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Motivation and emotion/Book/2010/Personality and motivation

Overview
This chapter explains how personality theories relate to and affect motivation concepts. This introductory section explains the concepts of motivation and personality and key underlying questions.

Why do people behave the way they do? Why do some people choose to attend university? Why do some people play sport? Why do some people drink alcohol? According to motivational psychologists, people do such things because they are motivated to do so. There are many different reasons for such motivations and some of these will be discussed in this chapter.

But also consider, why do people vary in their motivations and behaviours? Why are people motivated towards different things? Whilst there are many possible answers to these questions, this chapter concentrates on the role of personality factors in understanding motivational and behavioural differences between people.

So what is motivation? Motivation definitions generally have two elements in common - that motivation provides a direction and energy to initiate and persist with behaviours in order to satisfy needs (Paulsen & Feldman, 1999, Young Sung & Nam Choi, 2009). To learn more, see What is motivation?

Now we know what motivation is, what is personality? Psychologists define personality as the characteristics and qualities that an individual displays, these characteristics influence the way people behave and is known as a psychological construct (Maltby, Day, Macaskill, 2007). Allport defined personality as ‘a dynamic organisation, inside the person, of psychophysical systems that create the persons’ characteristic patterns of behaviour, thoughts and feelings’ (Allport, 1961, p. 11). This definition means a process is continually changing in response to the environment and the experiences a person has. Personality is related to both the mind and the body and the characteristics are seen has being relatively stable over time and across different situations and indicate an individual’s general tendencies and predispositions (Major, Turner & Fletcher, 2006; Maltby et al.).

Personality is a widely studied area in psychology as it can influence so many aspects of an individual’s life. Due to this, over time many different personality theories have been developed and in this chapter we will cover the main theories relating to the trait perspective of personality and their relation to motivational concepts. There are other perspectives relating to personality but this chapter will mainly look at the trait perspective.

Every individual is different, their personalities differ and because of this people have different needs that need satisfying and therefore, behave in different ways. An example could be that you and your sibling grew up in the same environment with the same influences yet, you were motivated and felt the need to attend university but your sibling wanted to go straight into the workforce. A reason for this could be your different personality factors as the majority of your environment while growing up was very similar.

 * Focus questions

 * What is motivation?
 * What are the different theories of personality?
 * What are some of the motivational concepts research has shown to be affected by personality?

Self-determination Theory
Self-determination theory addresses the types of motivation that influence an individual towards goal related behaviour such as intrinsic, extrinsic and amotivation (Faye & Sharpe, 2008; Phillips, Abraham & Bond, 2003). This theory shows the multidimensional aspect of motivation on a continuum. It places influencing motivational aspects along this continuum ranging from amotivation, which is no motivation or a lack of motivation, to extrinsic motivation then intrinsic motivation (Faye & Sharpe; Phillips et al.). This theory identified four types of extrinsic motivation; external regulation (behaviour due to means external to the individual), introjection (behaviour influenced by both external environment and an internal reward or punishment), identification (behaviours influenced by individual's choice of what they see as important) and integration, as you move up the continuum from external regulation to integration an individual becomes less motivated by external rewards (Areepattamannil & Freeman, 2008; Faye & Sharpe). There are also three types of intrinsic motivation that have been identified; intrinsic motivation to know, intrinsic motivation toward accomplishment and intrinsic motivation toward stimulation (Faye & Sharpe).

Some related concepts to this theory surrounding intrinsic and extrinsic motivation are:

Intrinsic and Extrinsic Motivation
The main way people are motivated is by either intrinsic or extrinsic motivation. Intrinsic motivation is a type of motivation that comes from within a person (Hart, Stasson, Machony & Story, 2007). This type of motivation is due to enjoyment and the energy comes from the desire to master a task, explore something new and from something that sparks an individual’s interest (Young Sung & Nam Choi, 2009). While extrinsic motivation is when, an individual is motivated by the outcomes of completing a task (Prabhu, Sutton & Sauser, 2008, Tanaka, Mizuni, Fukuda, Tajima & Watanabe, 2009). An individual works towards a goal so they can attain something in the end such as a reward or compensation (Hart et al.; Young Sung & Nam Choi).

Leisure Motivation
Leisure motivation is the motivation to take part in leisure activities such as sports and exercise (Ying-Chao Lin, Shui-Lien Chen, Shih-Tse Wang, Ming-Sung Cheng, 2007). Intrinsic and extrinsic motivators can influence the extent of participation in leisure motivation (Ying-Chao et al.).

Creative Motivation
Creative motivation is about how a person is motivated, either intrinsically or extrinsically to come up with novel, unique and original ideas (Prabhu et al.; 2008, Young Sung & Nam Choi, 2009). Personality is believed to be a strong influencing factor on creativity, with the type of motivation acting as a moderator or mediator between the two factors (Young Sung & Nam Choi). How individuals achieve the results of producing these ideas will depend on how they are motivated and the type of motivation will also allow for a strong or weak effect of personality on creativity (Prabhu et al.; Young Sung & Nam Choi).

Academic Motivation

Academic motivation is how motivated an individual is towards academic achievement (Areepattamannil & Freeman, 2008). It is highly related to the self-determination theory as an individual’s motivational level towards achievement is influenced by whether they are motivated either intrinsically or extrinsically or not motivated at all (Areepattamannil & Freeman). If an individual is amotivated towards academic achievement then they will tend to drop out and not complete their studies and research has shown the more intrinsically motivated an individual is, the more likely they are to stay studying, have positive academic achievement, gain more enjoyment from their studies, have a greater learning and have higher self esteem (Areepattamannil & Freeman).

Another related concept is the motivation to learn, this is the want to participate in training and development tasks, to learn the content associated with training and to partake and enjoy the training experience (Major et al., 2006).

Goal Setting Theory
Goal-setting theory proposed by Locke and Latham suggests goals that are more difficult to attain and goals that are more specific, not an abstract such as I will do better, tend to motivate individuals more to achieve these goals, which in turn results in higher achievement (Erez & Judge, 2001; Locke & Latham, 2006). Reasons as to why there is increased motivation could be due to individuals being more committed and more competent at achieving the goal, also because when a high goal is set there is a large discrepancy between where an individual is currently at and where they would like to be, so this discrepancy causes the higher motivation to achieve the goal and finally reaching a higher set goal results in a greater feeling of success and this feeling can act as a motivator towards attainment of the goal (Locke & Latham). A related concept to the goal setting theory is goal orientations; these are the cognitive representations of goal setting that direct behaviour to specific goals (Steinmayr & Spinath, 2008). There are four main types of motivating goals that relate to goal orientations that can be associated with learning outcomes and therefore achievement, these are: The more specific these goals the higher the motivation to learn and achieve and therefore, demonstrating a higher level of success (Steinmayr & Spinath).
 * Learning goals: these show the desire to develop competence
 * Performance approach goals: motivation to show high competence
 * Performance avoidance goals: motivation to not show low competence
 * Work avoidance: showing as little motivation to work as possible

Theory of Planned Behaviour
The theory of planned behaviour is a model of goal-specific cognitions; it predicts intention and believes intention is the most important influence on behaviour (Phillip et al., 2003). Motivational factors are predicted through the amount of intention an individual has, as this shows how hard an individual will work to reach their goals (Phillips et al.). Phillips et al. showed there are three things that may predict intentions these are:
 * Perceived behaviour control: this is a predictor of intentions because how likely an individual is of reaching their goal will determine the intention they have to pursue that goal. Perceived behaviour control affects goal achievement through an individual’s confidence level; if they are high in confidence then they are more likely to persist with reaching the goal.
 * Attitude: predicts intentions by an individual’s overall attitude towards the goal and the evaluation of the goal.
 * Subjective Norms: predicts intention by how much an individual believes others would like them to pursue the goal.

Motivational Strivings
Motivational intentions show a specific focus on an individual’s motivation towards their social needs (Barrick, Stewart & Piotrowski, 2002). There are three different motivational intentions each relating to a specific social need (Achievement, Affiliation and Intimacy and Power) as described by Reeve, 2009. Based on Barrick et al., the three motivational strivings are:
 * Communion Striving: the motivation to gain acceptance in personal relationships, such as friendship and intimate relationships and the motivation to effectively work with others in environments such as work and study.
 * Status Striving: this is the motivation towards gaining power and dominance within a hierarchy setting.
 * Accomplishment Striving: the motivation to achieve tasks.

Achievement Motivation

Achievement motivation is a social-psychological theory of motivation (Steinmayr & Spinath, 2008). This type of motivation falls under the category of social needs and is defined as the need to excel relative to a standard of excellence (Reeve, 2009). Situations that involve achievement can be divided into two main characteristics either approach or avoidance that in turn create feelings of hope for success or fear of failure (Steinmayr & Spinath). Cassidy and Lynn (1989), created a measure of achievement motivation and this is assessed through seven different dimensions; pursuit of excellence, work ethic, status aspiration, competitiveness, acquisitiveness, mastery and dominance. Hart et al., 2007, managed to reduce the number of dimensions assessing achievement motivation into a two-dimensional model where all the pervious dimensions fell into either extrinsic (status aspiration, competitiveness, acquisitiveness, dominance) or intrinsic (pursuit of excellence, work ethic, mastery) motivation.

Expectancy-Value Theory
The expectancy-value theory is related to achievement behaviour, there are two main concepts surrounding this theory, expectancies and values (Paulsen & Feldman, 1999; Steinmayr & Spinath, 2008). This theory states when an individual sees an academic task as having personal value to themselves and they expect they will succeed in completing the task then they will take on the task (Paulsen & Feldman). Expectancy is related to the probability of future success in a task and is believed to be influenced by an individual’s beliefs about their self-efficacy, internal control and ability to complete the task, while values relates to whether the task is of importance or value to the individual, it is influenced by both the task and personal characteristics such as personality and interest (Paulsen & Feldman; Steinmayr & Spinath).

Belief-Importance Theory
Belief importance theory is very similar to the expectancy value theory as there are two main components that imply the same thing; belief, the individual's belief they can reach a goal and importance, how important the goal is (Petrides, 2010). This theory relies heavily on the idea that personality traits have a strong influence on the beliefs in achieving goals and the importance of these goals to the individual, with the general motivation idea being the more an individual values and believes in themselves to achieve a goal the more time and effort they will put into reaching that goal (Petrides). According to Petrides this theory breaks down its four aspects of affect and motivation into quadrants and relates each aspect to a particular personality trait, the four aspects and their related personality traits are:
 * Hubris (excessive pride or presumption), related to trait emotional intelligence.
 * Motivation, related to conscientiousness.
 * Depression, related to neuroticism.
 * Apathy, related to introversion.

Self-Efficacy Theory
Self efficacy theory was proposed by Bandura, 1997, it refers to how much an individual believes they can complete and perform set tasks and goals (Ogilvie & Stewart, 2010, Prabhu et al., 2008). Being high in self efficacy means an individual believes they have the necessary skills to perform tasks to achieve their goals, whereas low self efficacy means an individual feels they cannot complete the tasks they need to (Paulsen & Feldman, 1999). Self efficacy has been shown to affect goal setting with individuals higher in self efficacy generally setting themselves higher goals to achieve (Phillips & Gully, 1997). An individual’s level of self efficacy can relate to the motivation they feel towards completing or beginning a task and the achievement of that task, this theory can help explain academic motivation (Ogilvie & Stewart).

Stop and Review Questions Box 1

Answer these fill in the blank questions to test your understanding of the material covered so far.

Questions

 * 1) Motivation is a combination of ____________ and _____________ that initiates and persists behaviour.
 * 2) The characteristics and qualities an individual displays that can infulence their behaviour is know as ___________.
 * 3) The _____________ Theory defines three types of motivation; amotivation, extrinsic motvation and intrinsic motivation.
 * 4)  __________ motivation is when an individual works towards a task for the rewards and outcomes they will receive when the task is complete.
 * 5) How an individual is motivated to come up with novel, unique and original ideas is know as _________ motivation.
 * 6) The goal setting theory states there are two main points to goal setting that will increase motivation and higher achievement, these are setting _________ and __________ goals.
 * 7) Achievement, power and affiliation and intimacy are all types of _______ needs.
 * 8) ___________ motivation is an individual's need to excel relative to a standard of excellence.
 * 9) If an individual believes they can achieve a goal and the goal is important to them according to the _______________ theory of motivation, they will generally take on that goal.
 * 10) How well an individual believes they can perform and complete a task is know as ___________.

Five Factor Model and Motivation
The most researched theory of personality is the five factor model, this model has been shown to be related to many motivational concepts such as the influencing factors of intrinsic and extrinsic motivation, motivation to learn, creative motivation, goal directed motivation, performance motivation and motivation towards social needs. All of these will be explored in this section but first we will begin with learning and understanding what the five factor model of personality is.

The five factor model is a trait perspective used to describe personality, the idea that there is the possibly for five major factors that make up an individual’s personality is well supported by psychologists and research (Maltby et al., 2007). Costa and McCrae, 1992 described the five factors of personality as extraversion, neuroticism, conscientiousness, agreeableness and openness to experience, and each of these factors contains six different facets that contribute to the major factor (Major et al., 2006). Each of these factors are believed to be expressed in every individual and each factor is part of its own continuum for example at one end is extraversion and at the other end is introversion but what makes every person’s personality different is where each person sits on this continuum (Major et al.).

Extraversion is how much an individual likes to interact with the environment, people high in extraversion are more likely to seek stimulation, they are energetic, outgoing, sociable, they like large groups, excitement, they are assertive, talkative, active, adventurous, enthusiastic and positive (Barrick et al., 2002; Hart et al., 2007; Judge & Ilies, 2002; Major et al., 2006; Ying-Chao Lin et al., 2007; Young Sung & Nam Choi, 2009). The six facets of extraversion are warmth, gregariousness, assertiveness, activity level, excitement seeking and positive emotions.

Neuroticism relates to how emotionally stable and adjustable an individual is; someone high in neuroticism will generally experience negative affects and are emotional, sad/depressed, anxious, angry, fearful, insecure, and stressful, while at the opposite end of the continuum is emotional stability and people high in this are generally confident and relaxed (Barrick et al.; 2002, Hart et al., 2007; Judge & Ilies, 2002; Major et al., 2006; Young Sung & Nam Choi, 2009). The six facets of neuroticism are anxiety, anger, depression, self-consciousness, impulsiveness and vulnerability.

Conscientiousness relates to whether an individual follows social norms and participates in goal-directed behaviour, individuals high in conscientiousness are generally purposeful, responsible, organised, reliable, persistent, ambitious, self-disciplined, determined, achievement orientated, hardworking and they generally set clear goals (Barrick et al., 2002; Hart et al., 2007; Judge & Ilies, 2002; Major et al., 2006; Young Sung & Nam Choi, 2009). The six facets of conscientiousness are competence, orderliness, dutifulness, achievement-striving, self-discipline, deliberation.

Agreeableness is related to how cooperative an individual is to others, individuals high in agreeableness are generally kind, cooperative, trusting, unselfish, considerate, good natured and tolerant. They like to help people and do not like conflict with others, while someone low in this trait is generally manipulative and self-centred (Barrick et al., 2002; Hart et al., 2007; Judge & Ilies, 2002; Major et al., 2006; Young Sung & Nam Choi, 2009). The six facets of agreeableness are trust, morality, altruism, cooperation, modesty and sympathy.

The final trait is openness to experience and is related to the acceptance of new ideas, thoughts and experiences; individuals high on this trait are generally imaginative, curious, non-traditional, sensitive, broad-minded, flexible and creative (Barrick et al., 2002; Hart et al., 2007; Judge & Ilies, 2002; Major et al., 2006; Young Sung & Nam Choi, 2009). The six facets of openness to experience are imagination, artistic interests, emotionality, adventurousness, intellect and liberalism. This model is one of the most widely used and accepted models as it has been shown to generalise across populations and methods of measurement (Hart et al.; Major et al.).

Table Displaying the Five Factors of Personality and Their Associated Facets

So now we understand the five factor model of personality, how does this relate to motivation? There has been a lot of research into this area to see exactly what personality’s affect on motivation is, with much of the research concentrating on the influencing factors of intrinsic and extrinsic motivation. A study conducted by Hart et al, 2007 researched the relationship between the five factor model personality traits and achievement motivation; they wanted to find out if you were scored as high in certain traits are you more likely to be intrinsically or extrinsically motivated towards achievement. In this study they found individuals influenced by high intrinsic achievement motivation (IAM) were high in conscientiousness, openness to experience and extraversion and agreeableness was negatively associated with extrinsic achievement motivation (EAM). There was also a positive relationship found between EAM and extraversion and EAM and conscientiousness. Implications of these findings are related to work and school settings, by understanding an individual’s personality, you may be able to understand how they are motivated which in turn could allow them greater achievement in those settings.

Research has shown personality can have an affect on an individual's motivation to learn (Major et al., 2006). Major et al. showed extraversion, openness to experience and conscientiousness to positively predict motivation to learn. The facets of activity level and positive emotions within extroversion; intellect and liberalism within openness to experience and competence, dutifulness and achievement striving within conscientiousness were all shown to have significant effects on motivation to learn. Understanding these relationhips is very important as the implications can affect children's learning, they can help teachers to maximise children's learning so they can achieve to the best of their ability in their own individual way (Major et al.).

Research conducted by Phillips et al., 2003, looked at the relationship between personalities five factor traits, types of motivation using the self determination theory and goal directed intentions using the theory of planned behaviour. Their study showed both openness to experience and conscientiousness were both predictors of intention towards goal directed thoughts, which in turn could lead to higher and more goal setting which according to the goal setting theory means individuals should achieve greater outcomes. They also showed that conscientiousness helps to maintain intentional goal directed thoughts especially through autonomous intrinsic motivation. So overall individuals who are high in conscientiousness and openness to experience tend to perform better because they have stronger intentions relating to goal setting and achievement.

Studies have investigated the relationship between the five factor model of personality and performance motivation which is made up of three main theories; goal-setting theory, value-expectancy theory and self-efficacy theory (Judge & Ilies, 2002). Results showed that neuroticism is negatively related to all three types of motivation and conscientiousness is positively related to all three. The other traits obtained inconsistent results with only weak correlations. These results show that being high in conscientiousness and low in neuroticism means an individual is more likely to be performance motivated through goal setting, expecting they can achieve the goals and having the belief behind this expectancy.

The relationship between personality and the motivation towards social needs/ strivings has shown individuals higher in extraversion are more likely to be motivated by status or power strivings while individuals higher in conscientiousness are more likely to be motivated by accomplishment or achievement strivings (Barrick et al., 2002). The results also showed that status striving is more motivational than accomplishment striving in performance at work, while agreeableness was positively related to communion strivings showing that individuals high in this trait are more motivated to get along with people at work rather than perform better (Barrick et al.).

Relationships between personality and creative motivation have also been found with the main finding being the relationship between extrinsic motivation and creative performance, extrinsic motivation affects the openness to experience trait and motivates individuals high in this towards high creative performance (Young Sung & Nam Choi, 2009). Finally another motivational aspect influenced by the five factors of personality is leisure motivation, which shows that extraversion is positively related towards leisure motivation, with most members of fitness centres being both highly extroverted and leisure motivated (Ying-Chao Lin et al., 2007).

From this section of the chapter you should be able to see how influential personality can be on motivation in particular towards achievement and high performance. An individual's personality makeup has influencing factors towards how they are motivated either intrinsically or extrinsically, this has implications towards teaching and learning aspects helping allow individuals to achieve the best they can. By understanding someone's personality we help them perform better by equipping them with the tools they respond best to and working with them in ways they find best. The majority of research in this area has shown that individuals high in conscientiousness and openness to experience and individuals slightly more extraverted (some studies) will be more likely to perform better on tasks and achieve more due to higher goal setting, more self-efficacy, having a higher expectancy to achieve the goals they set and being more intrinsically motivated. These are the main ways personality can affect motivation.

If you would like to see what you would score on each of the five factors scales try this short version of the IPIP-NEO test IPIP-NEO Short Version

Locus of Control and Motivation

Another personality perspective is an individual’s locus of control, this theory of personality believes that people fall somewhere between having a external locus of control and internal locus of control on a continuum (Phillips & Gully, 1997). Locus of control is a measure of how much an individual believes that outcomes such as rewards and reinforcements are under their control or not (Earn, 1982, Phillips & Gully). Individuals that have an internal locus of control believe that the outcomes they receive are due to their own behaviour and abilities and that outcomes are completely under their control, they show perceived control of the task and environment which is related to the individual having greater self-efficacy(Earn, Phillips & Gully). Individuals who have an internal locus of control are more directive, confident and alert when trying to control the external environment (Ng, Sorensen & Eby, 2006). Individuals that have an external locus of control believe that outcomes are not under their own control but are due to powerful others such as God or fate, luck and other people, having an external locus of control has been shown to be related to learned helplessness and compliance (Earn, Phillips & Gully).

A study conducted by Earn (1982) researched the relationship between locus of control and intrinsic and extrinsic motivation. They gave participants money rewards as an extrinsic motivator to complete a task and after this task was complete they asked some participants to remain to do another study where they would either be paid the same amount, a larger amount or no money and they also gave them different information as to why they were asked to stay. Increasing the extrinsic reward of pay increased intrinsic motivation in participants with an internal locus of control but decreased intrinsic motivation in participants with an external locus of control. This was due to participants with an internal locus of control concentrating on the competency rewards of their efforts, they believed they were getting increase extrinsic motivation due to their own competencies and efforts while participants with an external locus of control concentrated on the controlling factors and believed they were not asked to stay due to their competency but just because the researchers needed participants. Another study researching the relationship between locus of control, goal setting and self-efficacy to predict individual performance was conducted by Phillip and Gully, 1997. The results showed if an individual has an internal locus of control then they will be more motivated to set and achieve goals with performance goal orientation and learning goal orientation being related to an internal locus of control. An internal locus of control is associated with the feeling of being in control of what you are doing, having this feeling can provide more motivation towards goal setting and the expectancy to complete the task and goal, this idea links into the theory of goal setting and the value-expectancy theory. Also internal locus of control was shown to be related to higher self-efficacy and having higher self-efficacy leads an individual to set higher goals, being more motivated to achieve these goals and therefore a higher performance. While having an external locus of control leads an individual towards wanting to avoid failure rather than achieve success and also makes an individual feel that because they have no real control over the outcome what is the point in trying so they lack the motivation to try and succeed.

Personality and achievement motivation has been explored so now we move to another related concept of personality and job motivation. Research has shown an internal locus of control to predict higher job motivation and greater effort towards work tasks (Ng et al., 2006). An individual with an internal locus of control believes they have more control over the external environment which increases the expectancy of hemselves achieving their goals, which then increases the motivation to reach the goals (Ng et al.). An internal locus of control is related to stronger internal motivation through higher goal setting (goal setting theory) and a stronger need for achievement (Ng et al.). An important basis of job motivation is perceived job opportunities, which comes from perceiving greater control over the environment, showing job motivation to be related to an internal locus of control (Ng et al.). Job motivation is indicated through internal motivation towards tasks, expectancy, instrumentality, job involvement, self-development, self-efficacy and psychological empowerment (Ng et al.). Results from a study examining the relationship between these variables of job motivation and locus of control found an internal locus of control was positively related to job motivation through these variables (Ng et al.). So having a high motivation to job performance is due to an internal locus of control as individuals with this type of control are higher in these variables (Ng et al.).

According to the research relating locus of control to motivation, having an internal locus of control is most beneficial as individuals with an internal locus of control are more likely to achieve more and and have higher job motivation due to having more intrinsic motivation.

If you would like to see what type of locus of control you have take this test Locus of Control Test and to see the scoring of this test see here Scoring

Eysenck's Theory of Personality and Motivation
Eysenck’s theory is based on three biological traits; extroversion, neuroticism and psychoticism (Acton, 2003). Eysenck’s theory explains personality through the functioning of an individual’s brain. It is based on how much arousal a person experiences and this would in turn influence how much a person would interact with the world around them (Acton).

Eysenck’s theory of personality consists of describing three main personality traits that every individual is believed to have extraversion, neuroticism and psychoticism (Hagemann & Naumann, 2009). An individual’s differences in behaviour and personality are thought of by Eysenck to be due to a person’s brain functioning (Hagemann & Naumann). He identified two brain systems, one controls the cortical arousal that reacts to incoming stimuli, this is known as the reticular-cortical system and the other controls the response that individuals have to incoming emotional stimuli known as the reticular limbic system (Gilliland & Matthews, 1999). Therefore Eysenck believed that people with low cortical arousal were extraverted people, as they did not have a lot of stimulation so are motivated by this low arousal level to go and search for more stimulation to gain the level of arousal that is needed (Hagemann & Naumann). Whereas introverts are seen to have already high stimulation and arousal and therefore do not need to go looking for extra stimulation as their optimal level of arousal has already been met therefore they do not have as much motivation towards sensation seeking as extroverts (Hagemann & Naumann). The differences in the cortical arousal are thought to result from the functioning of the ascending reticular activating system and this system will react to all types of stimulation not just specific groups of stimulation (Hagemann & Naumann). The reticular limbic system relates to the neuroticism trait, the more emotional stimuli there is, then the more arousal a person will experience, and if the arousal is very high they are likely to be neurotic rather than emotionally stable (Gilliland & Matthews). Although it may be difficult to determine if an individual is neurotic or not as the difference may only be viewed in emotional or stressful times (Gilliland & Matthews). Psychoticism is the final trait that was proposed by Eysenck, it is less researched and therefore not as well understood but it may be linked to dopamine (Gilliland & Matthews), it is very similar to the neuroticism trait but it lacks the fear and anxiety that is associated with neuroticism, this trait is associated with hostility, nonconformity and impulsivity and is generally associated with individuals who are seen as antisocial (Acton).

The main way Eysenck’s theory of personality related to motivation is through the extraversion trait, as Eysenck believed extraverts did not have enough baseline stimulation so they are more motivated to seek more to gain their optimal level of arousal, due to this extroverts are associated more with risk taking behaviour and have a sensation seeking nature (Farley & Farley, 1967, Hagemann & Naumann, 2009). Psychoicism has been shown to be related to addictive behaviours through the levels of dopamine, these people are motivated towards the addiction as the dopamine levels in their bodies act as rewards and reinforcers which motivates the individual to increase the behaviour causing the addiction (Eysenck, 1997).

Temperament, Character and Sensation Seeking Traits and Motivation

A study by Tanaka et al., 2009 examined the idea that personality falls under specific temperament and character traits and these traits affect how an individual is motivated towards academic achievement. The specific temperament traits were novelty seeking, harm avoidance, reward dependence and persistence, while the specific character traits were self-directedness, co-operativness and self-transcendence. The results showed a relationship between intrinsic motivation and persistence through a relation of intention to achieve. All the character traits were positively related to intrinsic academic motivation and a having a mature balance of these traits is essential for developing intrinsic motivation.

Finally a common personality trait that seems to be related to motivation is sensation seeking. Sensation-seeking is an individual’s tendency to seek exciting situations; this trait has been closely linked to Eysenck’s theory and the idea of impulsivity (Acton, 2003). The motivational component works similar to Eysenck’s idea that individuals high in sensation seeking are looking for more stimuli to arouse themselves to their optimal level; they like to search for new experiences and are more prone to risk taking behaviour which could lead to things such as addictions (Reeve, 2009). Zuckerman produced a sensation seeking scale to measure an individual’s level of sensation seeking behaviour, there are four sub-scales which are; thrill and adventure seeking, experience seeking, disinhibition, boredom susceptibility (Barnett, 2006). Thrill and adventure seeking refers to the motivation to participate in thrill-seeking, adventurous or risky activities, experience seeking refers to the motivation to participate in experiences that seek arousal through the mind and senses, disinhibition refers to the motivation an individual feels to seek release in social ways such as drinking, partying, sex and gambling, finally boredom susceptibility refers to the motivation to avoid situations or experiences that are viewed as repetitive or routine and even avoid individuals who are seen as boring (Barnett, 2006). These scales help show the relationship between the personality trait of sensation seeking and the motivation they are most likely to experience.

To see your own score of sensation seeking on these factors try this test, SSS with scoring instructions

Stop and Review Questions Box 2

Answer these fill in the blank questions to check your understanding of the material in this section

 * 1) According to the Five Factor Model of Personality there are five different traits that make up an individual's personality these are, __________, ____________, ___________, ____________, and ____________.
 * 2) Extraversion, openness to experience and conscientiosness are traits that positively predict an individual's _______________________.
 * 3) Individuals higher in ____________ are more likely to be motivated by status or power strivings while individuals higher in ______________ are more likely to be motivated by accomplishment or achievement strivings.
 * 4) In general individuals higher in openness to experience and conscientiousness are more likely to perform ___________ on tasks and achieve ________.
 * 5) Locus of control is a measure of how much control an individual feels they have over their environment. There are two types of control these are ___________ and ____________.
 * 6) An individual with an ____________ locus of control is more likely to have higher job motivation, be more intrinsically motiavted and have higher self-efficacy.
 * 7) Extraversion, neuroticism and psychotisim are all traits of ____________ biological based personality theory.
 * 8) ____________ is the main trait related to motivation, as Eysenck believed individuals high in this trait are more likely to be motivated to seek stimulation as they have __________ levels of arousal.
 * 9) The temperament trait, _____________ is related to intirnsic motivation through an intention to achieve.
 * 10) A trait that is associated with risk taking behaviour, experience seeking, disinhibition and bordem susceptibility is know as ______________.

Summary
An individual's personality is the characteristics and qualities they display that can influence their behaviour. Personality can affect the level of energy and the direction that energy is focused towards, in other words personality can affect motivation towards particular behaviours. Different theories of personality look at different ways personality affects an individual's motivation. The main theory of looking at this interaction is the five factor model of personality. This model of personality consists of five main traits; extraversion, neuroticism, conscientiousness, agreeableness and openness to experience and believes every individual's personality is thought to be made up of these five traits just to varying degrees. These personality factors have been shown to affect the type of motivation, either intrinsic or extrinsic, creative motivation, motivation to learn, motivation towards social needs, performance motivation and goal directed motivation. Research has shown the main influencing traits of this personality model to be conscientiousness and openness to experience and to a small degree extraversion, with these traits being positively related to high goal setting, higher performance and achievement and a higher motivation to learn. While neuroticism has been shown to be negatively correlated to these aspects of motivation. These are the main influencing factors of the five factor model on personality.

Locus of control is another personality perspective, there are two types of control either internal, this is where the individual feels in control of their environment and feels they can change and influence it and external, where then individual believes they have no control over their environment and everything that happens is due to luck, chance, others or a higher power. Research shows that individuals with an internal locus of control tend to have greater intrinsic motivation, they set higher goals, work harder to achieve these goals, perform better and have higher job motivation and self-efficacy. This is generally because they believe they can achieve the goals they set and believe what they do makes a difference to the outcomes they receive. Whereas an individual with an external locus of control generally lacks motivation towards anything because they feel they have no control over what happens anyway.

Eysenck's theory of personality has a biological basis; he believes individual's personality is made up of three main traits, extraversion, neuroticism and psychoticism. He showed extraversion is related to more motivational behaviours as extraverts have lower arousal levels than introverts so they are motivated to go out and interact with their environment to gain their own optimal level of arousal. This trait has been related to risk taking behaviour and a sensation seeking nature. Psychoticism has also been shown to be related to motivation and is thought to be related to dopamine. This trait can be related to addictive behaviours such as alcohol and drugs due to the dopamine providing rewards that reinforce the behaviour which in turn motivates the individual to continue the behaviour.

Finally temperament and character traits have been shown to be related to motivation. Research shows the temperament trait, persistence and character traits self-directedness, co-operativness and self-transcendence are all related to intrinsic motivation in terms of a need for achievement. Another trait relating to motivation is sensation seeking. Sensation seeking is an individual’s tendency to seek exciting situations and individuals high in this trait are generally looking for stimulation to increase their arousal level. This is a similar concept to Eysenck's theory. These individual's will generally take more risks and can possibly end up with addictions. These are the main ways personality can affect an individual's motivation.

Box 1

 * 1) energy, direction
 * 2) personality
 * 3) self-determination
 * 4) extrinsic
 * 5) creative
 * 6) more difficult, more specific
 * 7) social
 * 8) achievement
 * 9) expectancy-value
 * 10) self-efficacy

Box 2

 * 1) extraversion, neuroticism, conscientiousness, agreeableness, openness to experience
 * 2) motivation to learn
 * 3) extraversion, conscientiousness
 * 4) better, more
 * 5) internal, external
 * 6) internal
 * 7) Eysenck
 * 8) Extraversion, low
 * 9) persistence
 * 10) sensation-seeking


text:
User:Norton~enwikiversity/Wikistution/Amendment XXX

Section 1

Any citizen seventeen years of age or older has the right to vote.

Section 2

All ballots will be blank. To vote, a citizen writes the name of the chosen candidate.

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


text:
Survival Kit, software/Older versions

Before you begin
First you should download the source codes, examples and manual from boku.ac.at. Everything is for free, programs are open source. The manual in currently in form of a .ps file. If you don't have a program able to open .ps files you have to download one (e.g. Postscript Viewer) or convert it to .pdf (with e.g. ps2pdf). You are encouraged to Google for more possibilities.

Compilation
The word "compilation" means turning the source code (the Fortran program in text form) into an executable file which may be run by the operating system (in Windows .exe). The Fortran source codes need to be compiled before usage. The possible options for this include (but not limited to) Lahey, gfortran, Force compilers. You should also recompile the programs after any change in the source code. The necessity of (re)compilation is one of the major difficulties in using the Survival Kit v3.12 especially for novice users. This was required because the programs were initially written in Fortran77 allowing only matrices of fixed size. In the upcoming version the memory allocation possibilities of Fortran90 are used which makes the programs much more flexible.

Suggestion
In order to avoid at least some of the necessary recompilation, you may set/change the parameters in the "parinclu" file before the first compilation as follows: PARAMETER (SUPPLY_INPUT0=.true.) PARAMETER (SUPPLY_INPUT1=.true.) PARAMETER (SUPPLY_INPUT2=.true.) PARAMETER (SUPPLY_OUTPUT=.true.)

Simply open the parinclu file using your favorite text editor, modify the parameters and save. The outcome of this (after the compilation) will be that you will need to type the file names at running time, but it also gives more flexibility when the input file names are changed. In this description we will assume that you have done this, i.e. set all parameters to .true.

Directory
First thing you need to do is to copy small.dat, small.par, small.cox and small.wei along with the compiled executable files prepare.exe, weibull.exe and cox.exe. One of the common mistakes which novice users make is to keep multiple evaluations in one directory. This is not a technical problem, but after several runs the directory is filled with the results and additional files created by the Survival Kit which may lead to confusions and a big mess. Keep separate databases in separate directories. This is a practical experience...

Run Prepare
To do this you should start the program in the command prompt. Click Start then Run.. and write "cmd" and hit Enter. In the command prompt navigate to the directory with the prepare.exe file and run it. You will be asked for the name of the parameter file, write: small.par

If you get an error message saying something like "The value of the STATUS specifier in an OPEN statement..." then you have typed the file name for the parameter file incorrectly. If the program does not ask you about the file name, then the parameter SUPPLY_INPUT0 is set to .false. in parinclu. In this case you may change the name of your file to the one indicated in INPUT_FILE0 or change its value to .true. in parinclu and recompile the program (as explained here).

Run Weibull
You can run the Weibull program just after running the prepare.exe at least once, since it needs some files that are created by the Prepare program. These additional files contain the recoded values for your variables. You can find out more information about them in the manual, but please note that you don't have to modify them at all.

You should run the Prepare program before running Weibull.It doesn't mean however that you have to run Prepare every time. If you change the MODEL or adjust different settings you do not need to rerun Prepare again if every variable needed in the Weibull program is included in Prepare's OUTPUT statement. Please note that not every variable from this OUTPUT statement should be used in the MODEL (i.e. you can include all effects to the OUTPUT in Prepare and use just a few in Weibull's MODEL). If you run stratified analysis in Weibull the output data file from prepare (small2.dat in this example) should be sorted ascending by the STRATA variable.

When running the Weibull program you will be asked for input file names. Again "The value of the STATUS specifier in an OPEN statement..." error message may pop up here from the same reason as for Prepare. If this happens, check if the file names are entered correctly. The default entries for the "Small example" are:

 * first parameter file (=output from prepare) small.paa
 * second parameter file (=model specification) small.wei
 * detailed output file any_name_you_want or just_hit_enter

Notice the file extensions of .paa (contains the list of variables) and .wei (contains your specifications of the model you want to use). These are the default filename settings which may be altered changing parameters SUPPLY_INPUT1 and SUPPLY_INPUT2 in parinclu. Remember: after each change in the source code you have to recompile the programs.

Run Cox
Running the Cox program is very similar to Weibull. The major difference is that you have to sort the recoded data file (small2.dat in this example) ascending by time variable (1st column) and descending by censoring variable (2nd column). If you run a stratified analysis the sorting order modifies to: ascending by strata variable (the column number of the strata), ascending by time variable (1st column) and descending by censoring variable (2nd column).

The default entries when running the "Small example" are:

 * first parameter file (=output from prepare) small.paa
 * second parameter file (=model specification) small.cox
 * detailed output file any_name_you_want or just_hit_enter

Where the file with extension .cox contains the specifications of your Cox model.

title: Survival Kit, software/Older versions


text: File:Boiling cavitation.png

title: File:Boiling cavitation.png


text:
User:Egm6321.f2010.team5.riveros/hw5p4

=Problem 4=

Given
We are given the differential equation,
 * $$\displaystyle y'+P(x)y=Q(x)$$

where the homogeneous solution has been previously found to be,
 * $$\displaystyle y_h=Ae^{-\int{P(x)dx}}$$

Find
We are to find a particular solution, $$y_p$$, by variation of parameters.

Solution
We first let
 * $$\displaystyle y(x)=u(x)\cdot y_h$$

By taking the derivative we find,
 * $$\displaystyle y'(x)=e^{-\int{P(x)dx}}[u'(x)-u(x)P(x)]$$

We substitution this into the given equation,
 * $$\displaystyle e^{-\int{P(x)dx}}[u'(x)-u(x)P(x)]+P(x)u(x)e^{-\int{P(x)dx}}=Q(x)$$

Rearranging yields,
 * $$\displaystyle e^{-\int{P(x)dx}}[u'(x)-u(x)P(x)+u(x)P(x)]=Q(x)$$

Which then simplifies to,
 * $$\displaystyle e^{-\int{P(x)dx}}u'(x)=Q(x) $$

We solve for $$u'(x)$$
 * $$\displaystyle u'(x)=y_{h}^{-1}\cdot Q(x)=\exp [\int{P(x)dx}]\cdot Q(x) $$

Integrating,
 * $$\displaystyle u(x)=\int{\exp [\int{P(x)dx}]\cdot Q(x)dx} $$

Therefore, the particular solution is
 * $$\displaystyle y(x)=exp [-\int{P(x)dx}]\cdot \int{\exp [\int{P(x)dx}]\cdot Q(x)dx}$$

title: User:Egm6321.f2010.team5.riveros/hw5p4


text: Motivation and emotion/Textbook/Motivation/Self-concept/References


text:
User talk:Egm6321.f10.team5.oh/hw5

= Problem 1 - Higher order deriv.= From Meeting 26, p. 26-2

Find
Find $$y_{xxxxx}$$ in terms of derivative of $$y$$ with respect to $$t$$.

Author and Proof-Reader
[Author] Soo W. Jo

[Proof-Reader]

= Problem 2 - Solve using Method 2= From Meeting 26, p. 26-3

Find
Solve and plot $$x^2 y'' - 2 x y' + 2 y = 0$$ using the trial solution method where $$y = x^r$$ and boundary conditions are $$y(1) = 3$$ & $$y(2) = 4$$ or $$y(1) = -2$$ & $$y(2) = 5$$.

Solve
For $$y(1) = 3$$ & $$y(2) = 4$$ case, we get the following solution. For $$y(1) = -2$$ & $$y(2) = 5$$ case, we get the following solution.

Author and Proof-Reader
[Author] Soo W. Jo

[Proof-Reader]

= Problem 3 - Consider Char. eq.= From Meeting 27, p. 27-1

Given
The Euler L2-ODE-VC: $$ a_2x^2y''+a_1xy'+a_0y=0 \,$$ $$\displaystyle (Eq. 3.1) $$

The Euler L2-ODE-CC: $$ b_2y''+b_1y'+b_0y=0 \,$$ $$\displaystyle (Eq. 3.2) $$

The characteristic equation: $$ (r-\lambda)^2 = r^2-2\lambda r + \lambda^2 = 0 \,$$ $$\displaystyle (Eq. 3.3) $$

Find
1.1) Find $$a_2$$, $$a_1$$ , $$a_0$$ such that Eqn. 3.3 is the characteristic equation of Eqn. 3.1

1.2) Find the first homogeneous solution, $$y_1$$

1.3) Find the second homogeneous solution, $$y_2$$

1.4) Find the general homogeneous solution

2.1) Find $$b_2$$, $$b_1$$ , $$b_0$$ such that Eqn. 3.3 is the characteristic equation of Eqn. 3.2

2.2) Find the first homogeneous solution, $$y_1$$

2.3) Find the second homogeneous solution, $$y_2$$

2.4) Find the general homogeneous solution

Part 1.1
The coefficients of Eqn. 3.1 (a terms) can be found if we use the trial solution method. The trial solution for an Euler L2-ODE-VC is: $$ y=x^r \,$$ $$\displaystyle (Eq. 3.1.1) $$

Therefore we can calculate the first and second derivatives of the trial solution:

$$ y'=rx^(r-1) \,$$ $$\displaystyle (Eq. 3.1.2) $$

$$ y''=r(r-1)x^(r-2) \,$$ $$\displaystyle (Eq. 3.1.3) $$

Then substitute back into Egn. 3.1 so that it becomes,

$$ a_2x^2r(r-1)x^(r-2)+a_1xrx^(r-1)+a_0x^r=0 \,$$ $$\displaystyle (Eq. 3.1.4) $$

Then simplify,

$$ x^r[a_2r(r-1)+a_1r+a_0]=0 \,$$ $$\displaystyle (Eq. 3.1.5) $$

$$ a_2r^2-a_2r+a_1r+a_0=0 \,$$ $$\displaystyle (Eq. 3.1.6) $$

$$ a_2r^2+(a_1-a_2)r+a_0=0 \,$$ $$\displaystyle (Eq. 3.1.7) $$

We then set Eqn. 3.1.7 equal to the expanded out version of the characteristic equation (Eqn. 3.3) to obtain the values of the coefficients,

$$ a_2r^2+(a_1-a_2)r+a_0=r^2-2\lambda r+\lambda^2 \,$$ $$\displaystyle (Eq. 3.1.8) $$

It is then clear that,

$$ a_2 = 1 \,$$ $$\displaystyle (Eq. 3.1.9) $$

$$ (a_1-a_2)= -2\lambda ; a_1 = a_2-2\lambda = 1-2\lambda \,$$ $$\displaystyle (Eq. 3.1.10) $$

$$ a_0=\lambda^2 \,$$ $$\displaystyle (Eq. 3.1.11) $$

Part 1.2
To find the first homogeneous solution use the trial solution (Eqn. 3.1.1) and the characteristic equation (Eqn. 3.3). We find the roots of Eqn. 3.3 and substitute the first (real) one in for $$r$$ in the trial solution (Egn. 3.1.1). In this particular case the two roots are the same so $$r_1=r_2=\lambda$$. Substituting this into Eqn. 3.1.1 we get,

$$ y_1=x^\lambda \,$$ $$\displaystyle (Eq. 3.1.12) $$

Part 1.3
Since $$\lambda$$ has two identical roots we can find the second homogeneous solution using the form,

$$ y_2(x)=U(x)y_1(x) \,$$ $$\displaystyle (Eq. 3.1.13) $$

We then calculate the first and second derivatives of Eqn 3.1.13. The $$(x)$$ argument will be ignored to simplify the equations.

$$ y_2'=U'y_1+Uy_1' \,$$
$$\displaystyle (Eq. 3.1.14) $$

$$ y_2=Uy_1+2U'y_1'+Uy_1'' \,$$
$$\displaystyle (Eq. 3.1.15) $$

Plug Eqns. 3.1.13, 3.1.14, 3.1.15 into Eqn 3.1 and simplify,

$$ a_2x^2(Uy_1+2U'y_1'+Uy_1)+a_1x(U'y_1+Uy_1')+a_0Uy_1=0 \,$$
$$\displaystyle (Eq. 3.1.16) $$

$$ U(a_2x^2y_1+a_1xy_1'+a_0y_1)+U'(2a_2x^2y_1'+a_1xy_1)+Ua_2x^2y_1=0 \,$$
$$\displaystyle (Eq. 3.1.17) $$

This can be simplified further noting that $$U$$ is multiplied by Eqn 3.1, which equals $$0$$. So that completely eliminates one term in Egn. 3.1.17. We then substitute in the calculated values of the $$a$$ coefficients and the values for $$y_1$$ from part 1.1 and simplify,

$$ U'(2a_2x^2y_1'+a_1xy_1)+U''a_2x^2y_1=0 \,$$
$$\displaystyle (Eq. 3.1.18) $$

$$ U'[2x^2\lambda x^{\lambda -1}+(1-2\lambda )xx^\lambda ]+U''x^2x^\lambda =0 \,$$
$$\displaystyle (Eq. 3.1.19) $$

$$ U'[2x^2\lambda x^{\lambda -1}+(1-2\lambda )xx^\lambda ]+U''x^2x^\lambda =0 \,$$
$$\displaystyle (Eq. 3.1.19) $$

$$ U'[2\lambda x^{\lambda +1}+x^{\lambda +1}-2\lambda x^{\lambda +1}]+U''x^{\lambda +2} =0 \,$$
$$\displaystyle (Eq. 3.1.20) $$

$$ U'x^{\lambda +1}+U''x^{\lambda +2} =0 \,$$
$$\displaystyle (Eq. 3.1.21) $$

$$ (U'+ U''x)x^{\lambda +1} =0 \,$$
$$\displaystyle (Eq. 3.1.22) $$

$$ U'+ U''x =0 \,$$
$$\displaystyle (Eq. 3.1.23) $$

We then use variation of parameters to reduce the order of Eqn. 3.1.23,

$$ m=U' \,$$
$$\displaystyle (Eq. 3.1.24) $$

So we substitute in the change of parameters into Egn. 3.1.24 and use separation of variables to solve for $$m$$,

$$ m+ m'x =0 \,$$
$$\displaystyle (Eq. 3.1.25) $$

$$ m + x \frac {dm} {dx}=0 \,$$
$$\displaystyle (Eq. 3.1.26) $$

$$ m = -x \frac {dm} {dx} \,$$
$$\displaystyle (Eq. 3.1.27) $$

$$ \frac {m} {dm} = - \frac {x} {dx} \,$$
$$\displaystyle (Eq. 3.1.28) $$

Then invert to get,

$$ \frac {dm} {m} = - \frac {dx} {x} \,$$
$$\displaystyle (Eq. 3.1.29) $$

Then integrate each side and simplify,

$$ ln (m) = - (ln (x) + k_1) \,$$
$$\displaystyle (Eq. 3.1.30) $$

$$ m = \frac 1 x e^{- k_1} \,$$
$$\displaystyle (Eq. 3.1.31) $$

$$ k_2 = e^{-k_1} \,$$
$$\displaystyle (Eq. 3.1.32) $$

$$ m = \frac 1 x k_2 \,$$
$$\displaystyle (Eq. 3.1.33) $$

Then substitute the identity $$m = U'$$ into Eqn. 3.1.33 and integrate to solve for $$U$$,

$$ U = \int U' dx = \int \frac 1 x k_2 dx \,$$
$$\displaystyle (Eq. 3.1.34) $$

$$ U = k_2 [ln(x) + k_3] \,$$
$$\displaystyle (Eq. 3.1.35) $$

Substitute $$U$$ back into Eqn. 3.1.13 along with the known value of $$y_1$$ to obtain the 2nd homogeneous solution,

$$ y_2 = k_2 [ln(x) + k_3]x^{\lambda} \,$$
$$\displaystyle (Eq. 3.1.36) $$

Part 1.4
The general homogeneous solution of the Euler L2-ODE-VC will have the form,

$$ y(x) = C_1 y_1(x)+C_2 y_2(x) \,$$
$$\displaystyle (Eq. 3.1.37) $$

Plugging Eqns. 3.1.36 and 3.1.12 into Eqn. 3.1.37 and simplifying results in the general homogeneous solution,

$$ y(x) = C_1 x^{\lambda} + C_2 [k_2 [ln(x) + k_3]x^{\lambda}] \,$$
$$\displaystyle (Eq. 3.1.38) $$

$$ y(x) = x^{\lambda}[C_1 + C_2 k_2 ln(x) + C_2 k_3] \,$$
$$\displaystyle (Eq. 3.1.39) $$

$$ C_3 = C_1 + C_2 k_3 \,$$
$$\displaystyle (Eq. 3.1.40) $$

$$ C_4 = C_2 k_2 \,$$
$$\displaystyle (Eq. 3.1.41) $$

Therefore the general homogeneous solution simplifies to,

$$ y(x) = x^{\lambda}[C_4 + C_5 ln(x)] \,$$
$$\displaystyle (Eq. 3.1.42) $$

Part 2.1
The coefficients of Eqn. 3.2 (b terms) can be found if we use the trial solution method. The trial solution for an Euler L2-ODE-CC is: $$ y=e^{rx} \,$$
$$\displaystyle (Eq. 3.2.1) $$

Therefore we can calculate the first and second derivatives of the trial solution:

$$ y'=re^{rx} \,$$
$$\displaystyle (Eq. 3.2.2) $$

$$ y''=r^2e^{rx} \,$$
$$\displaystyle (Eq. 3.2.3) $$

Then substitute back into Egn. 3.2 so that it becomes,

$$ b_2r^2e^{rx} + b_1re^{rx} + b_0e^{rx}=0 \,$$
$$\displaystyle (Eq. 3.2.4) $$

Then simplify,

$$ e^{rx}[b_2r^2+b_1r+b_0]=0 \,$$
$$\displaystyle (Eq. 3.2.5) $$

$$ b_2r^2+b_1r+b_0=0 \,$$
$$\displaystyle (Eq. 3.2.6) $$

We then set Eqn. 3.2.6 equal to the expanded out version of the characteristic equation (Eqn. 3.3) to obtain the values of the coefficients,

$$ b_2r^2+b_1r+b_0=r^2-2\lambda r+\lambda^2 \,$$
$$\displaystyle (Eq. 3.2.7) $$

It is then clear that,

$$ b_2 = 1 \,$$
$$\displaystyle (Eq. 3.2.8) $$

$$ b_1= -2\lambda \,$$
$$\displaystyle (Eq. 3.2.9) $$

$$ b_0=\lambda^2 \,$$
$$\displaystyle (Eq. 3.2.10) $$

Part 2.2
To find the first homogeneous solution use the trial solution (Eqn. 3.2.1) and the characteristic equation (Eqn. 3.3). We find the roots of Eqn. 3.3 and substitute the first (real) one in for $$r$$ in the trial solution (Egn. 3.2.1). In this particular case the two roots are the same so $$r_1=r_2=\lambda$$. Substituting this into Eqn. 3.2.1 we get,

$$ y_1=e^{\lambda x} \,$$
$$\displaystyle (Eq. 3.2.11) $$

Part 2.3
Since $$\lambda$$ has two identical roots we can find the second homogeneous solution using the form,

$$ y_2(x)=U(x)y_1(x) \,$$
$$\displaystyle (Eq. 3.2.12) $$

We then calculate the first and second derivatives of Eqn 3.2.12. The $$(x)$$ argument will be ignored to simplify the equations.

$$ y_2'=U'y_1+Uy_1' \,$$
$$\displaystyle (Eq. 3.2.13) $$

$$ y_2=Uy_1+2U'y_1'+Uy_1'' \,$$
$$\displaystyle (Eq. 3.2.14) $$

Plug Eqns. 3.2.12, 3.2.13, 3.2.14 into Eqn 3.2 and simplify,

$$ b_2(Uy_1+2U'y_1'+Uy_1)+b_1(U'y_1+Uy_1')+b_0Uy_1=0 \,$$
$$\displaystyle (Eq. 3.2.15) $$

$$ U(b_2y_1+b_1y_1'+b_0y_1)+U'(2b_2y_1'+b_1y_1)+Ub_2y_1=0 \,$$
$$\displaystyle (Eq. 3.2.16) $$

This can be simplified further noting that $$U$$ is multiplied by Eqn 3.2, which equals $$0$$. So that completely eliminates one term in Egn. 3.2.16. We then substitute in the calculated values of the $$a$$ coefficients and the values for $$y_1$$ from part 2.1 and simplify,

$$ U'(2b_2y_1'+b_1y_1)+U''b_2y_1=0 \,$$
$$\displaystyle (Eq. 3.2.17) $$

$$ U'[2\lambda e^{\lambda x}+(-2\lambda )e^{\lambda x}]+U''e^{\lambda x} =0 \,$$
$$\displaystyle (Eq. 3.2.18) $$

$$ U''e^{\lambda x} =0 \,$$
$$\displaystyle (Eq. 3.2.19) $$

Therefore

$$ U'' =0 \,$$
$$\displaystyle (Eq. 3.2.20) $$

Then Integrate Eqn. 3.2.20 twice with respect to $$x$$

$$ U' = k_1 \,$$
$$\displaystyle (Eq. 3.2.21) $$

$$ U = x k_1 + k_2 \,$$
$$\displaystyle (Eq. 3.2.22) $$

Then plug Eqn. 3.2.22 and 3.2.1 into Eqn. 3.2.12 to get,

$$ y_2(x) = e^{\lambda x} (x k_1 + k_2) \,$$
$$\displaystyle (Eq. 3.2.23) $$

Part 2.4
The general homogeneous solution of the Euler L2-ODE-CC will have the form,

$$ y(x) = C_1 y_1(x)+C_2 y_2(x) \,$$
$$\displaystyle (Eq. 3.2.24) $$

Plugging Eqns. 3.2.23 and 3.2.12 into Eqn. 3.2.24 and simplifying results in the general homogeneous solution,

$$ y(x) = C_1 e^{\lambda x} + C_2 e^{\lambda x} (x k_1 + k_2) \,$$
$$\displaystyle (Eq. 3.2.25) $$

$$ y(x) = e^{\lambda x}[C_1 + C_2 + k_2] + C_2 k_1 x e^{\lambda x} \,$$
$$\displaystyle (Eq. 3.2.26) $$

$$ C_3 = C_1 + C_2 + k_3 \,$$
$$\displaystyle (Eq. 3.2.27) $$

$$ C_4 = C_2 k_1 \,$$
$$\displaystyle (Eq. 3.2.28) $$

Therefore the general homogeneous solution simplifies to,

$$ y(x) = C_3 e^{\lambda x} + C_4 x e^{\lambda x} \,$$
$$\displaystyle (Eq. 3.2.29) $$

Author and Proof-Reader
[Author]
 * Rob Carroll

[Proof-Reader]

= Problem 4 - Find particular solution= From Meeting 27, p 27-2.

Author and Proof-Reader
[Author]

[Proof-Reader]

= Problem 5 - Non-homog. L2-ODE-CC = From Meeting 28, p 28-2 to Meeting 29, p 29-1.

Author and Proof-Reader
[Author]

[Proof-Reader]

= Problem 6 - Show that lecture agree with the book = From Meeting 30, p 30-1.

Given
Particular Solution from meeting 30.

$$\displaystyle y_p(x) = u_1(x)\int{\frac{1}{h(x)}\left(\int{h(x)f(x)\,dx}\right)\,dx} $$
$$\displaystyle (Eq. 6.1) $$

Particular solution from King p. 8 (1.6)

$$\displaystyle y_p(x) = \oint{f(s)\left[\frac{u_1(s)u_2(x)-u_1(x)u_2(s)}{W(s)}\right]\,ds} $$
$$\displaystyle (Eq. 6.2) $$

Where $$\displaystyle W(x)$$ is the Wronskian defined as

$$\displaystyle W(x)=u_1(x)\,u_2(x)'-u_2(x)\,u_1(x)' $$
$$\displaystyle (Eq. 6.3) $$

Hint from meeting 30.

$$\displaystyle \frac{1}{h(x)}=\left( \frac{u_2(x)}{u_1(x)} \right)' $$
$$\displaystyle (Eq. 6.4) $$

Find
Show that 6.1 agrees with 6.2

Solve
Using quotient rule on equation 6.4 to solve for $$\displaystyle h(x)$$.

$$\displaystyle d\left(\frac{u}{v}\right)=\frac{v\,du-u\,dv}{v^2} $$

$$\displaystyle d\left(\frac{u_2(x)}{u_1(x)}\right)=\frac{u_1(x)\,u_2(x)'-u_2(x)\,u_1(x)'}{u_1(x)^2} $$
$$\displaystyle (Eq. 6.5) $$

Inverse of equation 6.5 solves for $$\displaystyle h(x)$$.

$$\displaystyle h(x)=\frac{u_1(x)^2}{u_1(x)\,u_2(x)'-u_2(x)\,u_1(x)'} $$
$$\displaystyle (Eq. 6.6) $$

Using integration by parts on equation 6.1

$$\displaystyle \int{u\,dv}=u\,v-\int{v\,du} $$

$$\displaystyle dv=\frac{1}{h(x)}=\left(\frac{u_2(x)}{u_1(x)}\right)' $$

$$\displaystyle u=\left(\int{h(x)f(x)\,dx}\right) $$

$$\displaystyle y_p(x) = u_1(x)\left\{\frac{u_2(x)}{u_1(x)} \left(\int{h(s)f(s)\,ds}\right)-\int{h(s)f(s)\frac{u_2(s)}{u_1(s)}\,ds}             \right\} $$
$$\displaystyle (Eq. 6.7) $$

Subsitute for h(s) as defined by equation 6.6

$$\displaystyle y_p(x) = u_1(x)\left\{\frac{u_2(x)}{u_1(x)} \left(\int{\frac{u_1(s)^2}{u_1(s)\,u_2(s)'-u_2(s)\,u_1(s)'}f(s)\,ds}\right)-\int{\frac{u_1(s)^2}{u_1(s)\,u_2(s)'-u_2(s)\,u_1(s)'}f(s)\frac{u_2(s)}{u_1(s)}\,ds}             \right\} $$
$$\displaystyle (Eq. 6.8) $$

Simplify equation 6.8

$$\displaystyle y_p(x) = \int{f(x)\frac{u_2(x)u_1(s)^2}{W(s)} \,ds}-\int{f(x)\frac{u_1(x)u_1(s)u_2(s)}{W(s)} \,ds} $$
$$\displaystyle (Eq. 6.9) $$

Author and Proof-Reader
[Author]

[Proof-Reader]

= Problem 7 - Finding two homog. solutions = From Meeting 31, p 31-1.

Given

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

$$\left( x+1 \right)y''-\left( 2x+3 \right)y'+2y=0$$
 * style="width:95%" |
 * style="width:95%" |
 *
$$\displaystyle (7.1)$$
 * }

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

$$\displaystyle y= {e}^{rx} $$
 * style="width:95%" |
 * style="width:95%" |
 *
$$\displaystyle (7.2)$$
 * }

Find
$$ u_1\ $$ and $$ u_2\ $$ of (7.1) using trial solution (7.2)

Solve
(7.2) ->
 * {| style="width:100%" border="0"

$$\displaystyle y'=r{{e}^{rx}}$$
 * style="width:95%" |
 * style="width:95%" |
 *
$$\displaystyle (7.3)$$
 * }

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

$$\displaystyle y''={{r}^{2}}{{e}^{rx}}$$
 * style="width:95%" |
 * style="width:95%" |
 *
$$\displaystyle (7.4)$$
 * }

(7.1) substitute with (7.3) and (7.4)
 * {| style="width:100%" border="0"

$$\displaystyle (x+1)r^2{e}^{rx} - (2x+3)r{e}^{rx} + 2{e}^{rx} = 0$$
 * style="width:95%" |
 * style="width:95%" |
 *
$$\displaystyle (7.5)$$
 * }

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

$$\displaystyle {e}^{rx} ((x+1)r^2 - (2x+3)r + 2) = 0$$
 * style="width:95%" |
 * style="width:95%" |
 *
$$\displaystyle (7.6)$$
 * }

Using basic knowledge of Quadratic equation
 * {| style="width:100%" border="0"

$$\displaystyle r= \frac{\left(2x+3 \right) \pm \sqrt{{\left(2x+3 \right)}^{2}-8\left(x+1 \right)}} {2 \left( x+1\right)}= \frac{\left(2x+3 \right) \pm \left(2x+1 \right) } {2 \left( x+1\right)} $$
 * style="width:95%" |
 * style="width:95%" |
 *
$$\displaystyle (7.7)$$
 * }

We can get two solutions about r

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

$$\displaystyle {r}_{1} = 2 \, \  {r}_{2}=  \frac{1}{ \left( x+1\right)} $$
 * style="width:95%" |
 * style="width:95%" |
 *
$$\displaystyle (7.8)$$
 * }

We choose $$r_1 $$ because it is constant
 * {| style="width:100%" border="0"

$$\displaystyle {u}_{1}(x) = {e}^{2x} $$
 * style="width:95%" |
 * style="width:95%" |
 *
$$\displaystyle (7.9)$$
 * }

Using (1) p.30-1

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

$$\displaystyle {u}_{2}(x)= \underbrace{{u}_{1}(x)}_{{e}^{2x}} \int \frac{1}{ u_1^2(x)}exp[-\int \underbrace{a_1(x)}_{\frac{-(2x+3)}{x+1}} \ dx] \ dx $$
 * style="width:95%" |
 * style="width:95%" |
 * }
 * }

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

$$\displaystyle \ = {e}^{2x} \int \frac{1}{ {e}^{4x}}exp[\underbrace{\int \frac{2x+3}{x+1} \ dx}_{2x+log(x+1)}] \ dx $$
 * style="width:95%" |
 * style="width:95%" |
 * }
 * }

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

$$\displaystyle \ = {e}^{2x} \int \frac{x+1}{{e}^{2x}} \ dx $$
 * style="width:95%" |
 * style="width:95%" |
 * }
 * }

Using wolfram mathematica

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

$$\displaystyle {u}_{2}(x) = - \frac{1}{4} (2x+3) $$
 * style="width:95%" |
 * style="width:95%" |
 *
$$\displaystyle (7.10)$$
 * }

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

$$ u_1 = {e}^{2x}, \ u_2 = - \frac{1}{4} (2x+3) $$
 * style="width:92%; padding:10px; border:2px solid #8888aa" align="center"|
 * style="width:92%; padding:10px; border:2px solid #8888aa" align="center"|
 * }
 * }
 * }

Author and Proof-Reader
[Author] Oh, Sang Min

[Proof-Reader]

= Problem 8 - Finding L2-ODE-VC(homog.) = From Meeting 31, p 31-3.

Given
Trial solution

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

$$\displaystyle y = \frac{{e}^{rx}}{x^2} $$
$$\displaystyle (8-1) $$
 * }
 * }

Character equation

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

$$\displaystyle r^2 + 3 = 0 $$
$$\displaystyle (8-2) $$
 * }
 * }

Find
L2-ODE-VC

Solve

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

$$\displaystyle y = \frac{{e}^{rx}}{x^2} $$
$$\displaystyle (8-3) $$
 * }
 * }

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

$$\displaystyle y' = \frac{r{e}^{rx}}{x^2} - \frac{2{e}^{rx}}{x^3} = \frac{{e}^{rx}}{x^2} (r - \frac{2}{x}) $$
$$\displaystyle (8-4) $$
 * }
 * }

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

$$\displaystyle y'' = \frac{{e}^{rx}}{x^2} {(r - \frac{2}{x})(r - \frac{2}{x}) + \frac{2}{x^2}} = \frac{{e}^{rx}}{x^2} (r^2 - \frac{4}{x}r + \frac{6}{x^2}) $$
$$\displaystyle (8-5) $$
 * }
 * }

 Using Reverse Eng.

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

$$\displaystyle \frac{{e}^{rx}}{x^2} [a_2(r^2 - \frac{4}{x}r + \frac{6}{x^2}) + a_1(r - \frac{2}{x}) + a_0] = \frac{{e}^{rx}}{x^2} (r^2 + 3) = 0 $$
$$\displaystyle (8-6) $$
 * }
 * }

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

$$\displaystyle a_2 r^2 + (a_1 - \frac{4a_2}{x})r + (\frac{6a_2}{x^2} - \frac{2a_1}{x} + a_0) = r^2 + 3 $$
$$\displaystyle (8-7) $$
 * }
 * }

Therefore

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

$$\displaystyle a_2 = 1, \ a_1 = \frac{4}{x}, \ a_0 = 3 + \frac{2}{x^2} $$
$$\displaystyle (8-8) $$
 * }
 * }

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

$$ y'' + \frac{4}{x} y' + (3 + \frac{2}{x^2})y = 0 $$
 * style="width:92%; padding:10px; border:2px solid #8888aa" align="center"|
 * style="width:92%; padding:10px; border:2px solid #8888aa" align="center"|
 * }
 * }
 * }

Author and Proof-Reader
[Author] Oh, Sang min

[Proof-Reader]

= References =

= Contributing members =

Soo W. Jo : Authored Problem 1 and Problem 2.

Rob Carroll : Authored Problem 3

title: User talk:Egm6321.f10.team5.oh/hw5


text:
User talk:Egm6321.f10.team5.steinberg/hw5

Part 1
We can rearrange Eqn. 5.1 into the following form:

When in this form, it is apparent that the equation is exact since it can be represented as

where

The 2nd condition of exactness involves two relations which are as follows:

Computing the partial derivatives for (5.1.5) and (5.1.6),

$$ f_{tt} = f_{ty} = f_{yy} = f_{yp} = f_{y} = 0 \! $$

$$ g_{tp} = g_{yp} = g_{pp} = 0 \! $$

$$ g_{y} = a_0 \! $$

In order for (5.1.5) to be satisfied, $$ a_0 \! $$ must be zero.

$$ (5.1.3) \Rightarrow \phi(t,y,p) = h(t,y) + \int a_2 dp \! $$

$$ \phi_t = h_t \! $$

$$ \phi_y = h_y \! $$

Substituting these results into (5.1.4) yields

From (5.1.7) we can solve for $$ h \! $$ to arrive at

Part 2
Let $$ h(t) = exp(\alpha t), \alpha \in \Re \! $$.

Multiplying both sides of Eqn. 5.1 and integrating yields

Part 2.1
Assume that the LHS of (5.2.1) will be of the following form

We set $$ \bar{a}_2 = 0 $$ to reduce the order, differentiate (5.2.2) and set it equal to the integrand of (5.2.1) as follows

$$ \frac{d}{dt}\Big[exp(\alpha t)(\bar{a}_2y+\bar{a}_1y'+\bar{a}_0y) \Big] = exp(\alpha t)\Big(\bar{a}_1 y + (\alpha \bar{a}_1+\bar{a}_0)y' + \alpha \bar{a}_0 y \Big) = exp(\alpha t)\big[a_2y''+a_1y'+a_0y\big] \! $$

The remaining coefficients of (5.2.2) are thus given by

$$ \bar{a}_1 = a_2 \! $$

$$ \bar{a}_0 = a_1 - \alpha a_2 = a_0/\alpha \! $$

Part 2.2
With

$$ a_1 - \alpha a_2 = a_0/\alpha \! $$

we can rewrite it in quadratic form by multiplying both sides by $$ \alpha \! $$ to result in the following

Part 2.3
Returning now to (5.2.1), we substitute (5.2.2) as the result of the LHS integration yielding the following reduced order equation

Dividing through by $$ exp(\alpha t) \! $$ and then by $$ \bar{a}_1 $$ results in the following

Part 2.4
With the L1-ODE-CC found in (5.2.5), we choose the integrating factor as

$$ h(t) = exp \Big[ \int \frac{\bar{a}_0}{\bar{a}_1} dt \Big] = e^{\beta t} \! $$

And since we have (5.2.5) in the correct form (see (2) p. 10-3), we can solve for y using (6) on p. 10-3

Part 2.5
$$ \beta = \frac{\bar{a}_0}{\bar{a}_1} = \frac{a_0/\alpha}{a_2} \Rightarrow \alpha\beta = \frac{a_0}{a_2} $$

$$ \beta = \frac{\bar{a}_0}{\bar{a}_1} = \frac{a_1 - \alpha a_2}{a_2} = \frac{a_1}{a_2} - \alpha \Rightarrow \alpha + \beta = \frac{a_1}{a_2} $$

Part 2.6
Eqn. (5.2.6) is actually the particular solution of the L2-ODE-CC given. Since $$ \alpha $$ and $$ \beta $$ are the roots of the characteristic equation, the complementary solution (or homogeneous solution) is found to be

Because the general solution is the linear combination of the homogeneous solution and particular solution, it is as follows

Part 2.7
If we use the trial solution lookup table for a particular solution if $$ f(t) = t^2 $$, we come up with a trial solution of

where $$ C_2 $$,$$ C_1 $$ and $$ C_0 $$ are undetermined constant coefficients.

To compare this particular solution to the one found in (5.2.6), we substitute $$ f(t) = t^2 $$ into (5.2.6) and find that

The result shown in (5.2.10) is clearly the same form as the trial solution in (5.2.9).

Part 2.8
We will now solve (5.1) for the forcing function $$ f(t) = exp(-t^2) $$.

Part 2.8.1
To begin with, since the characteristic equation is $$ (r+1)(r-2) $$, we know that the homogeneous solution is

and we know that the coefficients in (5.1) are

$$a_2 = 1 \!$$

$$a_1 = -1 \!$$

$$a_0 = -2 \!$$

Our integrating factor (p. 29-3) becomes

Now we turn to (2) p. 30-1 to find the particular solution

Part 2.8.2
To begin with, since the characteristic equation is $$ (r-4)^2 $$, we know that the homogeneous solution is

and we know that the coefficients in (5.1) are

$$a_2 = 1 \!$$

$$a_1 = -8 \!$$

$$a_0 = 16 \!$$

Our integrating factor (p. 29-3) becomes

Now using (2) p. 30-1 again to find the particular solution


text: Ideas in Geometry/Instructive examples/Section 2-3


text: File:Egm6321.f10.team2.oztekin.5.2solution.png


text:
Childhood obesity

Childhood obesity Heart disease. Type II diabetes. Arthritis. Asthma. Cancer. These diseases have traditionally been associated with the adult population, but they have overwhelmingly been appearing in the childhood population thanks to childhood obesity (MICA 2010). Obesity is defined as having a body mass index (BMI) of 30 or more. Body mass index is measured on a height-to-weight scale. Therefore, an individual who is 5’9 and weighs 180 pounds will have a higher BMI than an individual who is 6’0 and weights 180 pounds. BMI does not take into account lean tissue, such as in athletes, however children normally are unaffected by this flaw in calculation since they typically do not have a great amount of lean tissue.

Statistics In the past decade, obesity in children has risen dramatically. The percentage of overweight children in the United States is growing at an alarming rate, with 1 out of 3 kids now considered overweight or obese (CDC). Prevalence of obese middle school children has increased 75% in the last five years, and the prevalence of obese high school students has increased by 64% during the same time period (MICA 2010). The United States has seen a huge increase in the past five decades in obesity among all of its citizens. The rate of overweight men and women has doubled from the 1950’s to the 1990’s, while the level of obesity has increased more than threefold in the same time span. In 2008, more than one third of US children and adolescents aged 6–19 were overweight or obese (CDC). When looking at the United States’ children specifically, the rates are astonishing. 9.5% of children under the age of two are obese. That rate rises to 11.9% in the 2-9 year old age group (Ogden et al 2009). The rate is even for the children of Missouri. 14% of children are considered obese in Missouri (The Obesity Epidemic and Missouri Students 2009). Clay County is where the numbers get scary. Overall, the level of obesity for children is lower in Clay County than the rate for Missouri as a whole. 10.8% of 2-5 year olds and 10.2% of 5-20 year olds have a body mass index in the obese range (Crigler 2003). The level of children who are overweight for the same age ranges are significantly higher. 17.0% of 2-5 year olds and 19.6% of 5-20 year olds are overweight (Crigler 2003). These are the highest rates for the entire Kansas City area. All of these statistics are the driving force behind the Clay60 program of the Clay County Public Health Center.

Exercise The Centers for Disease Control and Prevention (CDC) have proclaimed that two modifiable factors that lead to obesity are diet and exercise (2010). The CDC’s following exercise requirements for children will combat obesity and lead to a higher overall quality of life: •	Children 6-17 should take part in aerobic activity for 60 or more minutes every day •	Children 6-17 should take part in muscle strengthening exercises (gymnastics, push-ups, etc) three days per week as a part of the 60 or more minutes •	Children 6-17 should take part in bone strengthening exercises (jumping rope, running, etc) three days per week as part of the 60 or more minutes Following these guidelines every day will help our children stay fit, and will actively combat obesity and the diseases associated with the debilitating condition. As a community, we need to support the physical education curriculum within Missouri’s school districts, and we absolutely must turn the T.V. off and force our kids to be active. Children who exercise build more lean tissue (muscle), have lower blood sugar levels, and have a lower risk for heart disease and diabetes than sedentary children. Besides the immediate health benefits associated with exercising, children who are fit enjoy a greater social experience, have more friends, and are happier overall more than obese children (CDC 2010). The slogan “Clay 60” is just a reminder that Clay County residents should make sure their children are playing and exercising for 60 minutes every single day so they can lead longer, healthier, and happier lives!

Nutrition In order to combat the change in eating habits, The United States Department of Agriculture has set forth guidelines for the recommended daily servings with the food guide pyramid as well as other tips for eating a healthy balanced diet. The general recommendations for kids are for an 1800 calorie diet with a balance of grains, vegetables, fruits, dairy and meat. It recommends 6 ounces of grains, two and half cups of vegetables, one and a half cups of fruits, 3 cups milk or dairy products and 5 ounces of meat and beans(United Stated Department of Agriculture). One ounce of grains is roughly once slice of bread or half a cup of cooked pasta. One cup of yogurt or one and a half ounces of cheese is equal to a cup of milk. One egg or one tablespoon peanut butter is equal to about an ounce of meat. In addition to these general recommendations, you can go to www.mypyramid.gov and determine your own specific guidelines for your height, weight, age and gender. The USDA also lists some general tips in addition to the diet recommendations already listed. When eating grains, try and make at least half of them whole grains. Fruits and vegetables need to be multiple different colors because they have different kinds of nutrients. Try to switch to low fat or fat free milk if you are currently drinking whole milk. Lastly, focus on lean meats such as poultry or lean beef and trim away excess fat before cooking.

Causes The driving factors behind these numbers are the same two things everyone keeps coming back to: diet and exercise. The children of today’s generation are much more sedentary than past generations. Multiple reasons for this have been stated, including video game usage and lack of safety for children to be playing outside. Looking at diet, there are a few driving factors. There has been a huge increase in portion size for foods as well as the amount of fat and sugar in the foods that children are eating. Also another key factor that brings together diet and exercise is caloric expenditure. Caloric expenditure occurs when a child eats more than they burn, this caloric uptake leads to the child’s weight being well above the average for their height and age. Besides diet and exercise, according to the Centers for Disease Control & Prevention, some of the other potential causes of childhood obesity are family environment/influence and genetics. In regards to genetics, if one parent is obese, a child has a 50% chance of being obese. Furthermore, if both parents are obese, the child has an 80% chance of being obese. Another cause that may be overlooked is a child not receiving the recommended amount of sleep. Sleep is an important part of a child’s life, but not getting enough sleep can actually lead to a higher chance of being overweight (Crothers et al., 2009). Simply adding an hour of sleep can lower an 8 to 12 year old child’s chances of becoming overweight by 30% to 34% (Crothers et al., 2009).

Future Problems Childhood obesity is not only is a serious medical condition but is also becoming a serious epidemic. Childhood obesity has a significant impact on the child’s self-esteem. A study at the University of Medicine and Dentistry of New Jersey found that obese girls ages 13 to 14 are four times more likely to experience low self-esteem than non-obese girls (Levey 1). If mental health issues weren’t bad enough, children are now dealing with health issues only once plagued by adults such as type II diabetes, high blood pressure, and high cholesterol. Type II diabetes is a disease in which the body becomes resistant to insulin. Insulin directs tissues in the body to absorb nutrients (especially sugar to be used and stored for energy), so resistance to insulin causes hyperglycemia (high blood sugar) which leads to high blood pressure, atherosclerosis (collection of fat in arteries), and other life-threatening conditions. Type II diabetes was once considered an adult condition, but the childhood obesity epidemic has caused the instance of diabetes to increase dramatically in children and adolescents. It is no wonder that heart disease, high cholesterol, and high blood pressure occur more frequently in obese children (MICA 2010). Besides the immediate health risks, 70% of obese children grow-up to be obese adults. With 39.4% of Missouri’s children being overweight, obese, or at risk to become overweight or obese, the CDC’s exercise requirements must be enforced and must be employed in our children’s daily lives.

References Center for Disease Control and Prevention. (2010,May 10). How much physical activity do children need.Retrieved October 6, 2010, from http://www.cdc.gov/physicalactivity/everyone/guidelines/children.html

Center for Disease Control and Prevention. (2015,August 14). Establish school environments that support healthy eating and physical activity. Retrieved September 20, 2015, from http://www.cdc.gov/healthyschools/npao/schoolenvironment.html

Crigler, J. (2003). METROPOLITAN KANSAS CITY. Kansas City: Prime Health Foundation.

Crothers, L., Kehle, T., Bray, M., & Theodore, L. (2009). Correlates and suspected causes of obesity in children. Psychology in the Schools, 46(8), 787-796. Retrieved from http://web.ebscohost.com/ehost/detail?sid=30e2573c-62cd-42a8-98ef-eede155e88d1@sessionmgr12&vid=3&hid=22&bdata=JnNpdGU9ZWhvc3QtbGl2ZQ==

Levey, Amy. "EurekAlert." EurekAlert. (2003): 1. Print. .

Ogden, C. L., Carroll, M. D., Curtin, L. R., Lamb, M. M., & Flegal, K. M. (2009). Prevalence of High Body Mass Index in US Children and Adolescents, 2007-2008. Journal of the American Medical Association.

Physical Activity for Everyone. (n.d.). Retrieved September 30, 2010, from Centers for Disease Control and Prevention http://www.cdc.gov/physicalactivity/everyone/guidelines/children.html

State of Missouri Department of Health and Senior Services. (2010,October 10). Community data profiles.Retrieved October 6,2010, from http://www.dhss.mo.gov/CommunityDataProfiles/index.html

The Obesity Epidemic and Missouri Students. (2009). Retrieved September	30, 2010, from Centers for Disease Control and Prevention:Http://www.cdc.gov/healthyyouth/yrbs/pdf/obesity/mo_obesity_combo.pdf

United States Department of Agriculture. (n.d.). Retrieved September 30, 2010, from My Pyramid ttp://www.mypyramid.gov/mypyramid/results.htmlname=undefined&age=1&gender=male&weight=89&heightfeet=4&heightinch=11&activity=sed&we       ightN=89&heightfeetN=4&heightinchN=11&validweight=0&validheight=0&

title: Childhood obesity


title: File:Y(x)=-13.5x+4.5x^2.jpg


text:
User:Charles Jeffrey Danoff/Learner Profile

Cf. my Spring 2011 Handmade Semester This is an experiment in creating a Learner Profile, as described by George Siemens in What are Learning Analytics?

 * I can also learn from Erkan Yilmaz Personal Learning Environment [PLE] diary, and by reading-up on PLE's. --Charles Jeffrey Danoff 17:26, 18 January 2011 (UTC)

Currently Studying
from Wiktionary entry for study.
 * 1) To revise materials already learned in order to make sure one does not forget them, usually in preparation for an examination.
 * Students are expected to start studying for final exams in March.
 * I need to study my biology notes.
 * 1) To take a course or courses on a subject.
 * I study medicine at the university.
 * 1) To acquire knowledge on a subject.
 * Biologists study living things.
 * 1) To look at minutely.
 * He studied the map in preparation for the hike.

Background
Lived in Japan for 6 years as a child, studied the language formally at school for 2. Later spent a year working there, where I put a lot of free time into practicing oral and aural Japanese. Essentially I am illiterate, being unable to read or write, aside from recognizing a few basic characters.

Current Study Plan

 * Attend a Weekly Beginner's Japanese Class
 * Study the Hiragana and Katakana Alphabets Independently

Short term goal

 * Memorize hiragana and katakana by November 19th.
 * Find an online friend to learn Japanese from/with, possibly by editing Japanese Wikipedia articles?

Background
Been thinking informally about the topic since I was 13-ish, started formalizing the process in college, then did formalize it in an October 2010 paper.

Current Study Plan
Add to User:Charles Jeffrey Danoff/How-to Build an NBA Dynasty Notes as I find ideas and article of interest and begin building my theory.

Short term goal

 * Keep moving on the 10,000 mile journey.

ELT
(English Language Teaching) as in, I am studying how to teach the English language.

Personal Finance

 * Reading Your Money: The Missing Manual

Currently Researching
from Wiktionary entry for research.
 * 1) transitive to search or examine with continued care; to seek diligently.
 * 2) intransitive to make an extensive investigation into.
 * 3) transitive to search again.
 * Paragogy, with User:Arided

Free Software
The idea and execution itself, as well as learning Linux and using it on my computer.

Finance
Specifically, I'd like to pass the CFA exam.

Law

 * 2 part video on the 5th amendment, hosted on RMS's website. --Charles Jeffrey Danoff 08:23, 6 February 2011 (UTC)


text:
User talk:Niko21

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 Hello Achayan, 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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 * 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.
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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. --Mu301Bot 07:18, 3 November 2010 (UTC)

Feel free to leave a message on my talk page if you have any questions or need help. --mikeu talk 07:18, 3 November 2010 (UTC)

title: User talk:Achayan


text:
User talk:Warg~enwikiversity

 Hello Warg, 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. --Mu301Bot 07:18, 3 November 2010 (UTC)

Feel free to leave a message on my talk page if you have any questions or need help. --mikeu talk 07:18, 3 November 2010 (UTC)

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 Warg. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Warg~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.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:47, 17 March 2015 (UTC)

Renamed
 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) 06:25, 19 April 2015 (UTC)

title: User talk:Warg~enwikiversity


text:
Talk:Motivation and emotion/Textbook/Emotion/Sport

Feedback
I've had a look over the draft the to date - good on you for getting this up and inviting comment. Overall, my main comments are to work on a stronger introduction (probably with focus questions), introductions to the main body sections, and a stronger summary conclusions (what are the answers to the key questions). This should hopefully help to tighten and narrow the focus. The second main area for improvement is to scrub out anything plagiarised and write in your own words. See below for some other more detailed comments: Sincerely, James -- Jtneill - Talk - c 08:36, 3 November 2010 (UTC)
 * 1) Introduction
 * 2) The chapter could benefit from developing the Introduction and particular some clear aims and/or focus questions.
 * 3) I guess there might be at least two aspects of sport, exercise and emotions to consider - antecedent emotions (i.e., emotions before exercise/sport) and emotional responses to participation. The overall structure reflects the responses part, but perhaps less so the antecendent emotions.
 * 4) You may wish to clarify and distinguish between sport and exercise (or perhaps refine the chapter to only one of these and emotion).
 * 5) Theories
 * 6) I think it makes sense to structure the first main body section by theory, but some more general introduction to the theory section could help a reader - what are these theories for and why have these particular ones been selected?
 * 7) At least some of the theory content appears to be plagiarised e.g., from http://psychology.about.com/od/cindex/g/cannonbard.htm - such content should be removed ASAP or used appropriately within attributed quotations. Otherwise, only present content that you have independently written. (Hint: A tell-tale sign is lack of citations - and citations without references.)
 * 8) APA style
 * 9) Direct quotes also need page numbers e.g., (Fehr & Russell, 1984)

-- Jtneill - Talk - c 00:57, 14 December 2010 (UTC)


text:
File talk:User page.png

hi every one This is sundeep from hyderabad I am a graduate in computer science

title: File talk:User page.png


text:
Latonic/Pronouns

Personal Pronouns
A recapitulation on the personal pronouns and their translation
 * Mego, me is "I"
 * Iégo, ié is a slightly more formal/archaic variant for "I"
 * Tú, te means "you" in the singular form. It may be emphasised as tuvi, which means "you there", or tuli which is more general, or simply tú
 * Elui /ɛlɥɪ/, il means "he"
 * Ella/elléa, la means "she"
 * Le means "it" and has no emphasised form (instead the demonstrative pronoun "illu/illo" is used)
 * Noste/nobi, no(s) is "we"
 * Veste/vobi, vo(s) is "you" in the plural or extra-formal form
 * Éi, i means "they (male)"
 * Éie, lé means "they (female)"
 * Li means "they (neuter/male)" and also copies it's emphasised form from the demonstrative pronoun "illa/-i"
 * Sego, se is used for the reflective third person (himself, herself, themselves) and for the imppersonal second person (see "Anomalities of the Verb")

Personal Pronouns for the Subject and Direct Object
The pronouns as a subject are the ones discussed above. As a direct object, most of them copy the subject. The direct form is also used with prepositions that use the accusative (i.e. Il vene a mego)

Personal Pronouns for the Indirect Object
The pronouns for the indirect object are a lot different from the ones used for the subject and the direct object. They are also used for prepositions which are normally with a dative (i.e. il sta a mibi)

Personal Pronouns for the Genitive and the Possessive Pronoun
When indicating possession or origin, these forms of the personal pronoun are used (míu/méu can be compared to mine). The same forms without an exit are used as possessive pronouns, their final vowel replaced by an -é if the following word is plural. *= Apply rules for 1st Class adjectives before the noun to nos, nostra and ves, vestra **= Apply rules for 1st Class adjectives behind the noun to meo, -a, -u, tuo, -a, -u, etc. ***= Apply rules for 2nd Class adjectives behind the noun to noster, -tri, -tre and vester, -tri, tre

title: Latonic/Pronouns


text: File:2010 11 02 14 58 42.djvu

title: File:2010 11 02 14 58 42.djvu


text:
User:Egm6321.f10.team2.reserve

Team2's reserve

HW1

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HW3

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title: User:Egm6321.f10.team2.reserve