)$$ Invent three more Exact N1-ODE

Solution

 * $$\left( 1 \right)$$ Find function $$F\left( x,y,{{y}^{1}} \right)$$:

 * Derivative of $$\phi \left( x,y \right)$$ is given by
 * {| style="width:100%" border="0"

$$
 * $$\frac{d\phi }{dx}=\frac{\partial \phi }{\partial x}+\frac{\partial \phi }{\partial y}\cdot {{y}^{'}}$$
 * $$\displaystyle (Eq. 4.4)
 * $$\displaystyle (Eq. 4.4)
 * }
 * }

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

$$
 * $$\frac{\partial \phi }{\partial x}=\left[ 2x{{y}^{{}^{3}\!\!\diagup\!\!{}_{2}\;}}+\frac{1}\cdot 3{{x}^{2}}{{y}^{2}} \right]=2x{{y}^{{}^{3}\!\!\diagup\!\!{}_{2}\;}}+\frac{3}{x}$$
 * $$\displaystyle (Eq. 4.5)
 * $$\displaystyle (Eq. 4.5)
 * }
 * }

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

$$
 * $$\frac{\partial \phi }{\partial y}=\left[ \frac{3}{2}{{x}^{2}}{{y}^{{}^{1}\!\!\diagup\!\!{}_{2}\;}}+\frac{1}\cdot 2{{x}^{3}}y \right]=\frac{3}{2}{{x}^{2}}{{y}^{{}^{1}\!\!\diagup\!\!{}_{2}\;}}+\frac{2}{y}$$
 * $$\displaystyle (Eq. 4.6)
 * $$\displaystyle (Eq. 4.6)
 * }
 * Substituting Eq.4.5 & 4.6 into Eq.4.4 yields:
 * Substituting Eq.4.5 & 4.6 into Eq.4.4 yields:

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

$$
 * $$\frac{d\phi }{dx}=\left[ 2x{{y}^{{}^{3}\!\!\diagup\!\!{}_{2}\;}}+\frac{3}{x} \right]+\left[ \frac{3}{2}{{x}^{2}}{{y}^{{}^{1}\!\!\diagup\!\!{}_{2}\;}}+\frac{2}{y} \right]\cdot {{y}^{'}}$$
 *
$$\displaystyle (Eq. 4.7)
 *
$$\displaystyle (Eq. 4.7)
 * }
 * Therefore:
 * Therefore:

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

$$F\left( x,y,{{y}^{1}} \right)=\frac{d\phi }{dx}=\underbrace{\left[ 2x{{y}^{{}^{3}\!\!\diagup\!\!{}_{2}\;}}+\frac{3}{x} \right]}_{M\left( x,y \right)}+\underbrace{\left[ \frac{3}{2}{{x}^{2}}{{y}^{{}^{1}\!\!\diagup\!\!{}_{2}\;}}+\frac{2}{y} \right]}_{N\left( x,y \right)}\cdot {{y}^{'}}$$ $$
 * style="width:2%; padding:1px; border:2px solid #FF0000" |
 * style="width:2%; padding:1px; border:2px solid #FF0000" |
 *
$$\displaystyle (Eq. 4.8)
 * }
 * }

 * $$\left( 2 \right)$$ Verify that $$F\left( x,y,{{y}^{1}} \right)$$ is an Exact N1-ODE:

 * The function $$F\left( x,y,{{y}^{1}} \right)$$ is a first order nonlinear differential equation as its highest order is 1 and does not satisfy the condtion of superposition (linearity).
 * The function $$F\left( x,y,{{y}^{1}} \right)$$ given in Eq. 4.8 has the structure of Eq.4.1 and hence first condition of Exactness is satisfied.

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

$$
 * $$\frac{\partial M}{\partial y}=\frac{\partial }{\partial y}\left( 2x{{y}^{{}^{3}\!\!\diagup\!\!{}_{2}\;}}+\frac{3}{x} \right)=2x\cdot \frac{3}{2}{{y}^{{}^{1}\!\!\diagup\!\!{}_{2}\;}}+0=3x{{y}^{{}^{1}\!\!\diagup\!\!{}_{2}\;}}$$
 *
$$\displaystyle (Eq. 4.9)
 *
$$\displaystyle (Eq. 4.9)
 * }
 * {| style="width:100%" border="0"
 * {| style="width:100%" border="0"

$$
 * $$\frac{\partial N}{\partial x}=\frac{\partial }{\partial x}\left( \frac{3}{2}{{x}^{2}}{{y}^{{}^{1}\!\!\diagup\!\!{}_{2}\;}}+\frac{2}{y} \right)=\frac{3}{2}\cdot 2x{{y}^{{}^{1}\!\!\diagup\!\!{}_{2}\;}}+0=3x{{y}^{{}^{1}\!\!\diagup\!\!{}_{2}\;}}$$
 *
$$\displaystyle (Eq. 4.10)
 *
$$\displaystyle (Eq. 4.10)
 * }
 * Eq.4.9 and 4.10 implies,
 * {| style="width:100%" border="0"
 * {| style="width:100%" border="0"

$$
 * $$\frac{\partial M}{\partial y}=\frac{\partial N}{\partial x}$$
 *
$$\displaystyle (Eq. 4.11)
 *
$$\displaystyle (Eq. 4.11)
 * }
 * Eq.4.11 satisfy the second condition of Exactness.
 * Eq.4.11 satisfy the second condition of Exactness.

 * Since both conditions of exactness are satisifed,
 * {| style="width:100%" border="0"

 * $$F\left( x,y,{{y}^{1}} \right)=\frac{d\phi }{dx}=\underbrace{\left[ 2x{{y}^{{}^{3}\!\!\diagup\!\!{}_{2}\;}}+\frac{3}{x} \right]}_{M\left( x,y \right)}+\underbrace{\left[ \frac{3}{2}{{x}^{2}}{{y}^{{}^{1}\!\!\diagup\!\!{}_{2}\;}}+\frac{2}{y} \right]}_{N\left( x,y \right)}\cdot {{y}^{'}}$$ is an Exact N1-ODE
 * }
 * $$\left( 3 \right)$$ Invent three more Exact N1-ODE:
 * Example 1:
 * Consider, $$\phi \left( x,y \right)=3x\cdot {{e}^{y}}+4{{y}^{2}}\cdot {{e}^{x}}= k $$
 * Example 1:
 * Consider, $$\phi \left( x,y \right)=3x\cdot {{e}^{y}}+4{{y}^{2}}\cdot {{e}^{x}}= k $$

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

 * $$\frac{\partial \phi }{\partial x}=3\cdot {{e}^{y}}+4{{y}^{2}}\cdot {{e}^{x}}\Rightarrow M(x,y)$$
 * }
 * {| style="width:100%" border="0"
 * }
 * {| style="width:100%" border="0"

 * $$\frac{\partial \phi }{\partial y}=3x\cdot {{e}^{y}}+8y\cdot {{e}^{x}}\Rightarrow N\left( x,y \right)$$
 * }
 * Now consider a function $$F\left( x,y,{{y}^{1}} \right)$$ such that $$F\left( x,y,{{y}^{1}} \right)=\frac{d\phi }{dx}$$
 * }
 * Now consider a function $$F\left( x,y,{{y}^{1}} \right)$$ such that $$F\left( x,y,{{y}^{1}} \right)=\frac{d\phi }{dx}$$

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

 * $$F\left( x,y,{{y}^{1}} \right)=\frac{d\phi }{dx}=M\left( x,y \right)+N\left( x,y \right)\cdot {{y}^{'}}=0$$
 * }
 * {| style="width:100%" border="0"
 * }
 * {| style="width:100%" border="0"

$$F\left( x,y,{{y}^{1}} \right)=\left[ 3\cdot {{e}^{y}}+4{{y}^{2}}\cdot {{e}^{x}} \right]+\left[ 3x\cdot {{e}^{y}}+8y\cdot {{e}^{x}} \right]\cdot {{y}^{'}}=0$$ $$
 * style="width:2%; padding:1px; border:2px solid #0000FF" |
 * style="width:2%; padding:1px; border:2px solid #0000FF" |
 *
$$\displaystyle (Eq. 4.12)
 * }
 * This is an Exact N1-ODE
 * This is an Exact N1-ODE

 * Example 2:
 * Consider, $$\phi \left( x,y \right)=5y\log \left( {{x}^{2}} \right)+3{{x}^{2}}\sin \left( {{y}^{3}} \right)=k$$

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

 * $${{\phi }_{x}}\left( x,y \right)=5y\cdot \left( \frac{1}\cdot 2x \right)+6x\sin \left( {{y}^{3}} \right)=10\frac{y}{x}+6x\sin \left( {{y}^{3}} \right)\Rightarrow M(x,y)$$
 * }
 * {| style="width:100%" border="0"
 * }
 * {| style="width:100%" border="0"

 * $${{\phi }_{y}}\left( x,y \right)=5\log \left( {{x}^{2}} \right)+3{{x}^{2}}\left( \cos \left( {{y}^{3}} \right)\cdot 3{{y}^{2}} \right)=5\log \left( {{x}^{2}} \right)+9{{x}^{2}}{{y}^{2}}\cos \left( {{y}^{3}} \right)\Rightarrow N\left( x,y \right)$$
 * }
 * Now consider a function $$F\left( x,y,{{y}^{1}} \right)$$ such that $$F\left( x,y,{{y}^{1}} \right)=\frac{d\phi }{dx}$$
 * }
 * Now consider a function $$F\left( x,y,{{y}^{1}} \right)$$ such that $$F\left( x,y,{{y}^{1}} \right)=\frac{d\phi }{dx}$$

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

 * $$F\left( x,y,{{y}^{1}} \right)=\frac{d\phi }{dx}=M\left( x,y \right)+N\left( x,y \right)\cdot {{y}^{'}}=0$$
 * }
 * {| style="width:100%" border="0"
 * }
 * {| style="width:100%" border="0"

$$F\left( x,y,{{y}^{'}} \right)=\left[ 10\frac{y}{x}+6x\sin \left( {{y}^{3}} \right) \right]+\left[ 5\log \left( {{x}^{2}} \right)+9{{x}^{2}}{{y}^{2}}\cos \left( {{y}^{3}} \right) \right]{{y}^{'}}=0$$ $$
 * style="width:2%; padding:1px; border:2px solid #0000FF" |
 * style="width:2%; padding:1px; border:2px solid #0000FF" |
 *
$$\displaystyle (Eq. 4.13)
 * }
 * This is an Exact N1-ODE
 * This is an Exact N1-ODE

 * Example 3:
 * Consider, $$\phi \left( x,y \right)=7{{x}^{3}}\cdot \cos \left( {{y}^{3}} \right)+2{{y}^{2}}{{e}^{{{x}^{2}}\cdot \sin y}}=k$$

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

& {{\phi }_{x}}\left( x,y \right)=7\times 3{{x}^{2}}\cdot \cos \left( {{y}^{3}} \right)+2{{y}^{2}}\cdot {{e}^{{{x}^{2}}\cdot \sin y}}\cdot \left( 2x\cdot \sin y \right)=21{{x}^{2}}\cdot \cos \left( {{y}^{3}} \right)+4x{{y}^{2}}\cdot \sin y\cdot {{e}^{{{x}^{2}}\cdot \sin y}}\Rightarrow M(x,y) \\ & \\ \end{align}$$
 * $$\begin{align}
 * $$\begin{align}

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

 * $${{\phi }_{y}}\left( x,y \right)=7{{x}^{3}}\cdot \left[ -\sin \left( {{y}^{3}} \right)\cdot 3{{y}^{2}} \right]+2\left[ 2y\cdot {{e}^{{{x}^{2}}\cdot \sin y}}+{{y}^{2}}\cdot {{e}^{{{x}^{2}}\cdot \sin y}}\cdot {{x}^{2}}\cdot \cos y \right]=-21{{x}^{3}}{{y}^{2}}\sin \left( {{y}^{3}} \right)+4y{{e}^{{{x}^{2}}\cdot \sin y}}+2{{x}^{2}}{{y}^{2}}\cos y\cdot {{e}^{{{x}^{2}}\cdot \sin y}}\Rightarrow N\left( x,y \right)$$
 * }
 * Now consider a function $$F\left( x,y,{{y}^{1}} \right)$$ such that $$F\left( x,y,{{y}^{1}} \right)=\frac{d\phi }{dx}$$
 * }
 * Now consider a function $$F\left( x,y,{{y}^{1}} \right)$$ such that $$F\left( x,y,{{y}^{1}} \right)=\frac{d\phi }{dx}$$

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

 * $$F\left( x,y,{{y}^{1}} \right)=\frac{d\phi }{dx}=M\left( x,y \right)+N\left( x,y \right)\cdot {{y}^{'}}=0$$
 * }
 * {| style="width:100%" border="0"
 * }
 * {| style="width:100%" border="0"

$$\left( x,y,{{y}^{'}} \right)=\left[ 21{{x}^{2}}\cdot \cos \left( {{y}^{3}} \right)+4x{{y}^{2}}\cdot \sin y\cdot {{e}^{{{x}^{2}}\cdot \sin y}} \right]+\left[ -21{{x}^{3}}{{y}^{2}}\sin \left( {{y}^{3}} \right)+4y{{e}^{{{x}^{2}}\cdot \sin y}}+2{{x}^{2}}{{y}^{2}}\cos y\cdot {{e}^{{{x}^{2}}\cdot \sin y}} \right]{{y}^{'}}=0$$ $$
 * style="width:2%; padding:1px; border:2px solid #0000FF" |
 * style="width:2%; padding:1px; border:2px solid #0000FF" |
 *
$$\displaystyle (Eq. 4.14)
 * }
 * This is an Exact N1-ODE
 * This is an Exact N1-ODE


text:
User:Jiangpx

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some relevant links:
 * EGM 6341 Course Wiki
 * EGM 6321 Course Wiki
 * EGM 6321 Team Page
 * EGM 6321 HW1
 * EGM 6321 HW2
 * EGM 6321 HW3
 * EGM 6321 HW5
 * EGM 6321 HW6
 * EGM 6321 HW7

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title: User:Jiangpx