text:
User:Egm6321.f10.team4.Yoon/HW32009

Solution

 * PART 1: Verify Exactness of Bessel Equation

 * The first condition for exactness of $$\displaystyle N2-ODE$$ is that it is in the following form:
 * {| style="width:100%" border="0" align="left"

F(x,y,p) = f(x,y,p)y'' + g(x,y,p)=0 $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 2.6)
 * }
 * }

 * where

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

p = y' $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 2.7)
 * }
 * }

 * Now comparing Eq.2.1 with the form of Eq.2.6,we can see that:

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

$$
 * $$\displaystyle f(x,y,p)={{x}^{2}}$$
 * $$\displaystyle (Eq.2.8)
 * $$\displaystyle (Eq.2.8)
 * }
 * {| style="width:100%" border="0" align="left"
 * {| style="width:100%" border="0" align="left"

$$
 * $$\displaystyle g(x,y,p)=x{p}+\left( {{x}^{2}}-{{\upsilon }^{2}} \right)y$$
 * $$\displaystyle (Eq.2.9)
 * $$\displaystyle (Eq.2.9)
 * }
 * }

 * Hence the first condition for exactness is satisfied.

 * Now verify second condition of Exactness:

 * (a) Using Method 1- Eq.2.2 and Eq.2.3

 * Taking derivative of Eq.2.8 yields:

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

\begin{array}{*{20}l} {f_x = 2x} & {f_{xx}  = 2} & {f_{xy}  = 0} & {f_{xp}  = 0 }  \\ {f_y = 0} & {f_{yy}  = 0} & {f_{yp}  = 0}\\ \end{array} $$.
 * $$\displaystyle
 * $$\displaystyle
 * }
 * }
 * Similarly taking derivative of Eq.2.9 yields:

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

\begin{array}{*{20}l} {g_x = p+2xy} & {g_{xp} = 1} & {{g}_{y}}={{x}^{2}}-{{\upsilon }^{2}} & {g_{yp}  = 0 }  \\ {g_p = x} & {g_{pp}  = 0} \\ \end{array} $$
 * $$\displaystyle
 * $$\displaystyle
 * }
 * }

 * Substituting the above values to Eq.2.3 (first relation) and Eq.2.4 (second relation):

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

 * $$2+2p\times 0+{{p}^{2}}\times 0=1+p\times 0-\left( {{x}^{2}}-{{\upsilon }^{2}} \right)$$
 * }
 * }
 * }

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

$$
 * $$\Rightarrow 2=1-\left( {{x}^{2}}-{{\upsilon }^{2}} \right)$$
 * $$\displaystyle (Eq.2.10)
 * $$\displaystyle (Eq.2.10)
 * }
 * }

 * So first relation for second exactness condition is not satisfied.

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

$$
 * $$0+p\times 0+2\times 0=0\Rightarrow 0=0$$, second relation is satisfied
 * $$\displaystyle (Eq.2.11)
 * $$\displaystyle (Eq.2.11)
 * }
 * }

 * Since the first relation is not satisfied, the Eq.2.1 is not Exact

 * (b) Using Method 2- Eq.2.4

 * Differentiating $$\displaystyle Eq.2.1$$, partially with respect to $$\displaystyle y,{{y}^{'}},{{y}^{''}}$$,

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

 * $${{f}_{0}}=\frac{\partial F}{\partial y}={{x}^{2}}-{{\upsilon }^{2}}$$
 * }
 * }
 * }

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

 * $${{f}_{1}}=\frac{\partial F}{\partial {{y}^{'}}}=x$$
 * }
 * }
 * }

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

 * $${{f}_{2}}=\frac{\partial F}{\partial {{y}^{''}}}={{x}^{2}}$$
 * }
 * }
 * }

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

 * Now, $$\frac{\partial {{f}_{1}}}{\partial x}=1$$, and $$\frac{\partial {{x}^{2}}}=2$$
 * }
 * }
 * }

 * Substittuting above values in $$\displaystyle Eq.2.4$$ yields,

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

 * $${{x}^{2}}-{{\upsilon }^{2}}-1+2\ne 0\Rightarrow $$not satisfied and hence the Eq.2.1 is not Exact.
 * }
 * }
 * }

 * PART 2: Make Bessel Equation exact using Integrating Factor Method

 * Multiply $$\displaystyle Eq.2.1$$ by Integrating Factor ($$\displaystyle Eq.2.5$$)$$\Rightarrow $$

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

$$
 * $$\underbrace_{f}{{y}^{''}}+\underbrace{{{x}^{m+1}}{{y}^{n}}{{y}^{'}}+{{x}^{m+2}}{{y}^{n+1}}-{{x}^{m}}{{y}^{n+1}}{{\upsilon }^{2}}}_{g}=0$$
 * $$\displaystyle (Eq.2.12)
 * $$\displaystyle (Eq.2.12)
 * }
 * }

 * New $$\displaystyle f$$ and $$\displaystyle g$$ are:

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

$$
 * $$f\left( x,y,p \right)={{x}^{m+2}}{{y}^{n}}$$
 *
$$\displaystyle (Eq.2.13)
 *
$$\displaystyle (Eq.2.13)
 * }
 * }

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

$$
 * $$g\left( x,y,p \right)={{x}^{m+1}}{{y}^{n}}p+{{x}^{m+2}}{{y}^{n+1}}-{{x}^{m}}{{y}^{n+1}}{{\upsilon }^{2}}$$
 *
$$\displaystyle (Eq.2.14)
 *
$$\displaystyle (Eq.2.14)
 * }
 * }

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

Analyzing the second relation of second exactness condition ($$\displaystyle Eq.2.3 $$):$$\displaystyle f_{xp} + pf_{yp} + 2f_{y} = g_{pp}$$, it can be noted that most of the terms drop out since $$\displaystyle f$$ is independent of $$\displaystyle p$$. Consequently all derivatives of $$\displaystyle f$$ with respect to $$\displaystyle p$$ become zero. Moreover $$\displaystyle {{g}_{pp}}=0$$ and hence $$\displaystyle Eq.2.3 $$ is simplified to,
 * }
 * }

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

$$
 * $$\displaystyle 2{{f}_{y}}=0$$
 *
$$\displaystyle (Eq.2.15)
 *
$$\displaystyle (Eq.2.15)
 * }
 * }

 * Taking derivative of $$\displaystyle (Eq.2.13)$$ with repect to $$\displaystyle y$$ and substituting to$$\displaystyle (Eq.2.15)$$ yields,

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

 * $$\displaystyle n{{x}^{m+2}}{{y}^{n-1}}=0$$
 * }
 * }
 * }

 * The above equation is true only when,

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

$$\displaystyle n=0$$ $$
 * style="width:2%; padding:1px; border:2px solid #FF0000" |
 * style="width:2%; padding:1px; border:2px solid #FF0000" |
 *
$$\displaystyle (Eq. 2.16)
 * }
 * }

 * As $$\displaystyle n=0 $$, the function $$\displaystyle f$$ and $$\displaystyle g$$ can be rewritten as:

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

$$
 * $$f\left( x,y,p \right)={{x}^{m+2}}$$
 *
$$\displaystyle (Eq.2.17)
 *
$$\displaystyle (Eq.2.17)
 * }
 * }

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

$$
 * $$g\left( x,y,p \right)={{x}^{m+1}}p+{{x}^{m+2}}y-{{x}^{m}}y{{\upsilon }^{2}}$$
 *
$$\displaystyle (Eq.2.18)
 *
$$\displaystyle (Eq.2.18)
 * }
 * }

 * Taking derivative of $$\displaystyle Eq.2.18$$ yields,

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

\begin{array}{*{20}l} {{f}_{x}}=\left( m+2 \right){{x}^{m+1}}, & {{f}_{xx}}=\left( m+2 \right)\left( m+1 \right){{x}^{m}}, & {f_{xy} = 0}, & {f_{xp}  = 0 }  \\ {f_y = 0}, & {f_{yy}  = 0}, & {f_{yp}  = 0}\\ \end{array} $$
 * $$\displaystyle
 * $$\displaystyle
 * }
 * }

 * Similarly taking derivative of $$\displaystyle Eq.2.17$$ yields,

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

\begin{array}{*{20}l} {{g}_{x}}=\left( m+1 \right){{x}^{m}}p+\left( m+2 \right){{x}^{m+1}}y-m{{x}^{m-1}}y{{\upsilon }^{2}}\\ {{g}_{xp}}=\left( m+1 \right){{x}^{m}}\\ {{g}_{y}}={{x}^{m+2}}-{{x}^{m}}{{\upsilon }^{2}}\\ {g_{yp} = 0} \\ \end{array} $$
 * $$\displaystyle
 * $$\displaystyle
 * }
 * }

 * Substituting above differentials in $$\displaystyle Eq.2.17$$ gives,

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

 * $$\left( m+2 \right)\left( m+1 \right){{x}^{m}}+0+0=\left( m+1 \right){{x}^{m}}+0-\left( {{x}^{m+2}}-{{x}^{m}}{{\upsilon }^{2}} \right)$$
 * }
 * }
 * }

 * Simplifying,

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

 * $$\left( m+2 \right)\left( m+1 \right)=m+1+{{\upsilon }^{2}}-{{x}^{2}}$$
 * }
 * }
 * }

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

 * $$\Rightarrow {{m}^{2}}+2m+\left( {{x}^{2}}-{{\upsilon }^{2}}+1 \right)=0$$
 * }
 * }
 * }

 * $$\displaystyle m$$ is obtained by solving the above quadratic equation:

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

$$m=-1\pm \sqrt{\left( {{\upsilon }^{2}}-{{x}^{2}} \right)}$$ $$
 * style="width:2%; padding:1px; border:2px solid #FF0000" |
 * style="width:2%; padding:1px; border:2px solid #FF0000" |
 *
$$\displaystyle (Eq. 2.19)
 * }
 * }

 * So the integration factor is obtained by substituting $$\displaystyle Eq. 2.16 $$ and $$\displaystyle Eq. 2.19 $$ in $$\displaystyle Eq. 2.5 $$:

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

$$h={{x}^{-1\pm \sqrt{\left( {{\upsilon }^{2}}-{{x}^{2}} \right)}}}$$ $$
 * style="width:2%; padding:1px; border:2px solid #FF0000" |
 * style="width:2%; padding:1px; border:2px solid #FF0000" |
 *
$$\displaystyle (Eq. 2.20)
 * }
 * }

 * Thus Bessel Equation can be made exact using the above integrating factor.

title: User:Egm6321.f10.team4.Yoon/HW32009


text:
User:Egm6321.f10.team4.Yoon/HW4

 * (a) Using Method 1- Eq.2.2 and Eq.2.3

 * Taking derivative of Eq.2.8 yields:

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

\begin{array}{*{20}l} {f_x = 2x} & {f_{xx}  = 2}\\ & {f_{xy} = 0}\\ & {f_{xp} = 0}\\ {f_y = 0}  & {f_{yy}  = 0}\\ & {f_{yp} = 0}\\ \end{array} $$.
 * $$\displaystyle
 * $$\displaystyle
 * }
 * }
 * Similarly taking derivative of Eq.2.9 yields:

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

\begin{array}{*{20}l} {g_x = p+2xy} & {g_{xp} = 1} & {{g}_{y}}={{x}^{2}}-{{\upsilon }^{2}} & {g_{yp}  = 0 }  \\ {g_p = x} & {g_{pp}  = 0} \\ \end{array} $$
 * $$\displaystyle
 * $$\displaystyle
 * }
 * }

 * Substituting the above values to Eq.2.3 (first relation) and Eq.2.4 (second relation):

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

 * $$2+2p\times 0+{{p}^{2}}\times 0=1+p\times 0-\left( {{x}^{2}}-{{\upsilon }^{2}} \right)$$
 * }
 * }
 * }

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

$$
 * $$\Rightarrow 2=1-\left( {{x}^{2}}-{{\upsilon }^{2}} \right)$$
 * $$\displaystyle (Eq.2.10)
 * $$\displaystyle (Eq.2.10)
 * }
 * }

 * So first relation for second exactness condition is not satisfied.

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

$$
 * $$0+p\times 0+2\times 0=0\Rightarrow 0=0$$, second relation is satisfied
 * $$\displaystyle (Eq.2.11)
 * $$\displaystyle (Eq.2.11)
 * }
 * }

 * Since the first relation is not satisfied, the Eq.2.1 is not Exact

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

title: User:Egm6321.f10.team4.Yoon/HW4


text:
User:Mrblong

helo

title: User:Mrblong


text:
User talk:Mrblong

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title: User talk:Mrblong


text:
Teaching EFL Listening via FUN WITH ENGLISH Books/7A/Playing Sports Lesson

Preface
Textbook focused lesson also addressing some administrative issues I had not resolved by lesson 3 like seating charts.

Focuses

 * Set Skill = "B" Text orientation and identifying context
 * Curriculum Statement = "4" Orientation to text
 * Specific Skill = "a" Familiarise students wit various exercises/evaluations.

Learning Outcome

 * Students will be to complete the written exercises by listening for the answers.

1 Greeting

 * How are you?
 * If they all say, "I'm fine thank you", go over alternative responses.
 * Ask "What will you do for the national holiday?" and follow up questions.
 * Ask "What will you do for the mid-autumn festival?"
 * See if the students have any questions for me.

2 Chapter Lead-In

 * What do you do for fun?
 * Write it on the board if they don't get it.
 * What do your grandparents do on the weekend?

3 Textbook

 * 6 (maybe), 7A, 8A &9
 * When finished with page 7, ask how much time we have in the period, before moving on.
 * I read them all.
 * Page 8A, ask "Which letter is number one?" "Which sport is *2" "Which letter is baseball?"
 * Page 9, for false statements ask "what's true?"

4 Seating Chart

 * If this class is going to change every couple of weeks, do it just to learn their names?

5 Telephone

 * Use diagram on the board to explain the game.
 * Only two teams, have students who are done go to the back of the room.

Extra Time

 * Hangman
 * Simon Says


text:
Talk:Electronics/Bipolar Junction Transistors

Links
Shouldn't there be some links in this article, for example, to NPN and PNP? --Mortense 16:11, 19 October 2010 (UTC)


text:
Collaborative play writing/A Yorkshire Tragedy

A Yorkshire tragedy

Dramatic characters (9)

Master Clutch

Lady Clutch

The duke of York

Oliver, steward to Clutch

Samuel, servant to Clutch

Ralph, servant to Clutch

Spruce, courtier

Counsel, friend to Spruce

Page to the duke

The duke's guardsmen

Time: Early 16th century

Place: Yorkshire, England

/Act_1/

/Act_2/

/Act_3/

/Act_4/

/Act_5/


text:
Collaborative play writing/A Yorkshire Tragedy/Act 1

Act 1. Scene 1. Calvary Hall

Enter Samuel and Ralph

Samuel. Our mistress squeezes her legs together without hands, pines, moans, wails somewhat about the rose-leaved one, her gallant man, who has not made her humor light for two entire days.

Ralph. Such lightness will eventually make her heavy, Samuel.

Samuel. It is the usual way.

Ralph. And makese away from such beverage, even with looking.

Samuel. I do, only to hear.

Ralph. I never yet beheld a hapy whore, laughter rising from the throat, not the lungs, no smile from a contented heart but grimacing in velvet. I would not trade away my honesty for all the greater ones wear on their backs, which death too soon discharges.

Samuel. Fearfully she shuns any advice, good or inane, sleeping with the bad to escape the bad.

Ralph. A woman enters the world like a warmed-up pot, consuming man's property and honor, first to vapor, then to ashes, should she relieve the monkey from her flank.

Samuel. "The monkey tickles her senses, makes her want more," said our parson last Sunday night, exhorting that such ills soon end.

Ralph. Does he wish to kill the third part of his audience? Women bear more easily loss of parents, husband, child, than their soft couches. Let our mistress lip a serpent's egg or pastes of flies crushed together rather than pick unlawful fruit.

Samuel. That's my conclusion, too.- What is that noise? Our master cursing?

Ralph. A friend, on whom devils will smile during our final day.

Enter Oliver

Oliver. Fellow men, fellow sufferers, welcome me again. News spurt from my lungs.

Samuel. Welcome, sir.

Ralph. Welcome, sir, virtuously adherent to our master's excesses all the singing to London.

Oliver. Burning off both means and self. Our rooms were so quiet that I heard a pistol shot two doors from my own, blasting with holes three children, her mother's hopes, which, when she saw, dismissed herself as well.

Samuel. Fearful! I hear the parson say-

Oliver. Always the priest on his lips, first tasted in his chilhood, I believe.

Samuel. To spurn religion is a fearful thing,

Worse than a murder, murdering the soul

And body.

Oliver. Also a comely fashion among the younger crew, their ornament, a jewel in the ear of fashion, the only opinion of university students. We met a scholar, well mocked at first for his treatises among the flowers of the swelling school, who, in a week, quaffed fresher draughts of atheism, which made him shine so fitly that he put twenty women on their backs after meeting them at a single supper, friends of all kinds accruing so thickly that he pushed them off for air.

Ralph. I vouch for that story's veracity, Oliver being Sybil's son.

Samuel. More news?

Oliver. Not worth the shaking of your ears.

Samuel. We expect the load. Of London people we gladly hear, how sins make them more cheerful, the things for which eyes, ears, and nose strain for in pleasure, dogs following each other through the hoop.

Oliver. Below the sign of the bull, I saw a boy of five, scarred to the teeth with streaks. He spoke of moaning while his sister roasted his cat above the hearth, when in desperate hopes of prevention this sister of twelve fell on him in the shape of a wooden rod, blazing, whose sparks nearly blinded him. There the fuming sister stood, before his bleeding face, triumphing, beyond her years in cruelty, chortling with shaking of the midriff that would attract no surprise from a witch's, after thrashing him with strokes that seemed to fetch their strength from hell. Battered and amazed under such hands, his hair fell in the fire with the cat in a shriek of doom, from which only he drew forth with painful steps towards the street, where I found him, a pained devil, or suffering ghost, on whose every step follows pestilence and death.

Ralph. Amazement! Dead?

Oliver. As fresh on him as any life we bear.

Samuel. Did you discover the wee murderess?

Oliver. I saw her leave the house, her stick in hand,

With which she erewhile played the woman's role,

When, clutching for the strangest punishments,

I accidently poked her eye with it.

What came out of her mouth I shrink to tell.

The soundless terror rings about my dreams.

Ralph. Are we safe?

Samuel. How, when children murder?

Oliver. Tush. Do you think I would have told such a story unless I were safe from the parents' revenges? So, do you still hunger for the world?

Ralph. Was an unknowing fellow punished because of your deed?

Oliver. No, thinking each had set on the other, in sweetest silence father and mother heard the news. Some said a kind of terrified joy suffused their looks, whether from thrilling pains beyond their capacities, or considering nothing else could ever be the worst.

Samuel. My ears swill for such news in spite of charity.

Oliver. What of our mistress?

Ralph. You know her, Oliver.

Oliver. What sheets have warmed her lately?

Samuel. Not ours.

Ralph. Does the crossed antler guess at all her tricks?

Oliver. It is feared he does, or shrewdly suspects it.

Ralph. Some say he does not care.

Samuel. O, irrelegion! With a thousand oaths

He prophesies her death, but for the sake

Of form or habit.

Ralph. His curses are his meal.

Oliver. Fools lead themselves.

Ralph. Our mistress moans so for her love that cats

Mistake her for their own, and louder wail

For sharp contention.

Oliver. Meanwhile, the gallant keeps a wife, secretly hidden from our mistress' knowledge.

Samuel. Out of the eye of God and men.

Ralph. You jest.

Oliver. A hog in mire with two sows.

Samuel. Devils bless such unions.

Ralph. He is married?

Samuel. Yesternight he almost beat out the eggshell he calls brain, after she threw away some pipes that half chew away his lips.

Oliver. A thousand pointed daggers Yorkshire boast

Of may cross out the evil he does here.

Ralph. Not one word, Oliver and Samuel, lest our mistress' head, in fury spent, runs to the wall, since her sharp husband refuses to give her what she needs.

Samuel. She seeks a woman's peace, a rising piece

Of flesh to quiet her.

Ralph. It is much feared impatience will bring us

All hell with her.

Samuel. Yes, in the shape of lovers.

Ralph. Can our master continue so his life? No life but prisons spent in tears, no suit of grace but hiding prodigality of drink, with shame written on his forehead.

Oliver. His lands he sells to feed his vices, which even I little know of, his plate, his coins he drowns in wine-skins, his wife's jewels fall inside the pit of a drunkard's mouth.

Samuel. Is it possible? Should we already look for work elsewhere?

Oliver. Does he strive to make Yorkshire rich in whores,

Or to make all whores rich? That sturdiness

Almost always on seats of pillowed laps!

Samuel. Friends must detest his sight.

Ralph. His younger brother feeds on toads because of whoredom's generosity.

Oliver. Too well known, to his shame. Moreover, he

Owes more to men than what he owns in bones.

Samuel. Are harlots thrifty?

Ralph. The wife below them, not as she would wish,

Below the master.

Oliver. On our journey calling her a piece of dung kept in a jewel case, and filthier names I rarely put my tongue on.

Ralph. More noise? Him?

Lady Clutch. (within

Is he in?

Oliver. No, madam, not yet.

Lady Clutch. (within

Warn me of that.

Oliver. Yes, certainly, good madam.

Samuel. His sons do not escape his enmity.

Oliver. Move farther ahead to escape detection.

Ralph. He call them bastards to their heavy face.

Oliver. Ashamed such an unnatural bore them.

Ralph. He uses such terms as "the whore, the pimp,

And bastards" as a blessing during meals,

As casual and familiar as good day.

Samuel. Let us leave him.

Oliver. No, for the children, then, are sure to starve.

The dam knows man's trade only on her back,

Between the knees of curious knaves of hire,

The children shaking fruit-trees for their meals,

Unless performing the same business as

She does and could again perform at will.

Ralph. We wait on time.

Oliver. The whore- I mean our mistress.

Enter Lady Clutch

Lady Clutch. Not come, then? Playing still the man, with all

His shirt-tails bloody? I wash carelessness,

Though loathing vice, also forgetfulness,

For loyalty is virtuous. Say then, rogues,

Are you afraid to speak? Where is my love?

Oliver. Your husband in a brothel sleeps away

Excess, as fearfully as dice on palm.

No convocation of untrifty thieves

And luckless braggarts must he ever shun,

But in despite of nature heaves his breast

As cheerful as he can into the hands

Of fortune, torturing all his pursuits

By little, till the madcap freezes like

A soul asleep, much stricken and abused.

Lady Clutch. Ah, ah, damnation in a little box,

Which pitches him from any thought of worth.

Samuel. The worried pastor-

Lady Clutch. Away! No smooth religion in my ears

To tell of things which never can run straight!

Instead, stab both of them with distaff points.

Samuel. Your best hope.

Lady Clutch. My torment, hold! More of his witless chores

With dice and revels end than any yet

Last year. With ear of fire, repeat again

What you of such a monstrous husband hear.

Oliver. Your husband's meetings with both enemies

And friends are always spent in tossing pots,

With revelling to drown out virtuous ears

In flowing songs, his boastings at each hour

A neighbor legend, saying he stays flat

Awake while all the company fall off

On tiles of vomit, cesspools of their songs,

To quarrel, laugh, and monger is the stuff

Of men they know about, to dream with thoughts

Awake, to traffic in man's devilry,

To clap companions on the shoulder, quaff,

And surfeit, quaff again a second time,

With all of them, provided they bear mouths

To swill and tongues to curse.

Lady Clutch. You see how terribly I am abused.

Oliver. Who doubts your virtue?

Lady Clutch. Though virtue is an ass in such a case.

Beat women hard whenever they complain

Of husbands' wrongs, for do we not possess

The will and means to leave them when we should?

Oliver. Or else avenge yourself with other loves.

Lady Clutch. I charge you, clamp your lips with nails and screws.

Oliver. Who ever knew a prating pimp? Come, come,

I am your man, as everyone agrees.

Lady Clutch. Remember you are so, lest you become

No one at all.- Go, servants, to your tasks

Whenever this most cruel master comes.

Exeunt Samuel and Ralph

So open, fool? A babbler I detest.

Oliver. O, madam, why bites lips that make men swoon?

Lady Clutch. You bait me still.

Oliver. I sink in silence.

Lady Clutch. Vile polecat, do you sneer?

Oliver. You may not conjure me; I know your ways.

Lady Clutch. I will have you bound to your mother's corpse

If you but breathe against my chastity.

Cease all your loosely prating mummeries,

Lest thunder smoke you out where you are found.

Oliver. Ho, I am tamed.

Lady Clutch. Tongued ferret, peace. What if I choose to clasp

Some other love? I'll have him warm, if but

To vex my bold carouser in his cans,

In no wise enterprising where he should.

He kisses bowls of wine more often than

His wife: what marvel if I kiss elsewhere?

Oliver. No marvel, if you have a woman's crotch.

Lady Clutch. Rat-hound, clamp to. Lay patience on your lips,

Lest I decide to smack the devil from

His country mansion.- To our business next.

Say, did my husband buy the ring I want?

Oliver. What with his whoring, dicing, cardplaying,

He never found the time to think about

His long-faced wife.

Lady Clutch. Why did I marry? All my friends averred

Such unions are not worth our toenails when

We cut them off, although once grown on us.

Oliver. You'll cut off husband, too?

Lady Clutch. Hah? Keep below the hatches, swelling rat.

Oliver. What of the children?

Lady Clutch. Too true, I had almost forgotten them.

I stifle in these drudgeries, I pine.

Oliver. Rise, madam. Many other joys await.

Lady Clutch. Oh, no, let me but dive into the earth.

Oliver. How can a man permit his wife's train thus

To sweep the ground with dust and misery?

Lady Clutch. He throws me down to earth where dwell my thoughts.-

I hear his coach. On trenchers fix your mind,

When duty like a plague-sore rubs on me.

Oliver. I will, and not be slow in tarrying.

Exit Oliver and enter Master Clutch with papers in his hand

Lady Clutch. Ah, husband, will you stay till suppertime?-

Ha, are you well?- The meaning of this gloom?

Exit Master Clutch

O, gross! The viper hides his mood in weeds

For swifter striking.- My man, Oliver!

Re-enter Oliver

Oliver. Am I alive again?

Lady Clutch. No further jibes, but answer truthfully:

Is my life come? I'll surely despair

The whole night long should he but once miss out

His turn with me in bed.

Oliver. There are in houses secret passages,

A bed for more than one. I said before

A steward knows at all times what he knows.

Lady Clutch. But dare not breathe one word of it, unless

You wish that instant as your very last.

Oliver. The pleasure of deep whoring is in sleep,

Sweet, secret sleep, exactly as when we

Steal without being caught, our pillowcase.

Lady Clutch. Is it my husband's birthday? I think so.

Here are my savings for a husband's gift

To buy two pillows.

Oliver. Good. He will spend the day his mother groaned

Almost to the same use as her and you.

I'll pray for him wherever candles burn

As hot as he.

Lady Clutch. More often, if you wish that knave unsinged

After his death. Meanwhile, fetch me at once

My honey love, for such a husband no

Doubt plans to riot on his birthday night.

Oliver. I'll be your worker bee, sometimes aloft

With wax, not honey.

Lady Clutch. One or the other if you fly elsewhere.

Oliver. A worker bee cleans cells of detritus

From previous occupants.

Lady Clutch. So you arrange my bed, when Spruce departs

Before a drowsy husband staggers back.

Oliver. A worker bee builds alveolar cells

Of constant thickness for his treasure's store.

Lady Clutch. So you prepare my room when Spruce comes in.

Oliver. A worker bee is guardian of the hive.

Lady Clutch. To keep away strong insects from my store,

Our officers of law, adultery's

Dread, brushing them away with wings of force,

Or stinging them if once they creep within.

Oliver. I can do so.

Lady Clutch. Do so if you like gold more than your wax.

Exit Oliver and re-enter Master Clutch

Am I of glass? Does sunlight pass through me?

Master Clutch. A part of it, if we believe della Porta's refractions, the rest is blue at the base, red at the top, when your feet freeze and your face reddens.

Lady Clutch. What wife would not be aflame with such a husband?

Master Clutch. What do these shiftings mean? My man of trust

Possesses spurs to kick away his heels.

Is there a fire beside that guilty blush

Which gives the world a triple blazon that

You meditate adultery and sin?

Lady Clutch. I blush for you, suspecting innocents

When you sin earlier than most men awake,

Not pausing to salute your smiling wife

When passing by for papers.

Master Clutch. My papers fill our belly.

Lady Clutch. A thinner crust each day.

Master Clutch. Because of satin gowns unseemly cut

And spliced in many places, fit for whores.-

Why are you startled? Is the merest word

Enough to scare the guilty? Do not fret.

All's one for that and more, but, strained too far,

Remember my ten fingers, which press down

The scale on which you cheat.

Lady Clutch. Remembered on my cheeks too often still.

Master Clutch. Avoid my presence.

Lady Clutch. Should I be pushed away like cushioned seats?

Master Clutch. With prating never madden me today,

A woman's pride, but shame to any man.

Lady Clutch. What melancholy looks you cast about!

Is not all well in business?

Master Clutch. Yes,- no.- Is that your care? Another day

To fill our bellies nearly well enough:

Are you content?

Lady Clutch. Some fiend begins to snatch away your brain.

Master Clutch. Hell never can be peopled with such fiends

As we behold in Yorkshire. Go away.

Familiarity breeds security

When husbands know their wives.

Lady Clutch. Do not think wisdom breathes in you: this calm

Of violent melancholy is the perfect glass.

Master Clutch. If you once fail to please your husband's lust,

May putrid boils infect your busy loins.

Lady Clutch. Suspicion mars you. Papers everywhere

About to say what?

Master Clutch. A loss, dear wife, most of my pockets cut,

My wallet in a mire. Few things remain

Except to have my wife saw off my throat.

Lady Clutch. A devil leads your business acumen.

Master Clutch. Of lucre filched, bereft almost of life.-

What, tears? Out, out! You'll spoil my greasy coat.

Lady Clutch. What will we do?

Master Clutch. Still breathing, wife? Unlikely to last long.

Lady Clutch. Do you behold this world? How can a man

Born with your means so little money gain?

Master Clutch. Some do, some do not: reasoning on it

Irrelevant. Instead of thinking of

Investments, steal and kill: a better deal

In London business.

Lady Clutch. Is there no ample precedent at large

Of violent men by violent means pursued

Until our structure topples?- What, at last

My man in tears?

Master Clutch. But rest content it is no dew of blood,

Good medicine for what ails oftenest.

Re-enter Samuel

Samuel. Should the cook serve yet, madam?

Lady Clutch. My belly is already filled with griefs.

Master Clutch. Can she cook tasty poisons?

Samuel. Do you think God cannot look down, or fiends

Look up? Despair will sooner kill you, sir,

Than any loss of trivial merchandise.

Master Clutch. O, I am damned as certain as we speak.

Samuel. No, master, none, unless he dares to touch

The fingers of degenerate despair.

Lady Clutch. Off to your pots and handles!

Exit Samuel

Master Clutch. Damned, damned, for certain damned, no better fate,

A little more in sinking every day,

Until the devil pulls my beard to make

Us dance.

Lady Clutch. O, husband, cease this quailing.

Master Clutch. My terrors strike down flat the porcupines

Of commerce bristling up against my will,

So that all men investing with me fear

With me and let me go.

Lady Clutch. The dust on our graves covers all with grass.

Master Clutch. Philosophers sometimes kiss tongue to tongue

Your reasoning, spurned from my bosom still.

Lady Clutch. Who speaks of lovers? Do you see them near?

Master Clutch. Be careful: knives are sharp.

Lady Clutch. Away, strong guilt's suspicion! Say you lose

Investing, will you hazard all we have

On rolls of dice?

Master Clutch. If you suspect my judgment, I will rise

To tumble you, but not on beds of love.

O, poverty, we breathe on you again,

Pah! Pah! I scarcely bear my frame upright,

I lug the form of weeping carcasses,

Belonging to the tribe of market men

Who lose their money. Penury: a death

Is kinder than you are and frightens less.

A coinless man is nothing, wearied leaf

Spurned by November winds.

Lady Clutch. The saddened antic raves in autumn smoke.

Master Clutch. My mind has roses burning deep within,

All laws of nature blackly stifling in

Impossibilities of garden plots.

Lady Clutch. Peace, goat-head, peace.

Master Clutch. I will not lecher yet before your eyes,

But you will guess the thoughts of man anon,

The waiting long, the deed as sure as death.

I will arouse the earth with cries, surprise

Priests sleeping in church to their whorehouses

Until the nave cracks. No mute whining here!

Lady Clutch. Unsightly grief, where are you taking him?

Master Clutch. O, poverty! I stare you down at last,

Not with a hydra's head, but with my wife's.

The more I deal, the deeper is my grave,

Worms sounding out my name each night abed.

Lady Clutch. Your dire conclusion: not a coin, all drowned

In lechery and drink? If so, beware:

I'll be a female devil to you yet.

Master Clutch. You whisper death out of his sleep. No more.

We tread on grass with many holes in it.

All one, all trivial! But the very worst

Of ills myself inflicted on myself:

I have a wife, who still abhors my sight. (striking her

Lady Clutch. Ha! Ha! Where are my needles and your eyes?

Master Clutch. The locust singing in my gardenhouse!

Lady Clutch. In darkness, our unknowing hands arise

Against our very lives.

Master Clutch. Have you no lip to mend me? What worth springs

From branches when the root is rotting? Ha,

A marriage, sot? My eldest son must be

Either a rich thief or else a poor fool,

His patrimony lopped, next to garbage pails,

Or shavings of unlucky carpenters,

In famine's pinch, my second son the sport

Of rich men's beds, another one each day,

On whom they wipe themselves, my third, or turd,

Should he refuse to be the loathsome bawd

Of a lascivious duchess, I cannot

Love him again, for next term he should hang.

O, beggary! O, filth! How mean man is

Beneath your burdens!

Lady Clutch. A lousy loser and a beggar slave!

Master Clutch. The devil in his flesh out of the flames

Would scorn to be what I each day become.

Lady Clutch. Base, abject, carnal, filthy poverty!

Master Clutch. A maggot proudly bears more state than I.

Lady Clutch. On finding our fresh meat inside the grave,

Each starving worm will grimace on its piece.

Master Clutch. Love is our meat beneath the sun: within

A day, the beetles feed on maggot-pies,

The pulsing grey and juicy orange ones.

Lady Clutch. I'll give you jewels of my wedding-day.

Master Clutch. O, excellent! In what bin did my thoughts

Stray off? You have some money. Spill them here.

If you possess no more, I will please you

With what you least expect.

Lady Clutch. No more.

Master Clutch. I'll pound you in a cistern if you keep

Your money in a closet. Where is it?

Lady Clutch. No more.

Master Clutch. Send for your uncle, who has more and more.

Lady Clutch. Must your wife beg?

Master Clutch. Yes, vehemently, shamefully, for coins

Are what I am turned to, without which

I am a kind of nothing wanting more.

Lady Clutch. Man's reason warps before unpainted walls.

Master Clutch. Throw reason to your cat: it cannot feed

A man, a woman, and three shrinking sons.

My mortage buried, debts up to the lips,

My promises of money like caught flies

Awaiting on their web for spider laws,

What more than manly brain can fabricate

To get more money not thought out as yet?

Lady Clutch. I blush to share your bed.

Master Clutch. That sharing comes well in. You share my bed

With strangers few hear of. What winds blow me?

I must be pleasant to this wife for once

If I need money. I will please you, dear.

Lady Clutch. A pleasant pill that eats my brain away.

Master Clutch. I vow by all the stars that vomited

On my nativity, that never more

I'll shake the sheets with you, or muss your hair

With sighing if your hands by the next moon

Bear not my life on them, some silver, gold,

Or anything we barter with. To it

With hopping speed! I have not jested yet

This year, and we are in September. I

Last laughed when my sick father heaved at last

His suffering ghost, though I loved him well.

Lady Clutch. A wife is yours, so long as husbands keep

Her always warm in bed.

Master Clutch. A lovely union! Friends do not believe

My weighty maxim: man's for woman made,

For she deserves no better. Come to bed:

We'll seal this novel pact with heated blood.

Exeunt Master Clutch and Lady Clutch

Act 1. Scene 2. Calvary Hall

Enter Oliver and Ralph

Ralph. Why did she strike you?

Oliver. For being too quick in guiding her lover inside the house.

Ralph. Because the husband stayed.

Oliver. How could I know?

Ralph. Well served, bad bawd.

Oliver. It was a bad good idea.

Exeunt Oliver and Ralph


text:
Collaborative play writing/A Yorkshire Tragedy/Act 2

Act 2. Scene 1. A street in York

Enter Spruce and Counsel


text:
Collaborative play writing/A Yorkshire Tragedy/Act 3

Act 3. Scene 1. The duke's palace

Enter the duke and Master Clutch


text:
Collaborative play writing/A Yorkshire Tragedy/Act 4

Act 4. Scene 1. The duke's palace

Enter Master Clutch and a page


text:
Collaborative play writing/A Yorkshire Tragedy/Act 5

Act 1. Scene 1. A room in Spruce's house

Enter Oliver and Spruce


text:
User talk:Hazard-SJ

 Hello Hazard-SJ, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

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title: User talk:Hazard-SJ


text:
User talk:Cap356

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title: User talk:Cap356


text:
User:Egm6321.f10.team5.abc/숙제4

Problem 3
Find $$X(x)$$ in terms of $$\sin$$, $$\cos$$, $$\sinh$$, and $$\cosh$$. Note that $$\exp (i \theta) = \cos (\theta) + i \sin (\theta)$$ and $$\exp (\theta) = \cosh (\theta) + \sinh (\theta)$$.

Solution 3
Assume that $$X(x) = \exp(rx)$$. From the equation of $$K^4 X^{(4)} = X$$, it was already derived in the lecture notes that $$r_{1,2} = \pm \frac 1 K$$ and $$r_{3,4} = \pm \frac i K$$. Since there are four solutions for $$r$$, we make a linear combination to express $$X(x)$$. Substitute the values of $$r$$s into the equation and we get Now use the expression of exponential in terms of trigonometric functions. From the trigonometric identity, it is defined that $$\sin (- \theta) = - \sin (\theta)$$, $$\cos (- \theta) = \cos (\theta)$$, $$\sinh (- \theta) = - \sinh (\theta)$$, and $$\cosh (- \theta) = \cosh (\theta)$$. Apply the relations to the equation of $$X(x)$$. Then the equation can be simplified as

title: User:Egm6321.f10.team5.abc/숙제4


text:
User:Egm6321.f10.team5.abc/a4

Problem 3
Find $$X(x)$$ in terms of $$\sin$$, $$\cos$$, $$\sinh$$, and $$\cosh$$. Provided identities are $$\exp (i \theta) = \cos (\theta) + i \sin (\theta)$$ and $$\exp (\theta) = \cosh (\theta) + \sinh (\theta)$$.

Solution 3
Assume that $$X(x) = \exp(rx)$$. From the equation of $$K^4 X^{(4)} = X$$, it was already derived in the lecture notes that $$r_{1,2} = \pm \frac 1 K$$ and $$r_{3,4} = \pm \frac i K$$. Since there are four solutions for $$r$$, we make a linear combination to express $$X(x)$$. Substitute the values of $$r$$s into the equation and we get Now use the expression of exponential in terms of trigonometric functions. From the trigonometric identity, it is defined that $$\sin (- \theta) = - \sin (\theta)$$, $$\cos (- \theta) = \cos (\theta)$$, $$\sinh (- \theta) = - \sinh (\theta)$$, and $$\cosh (- \theta) = \cosh (\theta)$$. Apply the relations to the equation of $$X(x)$$. Then the equation can be simplified as

title: User:Egm6321.f10.team5.abc/a4


text:
User talk:EnzingerCK

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To :

The project Wikistution has been moved to User:Norton~enwikiversity/Wikistution

Yours truly, --Guy vandegrift (discuss • contribs) 19:22, 6 December 2022 (UTC)

This project had subpages:

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User talk:DanD

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User talk:PAC2

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User talk:Toro04~enwikiversity

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

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User talk:GSBundela

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User talk:Jimhowes

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User talk:Zac~enwikiversity

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title: User talk:Zac~enwikiversity


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User talk:Daniel Quinn

 Hello Daniel Quinn, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

 * Take a guided tour and learn to edit.
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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. --La comadreja formerly AFriedman RESEARCH (talk) 01:04, 20 October 2010 (UTC)

 Hi! My name is WikiversityJack. I am a pumpkin and a Wikiversity mascot. My aunt told me that fun + learning = Wikiversity. Let me know if I can help you out.

title: User talk:Daniel Quinn


text:
User talk:Sashachids

 Hello Sashachids, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

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And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --La comadreja formerly AFriedman RESEARCH (talk) 01:05, 20 October 2010 (UTC)

 Hello , we are the Baah and Bahh twins and we'd both like to welcome you to Wikiversity. While you sit back and explore Wikiversity, enjoy some of our fresh goat milk. You can help us learn by creating new learning resources or help us by improving the guided tours and other exploration tools. We look forward to seeing you around. Baaaahbye for now.

title: User talk:Sashachids


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User talk:MrEcho

 Hello MrEcho, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

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And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --La comadreja formerly AFriedman RESEARCH (talk) 01:05, 20 October 2010 (UTC)

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

title: User talk:MrEcho


text:
User talk:Chem prof2000

 Hello Chem prof2000, 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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text:
MRSA in Schools

Symptoms and Diagnosis: Methicillin-resistant Staphylococcus aureus, better known as MRSA or Staph infection, is a bacterium which lives atop the superficial layers of human skin and is generally harmless on its own. However, it can potentially become a problem if it gets into the deeper layers the skin via an open cut, abrasion, or wound because deep MRSA infections are not easily treated (Wash). If not treated, it can reach into the organs which can in turn become infected, causing serious complications. MRSA is highly contagious and can be spread easily by skin-to-skin contact with an infected person, as well as through contact with an object that an infected person has had contact with. There are two types of MRSA infection, one which affects those living or working in a health care facility, called health care-associated MRSA (HA-MRSA). Health professionals are likely to come into contact with MRSA if they work in hospitals, nursing homes, other dialysis centers, or anywhere they could be exposed to a patient’s open wounds. The other type of MRSA is community-associated MRSA (CA-MRSA), which can be spread among those living in crowded or unsanitary conditions, those participating in contact sports, or men who have sex with men. Even sanitary environments such as daycare centers, dormitories, and classrooms, among others; CA-MRSA cases account for 14% of reported MRSA cases. (CDC) Being in close quarters with others is one of the most common ways Staph infections occur, because even the slightest brush with an infected person can be the beginning of a new case (dermnetz), especially in someone with a weak immune system. MRSA causes a wide range of symptoms in infected persons; symptoms may vary by the stage of the infection. Usually a Staph infection begins resembling small spider bits covering the infected area. They may become inflamed, red, and very uncomfortable. It is not uncommon for these pustules to become painful and secrete drainage like pus. If not treated they will turn into deep abscesses; this happens when the bacteria burrow inside the body, beneath the shallow layers of the skin. These deep infections can adversely affect the bloodstream, lungs, heart valves, bones, and joints, which can be potentially fatal. The lungs are particularly susceptible, meaning Pneumonia is another serious complication of an untreated, long-term MRSA infection. Visible signs and symptoms commonly start on areas of the skin which have been scarred, bruised, or cut, or sometimes areas which are covered by hair. Symptoms will vary depending on the type and stage of an infection, as well as which setting it takes place in (CDC). MRSA is the result of years of overuse of antibiotics, due to lack of treatment knowledge. Its strong resistance can be attributed to the mec gene of the bacterium, a penicillin-binding protein. The gene inhibits the ability of the methicillin to bind to the cell, resulting in a futile effort to cure it. Unfortunately, MRSA has recently been referred to as “multiple resistant s. aureus”, because it is becoming defiant to more and more drugs. (CDC). A Staph infection can be diagnosed by testing a tissue sample from an infected area, and check it for the drug-resistant bacteria. It is placed in a Petri dish and saturated with nutrients which bring about bacteria within 48 hours. There is no at-home cure for MRSA, any attempt could worsen the infection, and potentially spread it to others. In the case of a superficial abscess a physician will drain it instead of treat it with drugs. MRSA is not easily treated with antibiotics due to its increasing resistant nature, but few options are available including a limited number of antibiotics and creams. Prevention is the best medicine, and preventing a Staph infection is very simple. In order to nip it in the bud, those persons who are most likely to be in contact with the bacteria should wash their hands often and thoroughly, keep cuts and abrasions clean and covered until they are healed, and avoid sharing personal hygiene items such as towels, razors, or soap with roommates or coworkers. In the case of someone who is already infected, a patient can prevent spreading their infection by covering the wounds, staying clean, keeping their surroundings clean, and keeping out of contact with others’ personal items.

Prevention and Intervention: When antibiotics were first discovered, one of their primary targets was the bacteria Staphylococcus aureus. Over the years, misuse of these medications has lead to strains of the bacteria that are resistant to medication, often referred to as “superbugs”. These resistant bacteria are called Methicillin Resistant Staphylococcus aureus (MRSA). Approximately one fourth of the population has colonies of these bacteria in their nose; however, less than 2% of these people carry MRSA. In fact, until recent years MRSA was primarily considered a hospital acquired infection and was very rarely seen in the community. Unfortunately, this is no longer the case and these community acquired infections have been increasing exponentially each year. As children ranging in age from infants to 18-years old are the most vulnerable population, this has become an issue of great concern in schools. Fortunately, there are many simple steps that the faculty and students can take in order to prevent contraction and spread of this disease. The Centers for Disease Control sites factors referred to as the 5C’s that make it easier for MRSA to be transmitted: crowding, contact, compromised skin, contaminated items and surfaces, and cleanliness. By targeting these factors within schools, prevention of MRSA is possible. As athletes, especially football players and wrestlers, have a significant amount of skin-to-skin contact and use of public equipment, they are at higher risk. Thus, it is important to implement prevention strategies and ensure that coaches and athletes are aware of them. Such strategies include cleaning exercise equipment and sports equipment, such as wrestling mats, with detergent-based cleaners or disinfectants that the Environmental Protection Agency has recommended. Furthermore, all other frequently touched surfaces within schools should be cleaned with these products routinely. It is important that the directions on the label of the products be followed. Taking such steps will kill the bacteria that may be living on these surfaces, preventing transmission. A seemingly obvious method of prevention is to encourage staff and students to practice good hygiene. Hand washing is a simple, but effective, tool at preventing many infectious diseases. It is important to encourage proper hand washing techniques, such as ensuring that they rub their hands vigorously for at least 20 seconds. Also, be sure to scrub the wrists, between the fingers, and under the fingernails. Antibacterial soap is not necessary as studies have shown that it is no more effective at killing germs than regular soap. Athletes should also shower immediately after sporting events. It is important to note that MRSA is not contracted by simply coming into contact with the bacteria; to cause an infection it must enter the skin. Thus, students must take appropriate precautions when they have cuts or abrasions. It is through these skin breaks that the bacteria can enter, so they must be covered with a clean dry bandage until healed. In particular, athletes should be certain to check for cuts or abrasions often, and to cover them accordingly before participating in sports. Finally, students with active MRSA infections may still attend school as long as their wounds can be sufficiently covered. However, these students should be prevented from participating in contact sports or activities. Treatment of MRSA often includes drainage of the infection and/or prescription of antibiotics. If prescribed an antibiotic it is essential that all of the doses are taken. MRSA is resistant to many antibiotics, including: oxacillin, penicillin, methicillin, and amoxicillin. The two primary antibiotics used in the treatment of these infections are vancomycin and linezolid. Unfortunately, there are even strains emerging that are resistant to those antibiotics. Therefore, much research is being conducted in search of an alternative to present remedies. One such alternative may be anti-pathogenic drugs. These do not kill the bacteria but block the activation of proteins essential for toxin release by the bacteria. Another promising discovery lies in the brains and nervous systems of cockroaches and locusts. Molecules from these tissues were shown to kill 90% of MRSA bacteria in a study at the University of Nottingham. Though these and other discoveries show potential in fighting antibiotic resistant bacteria, they are not yet available to the public. Therefore, it is important that healthcare professionals prescribed antibiotics wisely and that patients use them as directed.

References “Antibiotic Resistance.” doh.wa.gov. 2010. Washington State Department of Health. 2 August 2010. http://www.doh.wa.gov/topics/antibiotics/mrsa.htm “Definition of MRSA”. Centers for Disease Control and Prevention. August 2010. 8 September 2010. http://www.cdc.gov/mrsa/definition/index.html “Do Cockroaches Hold the Key to MRSA Treatment?”. Food Consumer. August 2010. 8 September 2010. http://www.foodconsumer.org/newsite/2/other_diseases/do_cockroaches_hold_the_key_to_mrsa_tretretre_090820101153.html “MRSA Infections.” cdc.gov. 2010. Centers for Disease Control and Prevention. 9 August 2010. http://www.cdc.gov/mrsa/index.html “MRSA in Schools”. U.S. Department of Education. October 2007. 8 September 2010. http://www2.ed.gov/admins/lead/safety/emergencyplan/mrsa.doc “MRSA Overview for Schools: Methinillin-Resistant Staphylococcus aureus”. Department of Health and Senior Services. 10 September 2010. http://www.dhss.mo.gov/MRSA/MRSASchools.pdf “Methicillin resistant Staphylococcus aureus.” Dermnetnz.org. 2010. DermNet New Zealand. 18 September 2010. http://dermnetnz.org/bacterial/methicillin-resistance.html “Researcher Discovers New “Anti-Pathogenic” Drugs to Treat MRSA”. PhysOrg. September 2010. 16 September 2010. http://www.physorg.com/print/203871637.html Rowson, Kevin.”Staph Infections Growing Exponentially in Children”. September 2010. 16 September 2010. http://www.11alive.com/cleanprint/?1284680888450 “Treatment of MRSA Infections”. Centers for Disease Control and Prevention. August 2010. 8 September 2010. http://www.cdc.gov/mrsa/treatment/index.html

title: MRSA in Schools


text:
User:Egm6321.f10.team5.steinberg/hw4

Given
Bessel Differential Equation

$$ F(x,y,y',y) = x^2y + xy' + (x^2-\nu^2)y,  ~\nu \in\mathbb{R}  \! $$.

Find

 * 1) Verify exactness of the given equation using 2 methods:
 * 2) Relations (1) and (2) p. 15-3 (Meeting 15)
 * 3) Equation (3) p. 22-4 (Meeting 22)
 * 4) If not exact, determine whether it can be made exact using integrating factor method (IFM) with $$ h(x,y) = x^my^n \! $$

Part 1
The first condition of exactness is satisfied since the Bessel differential equation is in the form

where

$$ g(x,y,y') = xy' + (x^2 - \nu^2)y \! $$

$$ f(x,y,y') = x^2 \! $$

The second condition of exactness from p. 15-3 has two relations given here.

where

$$ p := y' \! $$

Computing the partial derivatives for (3.2a) and (3.2b),

$$ f_{xx} = 2 \! $$

$$ f_{xy} = f_{yy} = f_{xp} = f_{yp} = f_{y} = 0 \! $$

$$ g_{xp} = 1 \! $$

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

$$ g_{y} = x^2 - \nu^2 \! $$

Now we substitute the derivatives into (3.2a) and (3.2b) to get

$$ (3.2a) \Rightarrow -1 = x^2 - \nu^2 \! $$

$$ (3.2b) \Rightarrow 0 = 0 \! $$

Clearly, the first relation (3.2a) indicates that the Bessel differential equation is not exact for all $$ x \! $$.

Alternatively, the second condition of exactness can also be verified using (3) p.22-4 which is as follows

where $$ f_i:=\frac{\partial F}{\partial y^{(i)}}, ~i=0,1,2,...,n \! $$

For the given equation

$$ f_{0} = \frac{\partial F}{\partial y^{(0)}} = x^2 - \nu^2 \! $$

$$ f_{1} = \frac{\partial F}{\partial y^{(1)}} = x ~\Rightarrow ~\frac{df_1}{dx} = 1 \! $$

$$ f_{2} = \frac{\partial F}{\partial y^{(2)}} = x^2 ~\Rightarrow ~\frac{df_2}{dx} = 2 \! $$

Substituting these results into (3.3) yields

$$ x^2 - \nu^2 - 1 + 2 = 0 \! $$

which is the same result obtained from (3.2a) above. Again, the Bessel equation is not exact for all $$ x \! $$.

Part 2
We will now employ the integrating factor method using $$ h(x,y) = x^my^n \! $$ to see if the given equation can be made exact.

$$ h(x,y)\Big(x^2y'' + xy' + (x^2-\nu^2)y \Big) = 0 \! $$

$$ x^my^n \Big(x^2y'' + xp + (x^2-\nu^2)y \Big) = 0 \! $$

Using the form of (3.1) yields

$$ g(x,y,p) = x^{m+1}y^n \! $$

$$ f(x,y,p) = x^{m+1}y^np + x^{m+2}y^{n+1} - x^my^{n+1}\nu^2 = 0 \! $$

To satisfy the 2nd condition of exactness, $$ f(x,y,p) \! $$ and $$ g(x,y,p) \! $$ must satisfy (3.2a) and (3.2b).

The partial derivatives for these 2 equations are

$$ f_{xx} = (m+1)(m+2)x^m y^n \! $$

$$ f_{xy} = n(m+2)x^{m+1} y^{n-1} \! $$

$$ f_{y} = nx^{m+2} y^{n-1} \! $$

$$ f_{yy} = n(n-1)x^{m+2} y^{n-2} \! $$

$$ f_{xp} = f_{yp} = 0 \! $$

$$ g_{xp} = (m+1)x^m y^n \! $$

$$ g_{y} = nx^{m+1}y^{n-1}p + (n+1)x^{m+2}y^n - (n+1)x^m y^n \nu^2 \! $$

$$ g_{yp} = nx^{m+1}y^{n-1} \! $$

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

Substituting these partial derivatives into (3.2a) and (3.2b) yields

$$ (3.2a) \Rightarrow (m+1)(m+2)x^my^n + 2pn(m+2)x^{m+1}y^{n-1} + p^2n(n-1)x^{m+2}y^{n-2} = (m+1)x^my^n + pnx^{m+1}y^{n-1} - npx^{m+1}y^{n-1} -(n+1)x^{m+2}y^n + (n+1)x^my^n\nu^2 \! $$

$$ (3.2b) \Rightarrow 0 + 0 + 2nx^{m+2}y^{n-1} = 0 \! $$

The second relation $$ (3.2b) \Rightarrow n = 0 \! $$.

Therefore, the first relation (3.2a) simplifies to

This relation (3.4) cannot be satisfied with any value of $$ m \! $$ to make the Bessel differential equation exact.

title: User:Egm6321.f10.team5.steinberg/hw4


text:
User:S. Champion

Will work on this soon! Back to learning on Wikiversity for the moment...

title: User:S. Champion


text: File:Experiments and simulations train.png


text:
Talk:Motivation and emotion/Book/2010/Antisocial personality disorder

Feedback - Hanging indent for references
Your page is well on its way. I was wondering if you could describe how one goes about putting in a hanging indent for the refs? Could you (if you've time) pop up the steps on moddle as there are a few of us wondering how you master such a wonderful technique. Cheers, Bec (U118827)

 * Actually, I'd be inclined to drop the indenting here - although it is APA style, separating the references into separate lines with a tab for the second line will create formatting problems down the track (e.g., for larger or smaller screen displays). If you do want to do hanging indenting, then try this:

Contributors' first names and initials(Last edited date). Title of resource using italics. Retrieved from http://Web address of the resource

Angeli, E., Wagner, J., Lawrick, E., Moore, K., Anderson, M., Soderland, L., & Brizee, A. (2010, May 5). General format. Retrieved from http://owl.english.purdue.edu/owl/resource/560/01/

which is achieved with

List of references -- Jtneill - Talk - c 21:04, 31 October 2010 (UTC)

Feedback - Introduction
I love the introduction, especially the engaging opening paragraph. I would suggest a little redrafting on the second and third paragraphs e.g., the sentence starting "Now, most psychological disorders reflect disturbances in a number of areas, " to improve the clarity, but this is a relatively minor suggestion. I'd suggest using ASPD once you've defined it - it's a bit of a wordful. -- Jtneill - Talk - c 23:58, 31 October 2010 (UTC)
 * This has improved I think, but could still do with some work in the subsequent paragraphs. I've edited a bit, but you might review and improve further. Ideally, this is a nice simple clear introduction to the topic and what will be covered in the rest. You could consider some focus questions and/or briefly overview the structure and direction of the chapter. Make sure the connection to motivation is clear. -- Jtneill - Talk - c 07:37, 5 November 2010 (UTC)
 * I added some extra sub-headings - usually a section would have no subheadings or at least two subheadings. -- Jtneill - Talk - c 07:38, 5 November 2010 (UTC)

Feedback - What is Antisocial Personality Disorder (APSD)?
-- Jtneill - Talk - c 00:42, 1 November 2010 (UTC)
 * 1) The opening sentence is a bit circular?
 * 2) Add citation to second sentence?
 * 3) The direct quote also needs a page number.
 * 4) "Individuals tend to have long histories of violating the rights of others,..." - what individuals? (Rewrite to improve clarity).
 * 5) This section seems heavy on DSM-IV description and a single reference source - use a broader range of references e.g., from peer-reviewed journal articles such as recent major reviews of APSD
 * 6) "They lack empathy and tend to be callous, cynical a..." - who? e.g., People with APSD?
 * 7) Maybe swap the two paragraphs around in "Clinical Description and Symptomology in APSD
 * 8) Maybe add a feature box / case study of someone who has APSD?
 * Maybe put the DSM Classification of APSD into a table or sidebox, since its not really main body text and is fairly literature from the DSM-IV I gather. -- Jtneill - Talk - c 07:40, 5 November 2010 (UTC)
 * Maybe distinguish between APSD and other related motivational disorders e.g., conduct disorder. What about if someone is less than 18 and has APSD symptoms? -- Jtneill - Talk - c 07:41, 5 November 2010 (UTC)

Feedback - Neurobiological theories

 * 1) Combine "Neurobiological processing of APSD" and "Neurobiological Theories of APSD".
 * 2) I'm not sure that you need the section on Emotion - not unless you are going to relate this back to motivation
 * 3) Shift this section "What is Motivation?" higher and merge perhaps in with the initial introduction which could perhaps be improved by explaining that this chapter explores motivational aspects of APSD i.e., it's not about APSD it is about motivation and APSD. All the theories you cover are then in some way about motivational aspects of APSD (which they are).

Feedback - The rest
Check the Moodle discussion list -- Jtneill - Talk - c 00:57, 1 November 2010 (UTC)
 * 1) I've added some empty sideboxes
 * 2) I fixed/tweaked the indenting of references
 * 3) The range of references looks excellent - are they are cited? (they should be, otherwise don't include them - just checking).

Feedback - Neurobiological Processing and Theories of APSD

 * 1) I think it makes sense to have brought these two sections together.
 * 2) Maybe offer a one paragraph introduction before diving into the specific sections
 * 3) Check APA style for direct quotation
 * 4) Consider adding a relevant picture e.g., from http://commons.wikimedia.org/wiki/Special:Search/amygdala

Feedback - Wiki links
-- Jtneill - Talk - c 07:53, 5 November 2010 (UTC)
 * 1) Consider adding links to key word articles on Wikipedia e.g., when words like amygdala are first mentioned.

Feedback - Conclusion

 * 1) Beef this up a bit into a stronger summary - perhaps provide summary answers to the focus questions. What have we learnt about motivation by looking at the APSD?

Feedback - Glossary
-- Jtneill - Talk - c 07:53, 5 November 2010 (UTC)
 * 1) Be selective about what goes in here - focus on key terms and leave out minor terms.

Feedback - References
-- Jtneill - Talk - c 07:53, 5 November 2010 (UTC)
 * 1) Lykken (1957) is cited but is not in references - if you didn't consult this resource then it should be cited as a secondary citation.
 * 2) Subsequent citations within a paragraph don't need the year e.g., Lykken (1957), but after that in the same paragraph, use Lykken. (without the year).

Feedback - Overall
Besides filling out the rest of your content and redrafting, proofreading etc. I think the main work here should be on the conclusion/summary - and also on making it really clear in the introduction what the aims and content of the chapter are - e.g., via focus questions and answers to those questions. -- Jtneill - Talk - c 07:57, 5 November 2010 (UTC)

-- Jtneill - Talk - c 03:49, 3 December 2010 (UTC)

-- Jtneill - Talk - c 13:26, 14 December 2010 (UTC)


text:
Talk:Motivation and emotion/Textbook/Motivation/Motivational toxicity

Feedback
Hi there! Your chapter is well on its way towards producing a very rich and organised resource, so well done. I was wondering if you could have a look and comment on my chapter (student motivation) as I think I've finished (but often there is a lot more that needs to be done). Any feedback would be greatful received. Cheers, Bec (your tutorial studybuddy) and wiki user: U118827

Hi. I really liked your chapter. (Although, it does not look to be complete, i.e., summary/conclusion). I was wonderring whether you should have a specific definition for motivational toxicity, next to the definition of motivation, and maybe differentiate it from addiction. Also, does the dopamine deficiency theory have any relevance to the reward deficiency syndrome? All in all, Your writing was really clear and easy to read. Thank you for your feedback. AlEdwardson 12:34, 28 October 2010 (UTC)

Great to see helping each other out. I agree with the AlEdwardson comment to just do a little more on making sure you have a clear definition of emotional toxicity - maybe even in its own highlighted box. And how it is different to addiction is an excellent point. Other things: -- Jtneill - Talk - c 02:17, 1 November 2010 (UTC)
 * 1) I've indented the references and adjusted the heading levels
 * 2) I suggest bigger pictures - at least 250px
 * 3) Add captions to your images (see the brain image as an example)
 * 4) Excellent work with the Wikipedia links. To improve them further, I've edited the introduction to adjust the external link format to the internal link format e.g., goals. Also note that it is only necessary to add such links once, on first mention. Afterwards just refer to goals etc. without a link.
 * 5) The reward system and how it is governed - excellent, well explained, easy to understand etc. maybe add a relevant diagram?
 * 6) Operant conditioning and the reward system - excellent, solid section, well written. I wonder whether motivational toxicity can also explain non-drug addictions? It could be worth considering another section here to consider this.
 * 7) APA style: Subsequent citations within paragraphs don't need the year e.g., Adinoff (2004). But later, just refer to Adinoff (in the same paragraph).
 * 8) Check were -> where
 * 9) Specific brain areas and their roles in the motivation of addiction
 * 10) A brain diagram would help here - see what you can find on Wiki commons or on related Wikipedia articles.
 * 11) This section was pretty dense - maybe put it in broader context here. Are you suggesting that addictive drugs cause damage to these areas - or perhaps pre-existing problems in these areas predisposes one to addiction? (e.g., is there a genetic link in addiction?). Or perhaps both. i.e., what is the big question here? How is motivational toxic related to brain structure and localisation?
 * 12) Grammar check: individuals -> individual's
 * 13) Dopamine and the pleasure pathways - good section - maybe add image and/or link to the WP article (could be worth repeating the link here at the start or in a feature box)
 * 14) The mesolimbic dopamine pathway - this is good info, but again is quite technical/neurological. Put it in some more context.
 * 15) Other things - can one overcome motivational toxicity (e.g., detoxify?) How? Are some people more vulnerable neurochemically to motivational toxicity (addictive personality?)? What is the relative role of genetics/environment? How can motivational toxicity be measured - just because someone has a neurological vulnerable will that person necessarily become addicted? Why or why not?
 * 16) Any quotes or case studies etc. of people with motivational toxicity? (Perhaps also make clear that this isn't a disorder per se but rather describes a neuro-motivational description of the reason for addiction.

Thanks for the feedback and tidy up - go easy people! Obviously the page is far from finished, that's why there arent more pics and links as yet, but there will be! I thought the definition of motivational toxicity (MT) was clear - when addiction takes control away from normal motivation systems - but then I've been absorbed in readings on it so maybe I wouldnt see it if it bit me on the nose! Anyway I've reworded it so I hope it's better now.

I've found it hard to find info on MT, the Esch article is the only one I've found actually using the term MT - it's obviously not commonly used. I havent come across any information on MT in non-drug addictions so I'm not sure if its relevant without a substance but I'll keep looking and see what I can find.

I'm still reworking the brain and dopamine sections, I'm planning to put in a brain map there but atm I'm trying to get make the technical info easier to understand without losing the details. I havent covered genetic links or similar because I assume those will be covered in addiction, I'm only looking at the neurobiology underlying the transition into dependence.

And I havent even started on the conclusion or what can be done about toxic motivation yet, but I'll get there! I'm pretty sure MT's not a disorder, rather a theory on the neurological underpinnings of addiction motivation, I havent found anything suggesting a separate disorder. Thanks for the help and ideas and please check back in a while when I've done more, Ta! M.Sell 04:46, 1 November 2010 (UTC)

-- Jtneill - Talk - c 13:10, 13 December 2010 (UTC)


text:
User talk:Polarnj

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title: User talk:Polarnj


text:
User:Egm6321.f2010.team5.riveros/hw4p2

= Problem 2 - Solve for Bessel equation = From Meeting 24, p. 24-1

Given
Bessel Differential Equation
 * $$ \displaystyle F(x,y,y',y) = x^2y + xy' + (x^2-\nu^2)y,  ~\nu \in\mathbb{R}  \! $$.

Find

 * 1) Verify exactness of the given equation using 2 methods:
 * 2) Relations (1) and (2) p. 15-3 (Meeting 15)
 * 3) Equation (3) p. 22-4 (Meeting 22)
 * 4) If not exact, determine whether it can be made exact using integrating factor method (IFM) with $$ h(x,y) = x^my^n \! $$

Part 1
The first condition of exactness is satisfied since the Bessel differential equation is in the form
 * {| style="width:100%" border="0"

where,
 * style="width:95%" | $$\displaystyle F(x,y,y',y) = g(x,y,y') + f(x,y,y')y$$
 * (2.1)
 * }
 * }
 * $$\displaystyle g(x,y,y') = xy' + (x^2 - \nu^2)y \! $$
 * $$ f(x,y,y') = x^2 \! $$

The second condition of exactness from p. 15-3 has two relations given here.
 * {| style="width:100%" border="0"

 * style="width:95%" | 1. $$\displaystyle f_{xx} + 2pf_{xy} + p^2f_{yy} = g_{xp} + pg_{yp} - g_y$$
 * (2.2a)
 * }
 * {| style="width:100%" border="0"
 * {| style="width:100%" border="0"

where
 * style="width:95%" | 2. $$\displaystyle f_{xp} + pf_{yp} + 2f_y = g_{pp}$$
 * (2.2b)
 * }
 * }
 * $$\displaystyle p := y'$$

Computing the partial derivatives for (3.2a) and (3.2b),
 * $$\displaystyle f_{xx} = 2$$
 * $$\displaystyle f_{xy} = f_{yy} = f_{xp} = f_{yp} = f_{y} = 0$$
 * $$\displaystyle g_{xp} = 1$$
 * $$\displaystyle g_{yp} = g_{pp} = 0$$
 * $$\displaystyle g_{y} = x^2 - \nu^2$$

Now we substitute the derivatives into (2.2a) and (2.2b) to get
 * (2.2a) $$\displaystyle \Rightarrow -1 = x^2 - \nu^2 \! $$
 * (2.2b) $$\displaystyle \Rightarrow 0 = 0 \! $$

Clearly, the first relation (2.2a) indicates that the Bessel differential equation is not exact for all $$x$$. Alternatively, the second condition of exactness can also be verified using (3) p.22-4 which is as follows,
 * {| style="width:100%" border="0"

where,
 * style="width:95%" | $$\displaystyle f_0 - \frac{df_1}{dx} + \frac{d^2f_2}{dx^2} = 0$$
 * (2.3)
 * }
 * }
 * $$\displaystyle f_i:=\frac{\partial F}{\partial y^{(i)}}, ~i=0,1,2,...,n$$

For the given equation,
 * $$ f_{0} = \frac{\partial F}{\partial y^{(0)}} = x^2 - \nu^2$$
 * $$ f_{1} = \frac{\partial F}{\partial y^{(1)}} = x ~\Rightarrow ~\frac{df_1}{dx} = 1$$
 * $$ f_{2} = \frac{\partial F}{\partial y^{(2)}} = x^2 ~\Rightarrow ~\frac{df_2}{dx} = 2$$

Substituting these results into (2.3) yields,
 * $$\displaystyle x^2 - \nu^2 - 1 + 2 = 0$$

which is the same result obtained from (2.2a) above. Again, the Bessel equation is not exact for all $$x$$.

Part 2
We will now employ the integrating factor method using $$h(x,y) = x^my^n$$ to see if the given equation can be made exact.
 * $$ h(x,y)\Big(x^2y'' + xy' + (x^2-\nu^2)y \Big) = 0 \! $$
 * $$ x^my^n \Big(x^2y'' + xp + (x^2-\nu^2)y \Big) = 0 \! $$

Using the form of (3.1) yields,
 * $$ g(x,y,p) = x^{m+1}y^n \! $$
 * $$ f(x,y,p) = x^{m+1}y^np + x^{m+2}y^{n+1} - x^my^{n+1}\nu^2 = 0 \! $$

To satisfy the 2nd condition of exactness, $$f(x,y,p)$$ and $$g(x,y,p)$$ must satisfy (2.2a) and (2.2b). The partial derivatives for these 2 equations are;
 * $$ f_{xx} = (m+1)(m+2)x^m y^n \! $$
 * $$ f_{xy} = n(m+2)x^{m+1} y^{n-1} \! $$
 * $$ f_{y} = nx^{m+2} y^{n-1} \! $$
 * $$ f_{yy} = n(n-1)x^{m+2} y^{n-2} \! $$
 * $$ f_{xp} = f_{yp} = 0 \! $$
 * $$ g_{xp} = (m+1)x^m y^n \! $$
 * $$ g_{y} = nx^{m+1}y^{n-1}p + (n+1)x^{m+2}y^n - (n+1)x^m y^n \nu^2 \! $$
 * $$ g_{yp} = nx^{m+1}y^{n-1} \! $$
 * $$ g_{pp} = 0 \! $$

Substituting these partial derivatives into (2.2a) and (2.2b) yields
 * (2.2a) $$ \Rightarrow (m+1)(m+2)x^my^n + 2pn(m+2)x^{m+1}y^{n-1} + p^2n(n-1)x^{m+2}y^{n-2} = (m+1)x^my^n + pnx^{m+1}y^{n-1} - npx^{m+1}y^{n-1} -(n+1)x^{m+2}y^n + (n+1)x^my^n\nu^2 \! $$
 * (2.2b) $$ \Rightarrow 0 + 0 + 2nx^{m+2}y^{n-1} = 0 \! $$

The second relation (2.2b) ⇒ $$n = 0$$. Therefore, the first relation (2.2a) simplifies to:
 * {| style="width:100%" border="0"

This relation (2.4) cannot be satisfied with any value of $$m$$ to make the Bessel differential equation exact.
 * style="width:95%" | $$\displaystyle (m+1)(m+2)x^m = (m+1)x^m -x^{m+2} + x^m\nu^2$$
 * (2.4)
 * }
 * }

title: User:Egm6321.f2010.team5.riveros/hw4p2


text: File:Process diagnostics.png

title: File:Process diagnostics.png