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Collaborative play writing/Aglaura/Act 1

Act 1. Scene 1. The The ducal palace

Enter Jacques and Jacqueline

Jacques. How, married! Do they sprout oak-leaves around

Their pates, secure from thunder?

Jacqueline. My own ears heard the curate bless the bond.

Jacques. O, murderous! Unprecedented scenes

Of death must follow.

Jacqueline. What thoughts make you so pale?

Jacques. What else but marriage, love's most fatal word

In any lexicon?

Jacqueline. On the church porch at Denis they stole that

Most happy of unhappy hours.

Jacques. I fear for them, perhaps for us far more.

Jacqueline. How, beard a duke, to sleep in peace? It must

Not be, or ever will. Before his eyes

Will they retire and huddle, rise to fall

And rise again, as if a nobleman

Sleeps while his subjects threaten?

Jacques. Is there a difference between their sex?

Are they of flesh and blood? O, Jacqueline,

This very night the lovers jump to it.

Jacqueline. Yes, but the duke, good brother!

Jacques. But lust, fair sister!

Jacqueline. O, very fine! We'll suffer, should we not,

For all their pleasures? You will not, I pray,

Breathe one fragmented letter of this tale.

Jacques. Drowned lips are not more certain.

Jacqueline. The frailty of our sexes!

Jacques. It must come out, like pus; our nature's so.

Enter Sementhe

Sementhe, my love's hope! Speak carelessly

Or not at all: should we be at it, girl?

Exit Sementhe

Ha, gone already? Misery of love,

When those we cherish shun our happy face!

Jacqueline. Ha? Do you weep?

Jacques. She with whom I have often dreamt about,

Still blushing in the folds of rose-leaves, still

Each evening careless of the time, our forms

A resting place of drowsy butterflies,

The idle nest of woodland choristers,

She, ingrate, our most tender passions mock.

Jacqueline. Love's gashes always fester in her heart.

Jacques. That would-be duke! Pah!

Jacqueline. A weighty one, to press us all to death

Unless we watch and serve.

Jacques. He can kill me, no worse.

Jacqueline. Not yet, I pray.

Jacques. The embryo-duke in glories hiding mine,

Like cloths of gold on diamonds! Should he fold

My love, I will undress him: desert shrubs

Will seem far greener when this knife cleaves him.

They say that time is a physician: I

Will prove he is a gravedigger as well.

Jacqueline. I see ahead the duke arrives.

Jacques. Our place to better.

Exeunt Jacques and Jacqueline

Act 1. Scene 2. The The ducal palace

Enter Ziriff and Lenu

Ziriff. Well, is the son near?

Lenu. The duke awaits him.

Ziriff. Wayward boy! Why should I befriend Thomas, dreaming of his father's death, or any man?

Lenu. Do you not pocket silver pieces from him?

Ziriff. I do, but what of that? I hate no less.

No man is yet acquainted with his thoughts,

Or mine as yet.

Lenu. When devils pay their servants, they are worth

The price of hell.

Ziriff. I loathe his manners almost as much as

I do my own.

Lenu. When wars struck our state with open-mouthed cannons, you were proven to be a general of resource and power, mounting ranks against oppressors, lifting declining files, refreshing shooting-pieces, speaking thunder against thunder, clasping last of all the war's garland as a first apprenticeship.

Ziriff. A knave must be precocious.

Lenu. Next, like a knight of ancient gallantries,

You caught at tilting our duke's favor. Ha,

A wondrous boldness!

Ziriff. Court-parasites whisper my name as if I were vermin to be rid of from the all-sheltering bark and leaves.

Lenu. Yet how effiminately you play the court wanton, simpering for his grace's truncheon, lisping sweet examples into his enchanted ear, playing music in his bed-chamber, a nightingale in satin!

Ziriff. Incredible deformities, but well accepted by the duke!

Lenu. Lords complain that you possess the vices of both sexes: brutish, insolent, and braving on one side, plaguy tearful, wanton, and secretive on the other.

Ziriff. Behold me well: both man and woman, possessing in my large bosom deep-seated treacheries specific in either.

Lenu. I'll cry mum to that, lest my teeth be blasted.

Ziriff. Greatness, what fools you make of us!

Lenu. Or maybe fools, what greatness makes of me!

Ziriff. I, creeping shadow of a prince's dream,

What am I? Atom, or true puissance?

When first I fed on his large dishes, he,

The satin-jack, first flouted me and spurned.

O, harshness of tame manhood! It prevents

His murder. Dull and foolish-base would my

State be should present handsomeness become

No sport to royalty! In wintry nights

Have I, attending on the duke's and son's

High profligacies, caperings, and jests,

Crept into greatness' favor. Will I pine,

Drop off the ducal plant when most it needs

Some gentle watering? Three winter years,

Like busy chemists, have I blown dead coals

Till my lungs ache, and must my stinking-pot

Be the reward of effort? Never! Winds:

I will not be your thin companion, night:

I will neglect you as my minion. Force

Is my elixir, with this bowl I crown

You mine, so will this trifling buzzing court

Shrink at the very sounding of my name,

Dull prisoners of all my glassy whims.

I must possess her. Sleep, my sorrows, sleep,

No longer lie between these puffy lids.

Instead, awake in other men's eyes, you

Are not as yet my ghost.- The duke arrives,

And father held in chains! There let him rest.

Enter the duke, Aglaura, and Paul, Campastes bound in chains

Duke. I say he will not live.

Paul. Good brother, as I know you are, or else

So you may one day be, some pity here!

Duke. The man you see is dead, a traitor caught,

Nursed in our court to find revengeful fangs

Fixed at his heart. Let no one be so bold

As plead for him. Should we gloss errors, what

Would then become of France and justice? Ruth

Is murderous. It is a sin to spare

A man plucked by the elbow with his coat

Lined with state-papers. Out with him to death!

No love or pity in our government

To harm the innocent! See it well done.

Ziriff. My lord-

Duke. Although his son, lose no breath pleading here.

He dies, and quickly.

Aglaura. My lord-

Duke. No breath, Aglaura. He is now no man,

Or father, but the axeman's.

Ziriff. This wrings some tears from me.

Duke. Tears for him, too, Aglaura?

Aglaura. My graceful lord, not so. I love the state

Too well to pardon such a man of grief

And darkness from the justest doom of all.

Paul. Ha? From his daughter?

Campastes. Can any father, sparing for his child,

Behold her stainless faces with no tear?

Aglaura, have I ever stabbed to death

Your hidden lovers, made a mince-pie of

A friend long-loved, destroyed and cut your hopes

With blasting of your maiden fruit, that you

Should stamp aground the withering leaf to

His final place? My daughter- not so here-

My former daughter, do not mar my cheeks

With fire and dirt. Do not. Ah, ah, do not.

Duke. These tears will not wear out or warp your rope.

Campastes. Ah, no more words for me, your counsellor?

Duke. Pitch him away. Let him be carted, flogged,

And hanged, to our declining subjects worth

Instruction on a traitor's theater.

Aglaura. It must be done, my lords. Away with him!

Lenu. Come, this way to your rest.

Exeunt Paul, Ziriff, Lenu, and Campastes

Duke. So early and so curiously enrobed,

Nice lady? These fair patterns, cool-reserved,

So luscious, big with love, are snares for hearts

In love with beauty. To be trussed up so

Looks like a set design. Say, mistress, speak,

Is it a massacre in full resolved?

Is conquest of a duke grown tediously

Base to allurements? Is a titled crown

So little worth that you must casually

Destroy us all in whitest witchery?

Aglaura. If women did so little mischief, duke,

Large hell would not be stuffed with men, nor would

Remorseless critics rail our active sex

As often as they do.

(Sounds of whipping and cries within

Duke. Ha, what is that?

Aglaura. A father cringing underneath the lash.

Duke. A daughter dutiful, so far above

Your kind, all-loving to our ducal state!

Aglaura. In faults, I should confess.

Duke. Such gentle rapes your beauty works on love,

And with such pleasing violence force love still,

Before allured sense, that he, undone,

Pleased to be so, now hurries pantingly

To death's enshrouded house his weary self,

As if in haste to be quite overthrown.

Is such a winless loss your victory?

Must we die to obtain your promised bliss?

I will try that.- Our watchful queen and son!

Enter Orbella and Thomas

Orbella. A package for your grace!

Duke. So. What is it?

Thomas. A picture, I deduce.

Duke. Ha, beauteous, far beyond example's reach!

Aglaura. Ah, no!

Thomas. Ah, better: heaven's image!

Aglaura. No.

Duke. Our tastes meet in one place. I should watch that.

Orbella. Is is so lovely? May I see at last?

Duke. No.

Thomas. May I not keep the portal of my bliss?

Duke. No.

Thomas. I will, nevertheless.

Duke. I see you must be tamed. (striking him

Thomas. Regret will suffer.

Exit Thomas

Orbella. What madness is this now?

Exit the duke

You are too beautiful today: such sights

Disorganize if not dismay weak man.

Aglaura. Most happy if not pleasing overmuch!

Exit Aglaura and re-enter Ziriff, kissing Orbella

Orbella. How glad I am to be of age to please!

Ziriff. No doubt you do, when beauty shines on you

With her most precious glass. A devil's hand

Could never mark so white an outside.

Orbella. Nor Persian ones.

Ziriff. I am a Persian when it pleases me

To be so, otherwise your lover and

Man's constant fear.

Orbella. You please me better than a husband, but

Some say you please my spouse in the same way.

Ziriff. More calumnies of court-tongues.

Orbella. Tonight, my Ziriff.

Ziriff. I will not fail. Ha! Ha!

Exit Orbella and enter Arnaud

Arnaud. The father being bound for stripes, do I

Hear laughter from the son?

Ziriff. Know, Arnaud, Persians do not weep unless

You tickle us.

Arnaud. Avaunt with merriment when statesmen bleed!

Exit Ziriff and enter Jacques

How odd a thing are crowds to such as I,

Though shining with some royalty, most base

And paltry! Nature meant I gape alone.

Had not that doting midwife in whose hands

My brother shrieked had hands too capable,

Tormenting me forever with his sight,

I would have been. Ah, death! To be born near,

But only near a crown!

Jacques. What grieves you here, my lord? What, fruitlessly

To sigh and groan atop a pyramid?

There is another way.

Arnaud. My brother is up, then his son comes next.

Jacques. You know his Thomas never loved you well.

Arnaud. Too well his Thomas never loved me well.

Jacques. Some say he loathes his uncle.

Arnaud. I loathe him, too.

Jacques. Hum, excellent! He lies so near the crown.

Arnaud. Too near.

Jacques. He has defied your brother.

Arnaud. How?

Jacques. By marrying his mistress.

Arnaud. Aglaura?

Jacques. Aglaura, watchful lord. Was that not bold?

Arnaud. O, very bold, and yet I'm glad of it.

Jacques. He is not yet a duke.

Arnaud. Not till the other dies. Does he not have

Dark thoughts, dark dreams, dark enemies of state?

Jacques. He does, I think, since who does not?

Arnaud. Bring all his enemies to me. Do it.

Jacques. My lord, I will.

Arnaud. What if I fail? Ha! Ha! I strike, they fall.

Success is promised. Not a surety?

Does the sun rise tomorrow?

Jacques. Should we be often folded thus, my lord,

The letters of our deeds would grow too big.

Arnaud. And this? The picture of the careless duke?

Jacques. The shape is quite familiar.

Arnaud. Aglaura!

Jacques. Indeed, she for whom a duke starves.

Arnaud. Ha, one step higher! It is not, good friend,

With the ascending to a mighty crown

As it is with the equidistant marks

Of staircases, most evenly the same

Up to the gilded rooftop, for to crowns

Each sharp, rough-hewn degree is varied, hard,

Uneven, treacherous, and slippery.

The slightest hesitation murders. I

Will make a snare of love, Aglaura's hair

As pillow to my brother and his son,

To hide the pit beneath. Court entrances

And passage-ways, dim chambers I must rule,

To make men drop and die: so will I be,

Or else not be at all.

Exeunt Arnaud and Jacques

Act 1. Scene 3. Ziriff's house

Enter Aglaura and Jacqueline

Aglaura. Ah, tired, yet I cannot sleep. Ah, ah!

Yawns hurt my face. Is it not late as yet?

Jacqueline. Quite late.

Aglaura. I know it is, you need not have said so.

Ah, brazen face, it was the longest day.

Jacqueline. It is not every day a woman finds

Her father executed.

Aglaura. Ha! I remember now, yet let us not

Reflect on that tonight. Unless I err,

The night will be more memorable yet.

Jacqueline. Why, madam?

Aglaura. My love stalks forth.

Jacqueline. How? In a house of mourning?

Aglaura. A slave is tedious. Will a father's law,

As I have often said and you perceived,

Restrain a daughter's pleasure? Never, girl,

You need not be a slave to think so ill

Of me. Besides, he's dead, is that not so?

I have your word on that.

Jacqueline. Both dead and buried, madam.

Aglaura. So, no more on that theme.

Jacqueline. Should I prepare the bed?

Aglaura. I will prepare the bed myself. Hide, shade:

My sun approaches.

Jacqueline. I'm gone already.

Exit Jacqueline and enter Thomas

Thomas. Come, let us grapple, love. The sleeping night

Is simple, skipping off so hurriedly

With her thin blanket when the enemy,

The prying dawn, winks on her naked shame

To make the heavens blush.

Aglaura. We must not be seen, otherwise I weep.

Thomas. The stars will weep all night long, mightily

Bound to their canopies, because they

Cannot do what we do.

Aglaura. You warm me well.

Thomas. Like death I come, while grooms and courtly ants

Inside their chambers fart and snore.- A kiss!

Aglaura. Ah! Sudden pleasures overflow the brim.

How wisely do forbidding stars restrain

And season pleasures with a pinch of dread,

Which otherwise would mar our appetite

With too much sweetness! Dear love and my own!

Thomas. For such love what death-passages I may

Not pass? Here lie bright heaven's promises:

I do not care for others. Let the world

Into one compact point contract

All its known beauties- pah! compared to yours-

A form like newer white!- they shine like mud.

Here lie its riches, which I enter here,

To bore like worms into forbidden fruit.

Aglaura. You need not pierce, my love, when a wide breach

Already may be seen. Alas, alas,

On innocence a man will triumph still,

For you obtain each night no less than all.

Thomas. Undo, undo. Your starry bed is like

The center-point of bliss. Be the rewards

Of man's ambitious frettings in the world

Never so near, they cannot overarch

The radius of our loves, from whose sharp point

Our pleasures radiate.- What sounds are these?

Only a devil dares to interrupt

A lovers' scene.

Re-enter Jacqueline

Jacqueline. Your brother, madam!

Thomas. Ha, Ziriff! If I know him well, quite lost

Forever!

Aglaura. Ah, love, we must part now.

Thomas. He has searched out our loves.

Aglaura. Be bold with him. What should a woman do

With brothers? Out with him!

Exeunt Aglaura and Jacqueline, enter Ziriff

Ziriff. Ha, friend, you start so, as if shaking hands

With someone in a horrid compact.

Thomas. What is your wish, half-man?

Ziriff. I can be angry. News I have for you.

Thomas. Lift up your veil.

Ziriff. The duke must have her.

Thomas. Aglaura? How?

Ziriff. I do not care how, but he must have her now.

Thomas. Death on your lips! I dreamt that she was mine.

On pale imagination's golden peak

Do weary varlets clamber till they freeze

Beside their pleasure. Then to plummet down

To the black base! Put me to sleep again,

Or let me die. May courteous hands snatch me

For what must come, for I espy below,

In contemplation's glass, not much of worth.

Ziriff. To sink in feathers of trim vanity?

Thomas. Enough! I cannot speak, my misery

To such a pitch that I am crushed in shades.

Here is my utmost reach of sail, the hulk

Against rocks splintering.

Ziriff. Yield me my sister.

Thomas. As willingly as virgins when sent off

To bridegrooms never asked for, so will she,

To nature's wayward fancy, not her own.

Ziriff. Both with such sweetly pleasant faces, too!

Thomas. In how much worse a state am I now than

If never I had of a woman known!

Teach me how to forget her in an hour,

Win me again to life. Do fathers raise

Us but to steal our women? Copulation

Done, let the green fruits drop as mush in their

Stink-pot. Can we not do at sixteen what

He does at fifty? I defy with grief

The buried tinder, old men lusting like

A sickly flamelet in December snow.

Ziriff. He'll have her, youth.

Thomas. I'll get her, sir.

Ziriff. I have not seen a man so crutchless slow

Since your obeying brother left the house

To marry gladly with his father's will.

Not done with puling yet?

Re-enter Aglaura and Jacqueline

Thomas. Take her.

Aglaura. How! To the duke?

Ziriff. Good sister, do not start on fortune's whim,

Since nicer women go the way you do,

And yet they thrive.

Aglaura. I'll follow. House affairs I must attend

Before I see my misery, to wring

One minute from my utmost proof of weal

And constancy.

Exeunt Thomas and Ziriff

Jacqueline. How, weeping still? Look to your face tonight.

This dream of love's a trifle.

Aglaura. You quite mistake me, slave: I weep for joy.

This paltry service to his dukedom will

Not hide my Thomas from my sensual light.

Although a duke's estate still keeps me warm,

With joyance I can live, defying all.

Exeunt Aglaura and Jacqueline


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User talk:Melanie Ferreira

 Hello Melanie Ferreira, 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.
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 * Find out about research activities on 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. --Ottava Rima (talk) 22:30, 5 October 2010 (UTC)

title: User talk:Melanie Ferreira


text:
User talk:Elizabethtaus

 Hello Elizabethtaus, 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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 * Find out about research activities on Wikiversity.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Ottava Rima (talk) 22:30, 5 October 2010 (UTC)

title: User talk:Elizabethtaus


text:
User talk:Orchidluo

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

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 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Ottava Rima (talk) 22:31, 5 October 2010 (UTC)

title: User talk:Orchidluo


text:
User talk:0925hjk

 Hello 0925hjk, 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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 * Give feedback about your initial observations
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And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Ottava Rima (talk) 22:31, 5 October 2010 (UTC)

title: User talk:0925hjk


text: File:Scanned 2.png

title: File:Scanned 2.png


text: File:Scanned Image 1.tif

title: File:Scanned Image 1.tif


text: File:Picture 2.png

title: File:Picture 2.png


text:
User:BigBear

 * Bachelor of Music at the Conservatorium van Amsterdam 2008
 * Master of Music at the Conservatorium van Amsterdam 2010

title: User:BigBear


text:
Talk:Motivation and emotion/Textbook/Motivation and emotion/Animals

Feedback
This textbook chapter is shaping up nicely - well done on putting your plan/outline up, wikifying it and experimenting with images and links. I've tweaked the image captions so that they display with the images and I've adjusted the heading levels to be consistent with the style for the textbook. Let me know if I can do anything else as you go along. BTW - Did you see this? http://www.youtube.com/watch?v=PL1-rFk2KDg Sincerely, James. -- Jtneill - Talk - c 00:49, 6 October 2010 (UTC)
 * Perhaps consider swapping the order of the emotion and motivation sections? (I mainly suggest this because the structure for the book will be motivation then emotion. -- Jtneill - Talk - c 00:51, 6 October 2010 (UTC)

Just popped in to see your page and wow it has really advanced over the past month - great effort. -- Jtneill - Talk - c 00:09, 2 November 2010 (UTC)

I've had a closer look over the draft so far - which is very well advanced, although I think it could now mainly benefit from a significant trimming with some =restructuring and redrafting to integrate and focus on theory and research about motivation and emotion in animals. Hope this helps. Some more specific suggestions are below: -- Jtneill - Talk - c 03:12, 4 November 2010 (UTC)
 * 1) The current draft is very long (over 12,000 words - thesis length!) - whilst there is no upper limit, the original suggestion was to aim for more like 2,500 for 4,500 - so where possible, in redrafting, look to abbreviate and concentrate the chapter on some key underlying focus questions and the main topic. Content that is less directly relevant (e.g. supplementary) could be put into subpages, allowing you to trim down the main chapter with links off to sub-pages with more detailed information.
 * 2) The heading structure should ideally use = for the title, then == (Level 2) for the chapter's next level of headings, then === for their sub-headings etc.
 * 3) The layout in general is very good, with excellent use of images.
 * 4) Introduction
 * 5) Maybe change "Theories of motivation and emotion in animals: An overview." to "Motivation and emotion in animals: An overview" or just "Introduction".
 * 6) Check grammar of sentence two.
 * 7) man's -> human's?
 * 8) scientists and pet lovers -> and psychology students?
 * 9) The image could have a more meaningful caption.
 * 10) I think this Introduction is promising and is currently reasonably good. I think that it would benefit from specifying either some focus questions and/or providing a more indepth outline of what topics will be covered in the chapter and why.
 * 11) I love the questions asked at the end of this section - perhaps these could go up front in the section to stimulate initial interest. But I don't think these are focus questions; focus questions should be more generic.
 * 12) What's the link for at the end: http://www.learner.org/discoveringpsychology/08/e08expand.html? (explain)
 * 13) Theories
 * 14) Excellent use of links to Wikipedia
 * 15) "There is plenty of literature available" - e.g., references?
 * 16) Darwin vs Lamarckian - lacks direct connection/application to motivation/emotion in animals (i.e., too general, broad) - how does it help to address the focus questions?
 * 17) Pavlov - this is a simpler, clearer section - but again, it could be made more obvious what the connection is to motivation/emotion in animals - yes, this is about animal behaviour, but what about motivation/emotion?
 * 18) Watson - ditto; this says nothing about motivatin/emotion in animals - it does perhaps say something about the use of animals in psychological research, but that is not the topic
 * 19) Rest of the theory sections - similar comments to above. This is a good summary of animal behaviour research, but some work needs to be done to tailor this section more closely to the motivation/emotion in animals. Perhaps it would make more sense to organise this not so much in terms of individual reseachers but more in terms of theoretical perspectives e.g., evolutionary, biological, and learning/behavioural paradigms. Alternatively keep this section very short of eliminate it and then incorporate relavant theory into subsequent sections.
 * 20) Seligman and learned helplessness could be added?
 * 21) Lorenz' work could be added?
 * 22) Emotion in animals
 * 23) It would be helpful to know how/why you are conceptualising emotion and motivation as separate constructs in animals - i.e., explain these concepts first before the specific focus here on emotion (also note that earlier I've suggested considering putting motivation first)
 * 24) Maybe incorporate both theory and research into this section e.g., something like "This section discusses current theory and research on emotions in animals and consider implications for animal welfare." For example, the discussion about Harlow is split across two sections; it would be good to integrate these. Similarly, discussion about Skinner's work is split across sections.
 * 25) The last paragraph is somewhat confusing - better to set up and connect to the immediately following section.
 * 26) "Do animals experience emotions such as love, fear, anger, rage, despair, frustration, boredom and contentment?" - why not just "Do animals experience emotions?"
 * 27) This section appears to be a response to a focus question (but it's not obvious). Perhaps a better question could be "What emotions do animals experience?" and "How do animal emotions differ between species?"
 * 28) This section is 1400 words and could definitely be abbreviated. There are lots of interesting ideas and information but the paragraphs seem to be quite disjointed. What's the overall of this section - provide an introduction, body and summary, then lead into the next section.
 * 29) Motivation in animals
 * 30) Where links to videos are added, it could be helpful to include in brackets how long the video is e.g., (2 mins)
 * 31) Maybe integrate the video placement with specific, relevant sections in the text.
 * 32) Again, some focus questions and/or stated aims could be helpful.
 * 33) I skimmed the rest of this section - it was quite long and definitely could be abbreviated - my main perception is that many similar topics (such as learning) were raised again, so there was much overlap. It could be better in this case to integrate discussion of emotion and motivation (it's not clear to me that there is sufficient justification for treating them as separate topics when discussing animals - they are different, but are also very related), focusing on the main theories and relevant research about each theory.
 * 34) Bringing man and animals together - interspecies communication
 * 35) I think having an applied section on training is an excellent idea. But it represents almost 4000 words and I suspect could perhaps even sit as a separate article/chapter, with the chapter itself containing just some highlights. Interspecies communication is interesting... but it is relevant to this chapter only to the extent that it bears direct relation to understanding theory and research about motivation and emotion in animals. So, I would suggest being quite selective about the examples to focus on and to explictly point out the connections with motivation/emotion and particularly previous theory and research.
 * 36) Recommended reading - not sure about this, seems to be a lot about horses as opposed to the chapter topic per se - maybe put into a separate page
 * 37) External links - as for Recommended reading. I would be quite selective and in general try to place the links in relevant places in the body text. Only put some very particularly relevant recommended links here at the end, or include all links on a separate sub-page.

-- Jtneill - Talk - c 14:04, 13 December 2010 (UTC)


text:
User talk:BigBear

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

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

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Ottava Rima (talk) 00:50, 6 October 2010 (UTC)

title: User talk:BigBear


text:
Talk:Ear training/Perfect pitch

Perfect pitch is always a relative pitch and learned, for tuning has changed through the centuries and the names for the notes (pitches) have to be learned at some stage. Of course if you notice earlier that you can remember them it is easier as with everything, no? --BigBear 01:19, 6 October 2010 (UTC)

title: Talk:Ear training/Perfect pitch


text:
User:Egm6321.f10.team2.oztekin/exp

=Exponantial Of Matrix=

Taylor series are consist of infinite components of function and its derivatives.The series are centered on any number that is interested in.

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

$$  \displaystyle f(a)+\frac{{f}'(a)}{1!}\left ( x-a \right )+\frac{{f}''(a)}{2!}\left ( x-a \right )^{2}+\frac{f^{3}(a)}{3!}\left ( x-a \right )^{3}........... $$     (N)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

For f(x)=expx can be characterized as the same way.

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

$$  \displaystyle e^{x}=\sum_{n=0}^{\infty }\frac{x^{n}}{n!}=1+x+\frac{x^{2}}{2!}+\frac{x^{3}}{3!}+........... $$     (N)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

And if we substitute matrix A into x we concluded that:

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

$$  \displaystyle e^{A}_{n\times n}=\sum_{n=0}^{\infty }\frac{x^{n}}{n!}=I_{n\times n}+A_{n\times n}+\frac{A_{n\times n}^{2}}{2!}+\frac{A_{n\times n}^{3}}{3!}+........... $$     (N)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

-

=Problem 6=

Given
Example given in MT15-3 as

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

$$  \displaystyle x({y}')^{2}+y{y}'+xy{y}''=0 $$     (N)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

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

$$  \displaystyle g(x,y,p)=x({y}')^{2}+y{y}' $$     (N)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

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

$$  \displaystyle f(x,y,p)=xy $$     (N)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

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

$$  \displaystyle h_{x}+h_{y}p=0 $$     (N)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

Find
Without assuming h=const. discuss other solutions.

Solution
For the condition given Eq. both terms must be zero. So

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

$$  \displaystyle h_{x}=0 $$     (N)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

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

$$  \displaystyle h_{y}p=0 $$     (N)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

And we know that h=h(x,y).Possible outcomes for the derivations;

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

$$  \displaystyle h_{x}=h(x,y) $$     (N)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

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

$$  \displaystyle h_{y}=h(x,y) $$     (N)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

By this way we can not find common h for stisfy Eq.

title: User:Egm6321.f10.team2.oztekin/exp


text:
UC Women's Group Mentoring Program/Participant 2's story

Contact details
Name of storyteller: Participant 2

Name of person recording story: Mark Spain

Location: Mizzuna’s

1. What changes have you noticed since you have finished the program?

 * 1) I’m in a higher role
 * 2) I was a younger woman observing a lot of very upset older women. Looking at them inspired me to not be like that. I don’t want to be a victim at 50 earning $50k.
 * 3) The connections and opportunity to meet people I don’t normally associate with. This opened avenues for me and how the uni functioned.
 * 4) I recommenced studying and it was nice to have the support of people encouraging me.
 * 5) One woman was in a terrible situation in her life. I was very proud of her growth during the year. She was shy and lacked confidence but we assisted her in growing stronger
 * 6) I personally gained a lot especially from the inspiration and energy of people in the academic group. Unlike our group they had found the the things they were passionate about. I never felt confident in my creativity but a woman in this group supported me to be creative on the day we shared together. I still remember this experience strongly.
 * 7) I’ve been in a very male dominated work area and it’s nice to have female contact. I made some really good friends and still keep in contact

2. What has been the MOST significant change?
My most significant change was that my self confidence grew. I strongly realized that I did not want to be a victim as I got older.

Beginning (situation before the change)

Before the program I didn’t have a lot of direction.

Middle (what happened)

During the program I had a lot of frustration with the group and how it was running. I recognize that this was my perception. It was very eye opening for me to learn what other people’s experience of their lives were. I’ve had a lot of negativity in my life but didn’t accept seeing myself as a victim. When I told my story other people admired me for not being a victim. They got energy from me. I felt that I was cold and distant during the program. I wasn’t interested in bitching. I was more an observer. I felt others may have been frustrated with me. On the last day I opened up and relaxed. We lacked direction and organization and didn’t know where we were going. The selection of leader was poor (ie didn't work for me).

End (situation after)

I’m in a bigger job now that is incredibly stressful. Two years ago I would not have done this job. I now have direction. I had a wonderful supervisor and I am now very fortunate to have an inspirational woman supervisor at the moment.

3. Why was this change significant for you?
I’ve worked because I have to. I’ve never been openly passionate about anything. What I’m doing now is more aligned to my more long term creative passion. I didn’t see this coming. I’m doing really exciting work. I’ve learned a lot over the last 12 months and I’ve got plans for the future.

We need to be drawing in the wonderful exciting passionate people who are working at the uni to have their energy rub off on others.

from Jess Dart	http://www.clearhorizon.com.au


text:
User talk:Kav252

 Hello Kav252, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

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

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Ottava Rima (talk) 03:21, 6 October 2010 (UTC)

title: User talk:Kav252


text:
User:Egm6321.f10.team1.allen/HW3

Find
Generalize Eq 5.1 to the case of SC_L1_ODE_VC.

Solution
For a L1_ODE_CC we have

$$ x(t)=e^{a(t-t_0)}x(t_0)+\int_{t_0}^{t}[e^{a(t-\tau)}]bu(\tau)d\tau $$.

and for a L1_ODE_VC we have

$$ x(t)=e^{\int_{t_0}^{t}a(\tau)d\tau}x(t_0)+\int_{t_0}^{t}[e^{\int_{\tau}^{t}a(s)ds}]b(\tau)u(\tau)d\tau $$.

Similarly, with

$$\begin{align} \underline{x} (t) = [e^{ \underline{A} (t-t_0)} ] \underline{x} (t_0) + \int_{t_0}^{t} [e^ {\underline{A} (t- \tau\,)} ] \underline{B} \underline{u}(\tau\,) d\tau\, \end{align}$$

Author Egm6321.f10.team1.allen 04:30, 6 October 2010 (UTC)

title: User:Egm6321.f10.team1.allen/HW3


text:
UC Women's Group Mentoring Program/Participant 10's story

Contact details
Name of storyteller: Participant 10

Name of person recording story: Mark Spain

Location: The Education Centre, 1C88

Date of recording: 3 September 2010

How did you become involved in UC WGMP?
I was involved in research and research grants. I was involved in collaboration in future groups. In subsequent years I was involved with academics group. I helped with residential. This was a great confidence builder. I knew who to go to for help. It was good for how to advance my career. I was younger and at a different stage of my career. I had seven years in the research office. I built on that and got involved in the Women’s Professional Development Committee. I was settled at uni and wasn’t looking outside. It gave me impetus and confidence for looking outside. I negotiated what I wanted in my job outside. It was a good outcome and came from lateral thinking. It was a higher level part-time job. I saw other women get higher status jobs outside. They used this time to set goals in a supportive environment. EAs still meet regularly. You know people as a result of the WGMP.

1. What changes have you noticed since you have finished the program?

 * 1) I was new to the uni. It gave me networks and helped me understand how the uni functioned.
 * 2) It also gave me the impetus to study. I will graduate this year.

2. What has been the MOST significant change?
The most significant change for me was the connections and the sense of impetus for the undertaking the next thing. I can use that experience as a template for a new job or a new house. It is good for goal setting and support for achieving goals with a network of support around you. It helped me define my goals. You can’t achieve something if you are too vague about it.

Beginning (situation before the change)

I had some strengths already. I built on these. I didn’t know anybody. I didn’t know how the uni functioned.

Middle (what happened)

I started to form relationships and a blossoming network. I noticed how we let the network emerge.

End (situation after)

I now see myself as a part of layers of networks – me, my group, the Women’s Group Mentoring Program, the University, Canberra. I also since have done the Springboard Program offered by PMP.

3. Why was this change significant for you?
It has helped me to achieve things beyond UC - my job outside and my studies. It has given me a structure to move ahead – setting a goal and achieving it. I am the Manager of the XYZ at ANU. This promotion and pay rise gave me kudos and a sense of recognition. UC was going through a difficult time and because of the additional strain people weren’t being recognized. It was good for me to be recognized and get a job outside.

from Jess Dart	http://www.clearhorizon.com.au


text: Open academia/Processes

title: Open academia/Processes


text:
Open education with Moodle and Wikiversity/Proposal

Proposal
This presentation will discuss how Moodle can be used in conjunction with Wikiversity as a platform for open education, with consideration of challenges, opportunities, pros and cons. Principles of open academia will be described, with demonstration of sites including:
 * 1) Survey research and design in psychology (Moodle/Wikiversity)
 * 2) Motivation and emotion (Moodle/Wikiversity)
 * 3) Psychology 102 (Moodle/Wikiversity)
 * 4) Social psychology (Wikiversity)


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

\documentclass{article} \usepackage[usenames]{color}

\begin{document}

\textcolor{BlueViolet}{This is BlueViolet color}.

\textcolor{Periwinkle}{This is Periwinkle color}.

\textcolor{CadetBlue}{This is CadetBlue color}.

\textcolor{CornflowerBlue}{This is CornflowerBlue color}.

\textcolor{MidnightBlue}{This is MidnightBlue color}.

\textcolor{NavyBlue}{This is NavyBlue color}.

\textcolor{RoyalBlue}{This is RoyalBlue color}.

\textcolor{Blue}{This is Blue color}.

\textcolor{Cerulean}{This is Cerulean color}.

\textcolor{Cyan}{This is Cyan color}.

\textcolor{ProcessBlue}{This is ProcessBlue color}.

\textcolor{SkyBlue}{This is SkyBlue color}.

\textcolor{Turquoise}{This is Turquoise color}.

\textcolor{TealBlue}{This is TealBlue color}.

\textcolor{Aquamarine}{This is Aquamarine color}.

\textcolor{BlueGreen}{This is BlueGreen color}.

\end{document}

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


text:
User:Egm6321.f10.team4.Yoon/frequent-edit

 * $$\displaystyle $$


text:
User:Egm6321.f10.team4.Yoon/HW12009

 See my comments or TA's comments below. Egm6321.f09 20:49, 19 September 2009 (UTC)

= Problem 2 - Method of Integrating Factor =

Given
A Linear 1st order ODE is given by

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

$$
 * $$\displaystyle y' + y = x$$
 * $$\displaystyle (Eq. 4)
 * $$\displaystyle (Eq. 4)

 * }
 * }

Find
Solve Eq. 4 for y(x) and show
 * {| style="width:100%" border="0" align="left"

 * $$\displaystyle y(x) = A e^{-x} + x - x$$
 * $$\displaystyle y(x) = A e^{-x} + x - x$$

 * }
 * }

Solution
To find the solution, we need to perform the exactness test which requires two steps:

1. Writing the ODE in the form of
 * {| style="width:100%" border="0"

 * style="width:95%" |
 * $$\displaystyle M(x,y)+N(x,y)y'=0$$
 * $$\displaystyle M(x,y)+N(x,y)y'=0$$

$$
 * $$\displaystyle (Eq. 5)
 * style= |
 * }

2. Checking the condition given by
 * {| style="width:100%" border="0"

 * style="width:95%" |
 * $$\displaystyle \frac{\partial M}{\partial y}=\frac{\partial N}{\partial x}$$
 * $$\displaystyle \frac{\partial M}{\partial y}=\frac{\partial N}{\partial x}$$

$$
 * $$\displaystyle (Eq. 6)
 * style= |
 * }.

Checking Condition 1

Re-writing Eq. 4 in the form of Eq. 5 gives

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

 * style="width:100%" |
 * $$\displaystyle (y-x)+ y' = 0$$
 * $$\displaystyle (y-x)+ y' = 0$$

 * style= |
 * }

where $$\displaystyle M=(y-x)$$ and $$\displaystyle N=1$$. It is shown that condition 1 is met.

Checking Condition 2

Now, we have to test if $$\displaystyle M_y=N_x$$

 * $$\displaystyle M_y = 1$$ and $$\displaystyle N_x = 0$$

Therefore, Eq. 4 is not an exact differential equation and an integrating factor is needed to force the ODE to be exact. The definition of the integrating factor is

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

 * style="width:95%" |
 * $$\displaystyle h(x)=\exp \int^x f(x)dx$$
 * $$\displaystyle h(x)=\exp \int^x f(x)dx$$

 * style= |
 * }

where

 * $$\displaystyle f(x)=\frac{1}{N}\left[ M_p - N_x \right ]$$

Substiuting the values of M and N yield

 * $$\displaystyle f(x)== \frac{1}{1}\left[ 1 - 0 \right ] = 1 $$

Therefore the integrating factor is
 * {| style="width:100%" border="0"

 * style="width:95%" |
 * $$\displaystyle h(x)= e^x$$
 * $$\displaystyle h(x)= e^x$$

 * style= |
 * }

Multiplying Eq. 4 by the integrating factor gives

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

 * style="width:95%" |
 * $$\displaystyle e^x y + e^x y' = xe^x$$
 * $$\displaystyle e^x y + e^x y' = xe^x$$

 * style= |
 * }

Now it can be seen that the left hand side is in the form of a derivative product. Recognizing this yields:

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

 * style="width:95%" |
 * $$\displaystyle (e^xy)' = xe^x$$
 * $$\displaystyle (e^xy)' = xe^x$$

 * style= |
 * }

Integrating both sides results

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

 * style="width:95%" |
 * $$\displaystyle (e^xy) = e^x(x-1)+A$$
 * $$\displaystyle (e^xy) = e^x(x-1)+A$$

Finally, dividing by e^x results in
 * style= |
 * }
 * {| style="width:60%" border="0"

$$\displaystyle y = Ae^{-x}+(x-1)$$
 * style="width:45%; padding:10px; border:2px solid #8888aa" |
 * style="width:45%; padding:10px; border:2px solid #8888aa" |
 * style= |
 * }

= Problem #3 = Show that the first order ODE $$(2x^2+\sqrt{y})+x^5y^3y^{\prime}=0$$ is nonlinear

Solution

Define a linear operator $$D\left ( \cdot \right )$$ such that $$D(\cdot )=2x^2+\sqrt{\left (\cdot  \right ) }+x^5\left (\cdot  \right ) ^3\frac{d}{dx}\left ( \cdot  \right )$$

The linearity condition then becomes$$\forall\alpha,\beta \in\mathbb{R}$$, $$D(\alpha u+\beta v)=\alpha D(u)+\beta D(v)$$ where u and v are any functions of x

Substituting in for the left side of the linearity condition gives:

$$D(\alpha u + \beta v)=2x^2+\sqrt{\alpha u + \beta v}+x^5\left ( \alpha u + \beta v \right )^3\frac{d}{dx}\left ( \alpha u+\beta v \right )$$

Substituting for the right side of the linearity condition:

$$\alpha D(u)+\beta D(v)=\alpha\left (2x^2+\sqrt{u}+ x^5u^3\frac{du}{dx} \right )+\beta\left ( 2x^2+\sqrt{v}+x^5v^3\frac{dv}{dx} \right )$$

Simplifying and comparing both sides of the linearity condition:

$$2x^2+\sqrt{\alpha u+\beta v}+\alpha x^5(\alpha u+ \beta v)^3\frac{du}{dx}+\beta x^5(\alpha u + \beta v)^3\frac{dv}{dx}\neq2x^2\alpha+\alpha\sqrt{u}+\alpha x^5u^3\frac{du}{dx}+2x^2\beta+\beta\sqrt{v}+\beta x^5v^3\frac{dv}{dx}$$

The condition is therefore not met, and $$(2x^2+\sqrt{y})+x^5y^3y^{\prime}=0$$ is a nonlinear 1st Order ODE.

= Problem 4 = Given:

$$\ F(x,y,y') = x^2y^5 + 6(y')^2 = 0 $$

Show that F(x,y,y')=0 in the above equation is a nonlinear 1st order ODE:

Like in homework problem #3, an ODE is linear if it has the form: an(x)y(n) + an-1(x)y(n-1) + ... + a1(x)y' + a0(x)y = Q(x) (see )

So we should only have "x" values and coefficients in each "y" term. If the "y" terms are dependent on other "y" terms, then it cannot be linear.

By inspection, the above equation cannot be linear because the $$y^5$$ and $$(y')^2$$ terms make it nonlinear.

Taking the derivative with respect to "x" yields an equation a high order "y" term:

$$\frac{d}{dx}(x^2y^5+6(y')^2)= \frac{d}{dx}(x^2y^5) + \frac{d}{dx}(6(y')^2) = 2xy^5 $$

Additionally by testing the equation against the principle of superposition in a similar fashion as it was done in problem 3, the results are as follows:

$$ \ D(.)= x^{2}(.)^{5}+6((.)')^{2} $$

$$ \ D(u+v)= x^{2}(u+v)^{5}+6((u+v)')^{2} = x^{2}(u+v)^{5} + 6(u'+v')^{2} $$

$$ \ D(u)= x^{2}(u)^{5}+6((u)')^{2} $$

$$ \ D(v)= x^{2}(.)^{5}+6((.)')^{2} $$

$$ \ D(u)+D(v)= x^{2}(u^{5}+v^{5})+6(u'^{2}+v'^{2}) $$

From the results presented it is concluded that the function does not meet the superposition requirement. Therefore:

F(x,y,y') is nonlinear

= Problem #5 = Part 1. Create an exact nonlinear 1st Order ODE of the form $$\Phi_x\left(x,y\right)+\Phi_y\left(x,y\right)y^{\prime}=0$$ using the equation $$\Phi\left(x,y\right)=6x^4+2y^{3/2}$$

Solution:

If,

$$\Phi\left(x,y\right)=6x^4+2y^{3/2}$$

Then

$$\Phi_{x}\left(x,y\right)=24x^{3}=M$$

and

$$\Phi_{y}\left(x,y\right)=3y^{1/2}=N$$

For a nonlinear, 1st order, ODE:

$$M + Ny^{\prime}=0$$

Therefore,

$$24x^3 + 3y^{1/2}y^{\prime}=0$$

We have forced exactness

Part 2. Create three more exact nonlinear 1st Order ODEs by inventing new $$\Phi\left(x,y\right)$$ functions.

Ex. 1

Choose $$\Phi\left(x,y\right)=x^{1/2}+y^{3}\quad\text{:}$$

$$ \begin{align} \Phi_{x}\left(x,y\right)&=0.5x^{-1/2}=M\left(x,y\right) \\ \Phi_{y}\left(x,y\right)&=3y^{2}=N\left(x,y\right) \end{align} $$

This leads to the following exact, first-order ODE:

$$M\left(x,y\right) + N\left(x,y\right)y' = \frac{1}{2}x^{-1/2}+3y^{2}y' = 0$$

Ex. 2

Choose $$\Phi\left(x,y\right)=3y^2+2x^5\quad\text{:}$$

$$\Phi_x\left(x,y\right)=10x^4=M\left(x,y\right)$$

$$\Phi_y\left(x,y\right)=6y=N\left(x,y\right)$$

This leads to the following exact, first-order ODE:

$$M\left(x,y\right) + N\left(x,y\right)y' = 10x^4+(6y)y' = 0$$

Ex. 3

Choose $$\Phi\left(x,y\right)=3x^2y^3\quad\text{:}$$

$$\Phi_x\left(x,y\right)=6xy^3=M\left(x,y\right)$$

$$\Phi_y\left(x,y\right)=9x^2y^2=N\left(x,y\right)$$

This leads to the following exact, first-order ODE:

$$M\left(x,y\right) + N\left(x,y\right)y' = 6xy^3+\left(9x^{2}y^{2}\right)y' = 0$$

title: User:Egm6321.f10.team4.Yoon/HW12009


text:
User:Egm6321.f10.team4.Yoon/HW22009

= Problem 1 - Integrating Factor Method =

Given
General form of a First Order Nonlinear Ordinary Differential Equations(N1-ODE) is given by,
 * {| style="width:100%" border="0" align="left"

F(x, y(x),\dot y(x)) = 0 $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 1)
 * }
 * }

By using $$\displaystyle F=\frac{d}{dx} \phi(x,y(x))$$ we get

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

F = \underbrace{\frac{\partial \phi}{\partial x}}_{M(x,y)} + \underbrace{\frac{\partial \phi}{\partial y}}_{N(x,y)} \frac{dy}{dx} = 0 $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 2)
 * }
 * }

We can multiply this by an Integrating Factor, $$\displaystyle h(x,y)$$, to get

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

h F = h M + h N \frac{dy}{dx} = 0 $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 3)
 * }
 * }

Then it follows that an exactness condition for an N1ODE's is, with equation 2 as the special case where $$h=1$$

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

(hM)_y = (hN)_x
 * $$\displaystyle
 * $$\displaystyle

$$ $$
 * $$\displaystyle (Eq. 4)
 * }
 * }

Given that $$\displaystyle h_x N = 0$$, it is found that
 * {| style="width:100%" border="0" align="left"

\Rightarrow -h_y M + h(N_x - M_y) = 0 $$ $$ or
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 5)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

\Rightarrow \frac{h_y}{h} = \frac{1}{M}(N_x - M_y) = -g(y) $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 6)
 * }
 * }

Find
Complete the details to obtain Euler's Integrating factor $$\displaystyle h(y)$$.

Solution
Integrate equation 6
 * {| style="width:100%" border="0" align="left"

\int \frac{h_y}{h} dy = - \int g(y) dy $$ $$ This yields
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 7)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

\ln h = - \int^y g(y) dy $$ $$ The final equation is
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 8)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

 * style="width:50%; padding:10px; border:2px solid #8888aa" |
 * $$ \displaystyle
 * $$ \displaystyle

h = e^{- \int^y g(y) dy} $$ $$
 * $$\displaystyle (Eq. 9)
 * }
 * }

= Problem 2 - Finding Integrating Factor =

Given

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

y' + \frac{1}{x}y = x^2 $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 1)
 * }
 * }

Find
1. Show that the solution for the integrating factor is $$h(x) = x$$ 2. Solve for $$y$$

Solution
1. With an integrating factor, $$h(x)$$, we should get the equation
 * {| style="width:100%" border="0" align="left"

(hy)' = h x^2 $$ $$ Using $$h(x) = x$$ yields
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 2)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

xy' + y = x^3 $$ $$ Dividing the above equation with $$x$$ yields the original equation
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 3)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

y' + \frac{1}{x} y = x^2 $$ $$ Hence, $$h(x) = x$$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle
 * }
 * }

2. Substituting $$h(x) = x$$ into equation 2 yields
 * {| style="width:100%" border="0" align="left"

(xy)' = x^3 $$ $$ Next, we integrate the above equation
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 4)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

xy = \frac{x^4}{4} + C $$ $$ where $$C$$ is a constant. The final form of this equation is
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 5)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

 * style="width:50%; padding:10px; border:2px solid #8888aa" |
 * $$ \displaystyle
 * $$ \displaystyle

y = \frac{x^3 }{4} + \frac{C}{x} $$ $$
 * $$\displaystyle (Eq. 6)
 * }
 * }

= Problem 5 - N2-ODE-VC Exactness =

Given
Consider the following equation
 * {| style="width:100%" border="0" align="left"

xy y'' + x(y')^2 + y y' = 0 $$ $$ Using
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 1)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

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

g(x,y,p) = x(y')^2 + y y' = 0 $$ $$ Equation 1 can be written
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 3)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

f(x,y,p) y'' + g(x,y,p) = 0 $$ $$ Hence, the first exactness condition is fulfilled.
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 4)
 * }
 * }

Find
Show that the second exactness condition is satisfied for equation 1.

Solution
Note: Equation 1 can be rewritten
 * {| style="width:100%" border="0" align="left"

(xyy')' = 0 $$ $$ First, we write $$f$$ and $$g$$ as
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 5)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

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

g(x,y,p) = x p^2 + y p = 0 $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 3)
 * }
 * }

The second condition of exactness is given by
 * {| style="width:100%" border="0" align="left"

f_{xx} + 2p f_{xy} + p^2 f_{yy} = g_{xp} + p g_{yp} - g_y $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 6)
 * }
 * {| style="width:100%" border="0" align="left"
 * {| style="width:100%" border="0" align="left"

f_{xp} + p f_{yp} + 2 f_y = g_pp $$ $$ Substituting $$f$$ and $$g$$ into equation 6 and 7 yields
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 7)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

0 + 2p \cdot 1 + p^2 \cdot 0 = 2p + p \cdot 1 - p $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 8)
 * }
 * {| style="width:100%" border="0" align="left"
 * {| style="width:100%" border="0" align="left"

0 + p \cdot 0 + 2 x = 2x $$ $$ or
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 9)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

2p = 2p $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 8)
 * }
 * {| style="width:100%" border="0" align="left"
 * {| style="width:100%" border="0" align="left"

2 x = 2x $$ $$ Hence, the second exactness condition is fulfilled.
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 9)
 * }
 * }

= Problem 6: Derive the second exactness condition for N2-ODE=

Given
A general N2-ODE is given in the form:

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

F(x,y,y',y) = 0 = f(x,y,p)y + g(x,y,p) $$ $$ where
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 1)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

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

g(x,y,p):=\phi_x + \phi_y(x,y,p)p $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 3)
 * }
 * }

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

p:=y'. $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 4)
 * }
 * }

Find
Derive the second condition of exactness (given in Eq. 5)

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

f_{xp}+pf_{yp} + 2f_y = g_{pp} $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 5)
 * }
 * }

Solution
Differentiate Eq. 3 with respect to p
 * {| style="width:100%" border="0" align="left"

g_p = \phi_{xp} + \phi_y + p\phi_{yp} $$ $$ Note that $$\displaystyle f = \phi_p$$, so
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 6)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

g_p = f_{x} + \phi_y + p f_{y} $$ $$ Differentiate a second time
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 7)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

g_{pp} = f_{xp} + \phi_{py} + f_{y} + p f_{yp} $$ $$ Substitute $$\displaystyle f = \phi_p$$ again
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 8)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

 * style="width:50%; padding:10px; border:2px solid #8888aa" |
 * $$ \displaystyle
 * $$ \displaystyle

g_{pp} = f_{xp} + p f_{yp} + 2f_{y} $$ $$ =Problem 3=
 *
$$\displaystyle (Eq. 9)
 * }
 * }

Given
A non-homogenous L1_ODE_VC

 * $$ \frac{1}{2}x^{2}y'+[x^{4}y+10]= 0 $$

Find
Show that the above non-homogenous L1_ODE_VC is exact

Solution
For the non-homogenous L1_ODE_VC to be exact it must staisfy satisfy the 2 conditions of exactness

\begin{align} N(x,y)y' + M(x,y) &= 0 \\ M_y(x,y) &= N_x(x,y) \end{align} $$

So the first condition is met by:

 * $$ \underbrace{\frac{1}{2}x^{2}}_{N(x,y)}y'+\underbrace{[x^{4}y+10]}_{M(x,y)}= 0 $$

Let's take a look at the 2nd condition:

\begin{align} M_y(x,y) & = x^4 \\ N_x(x,y) & = x \end{align} $$

Clearly $$M_y(x,y) \neq N_x(x,y)$$, so we make use of the integrating factor to see if we can make it exactly integrable.

So we re-write the ODE

 * $$ \underbrace{\frac{1}{2}x^{2}}_{N(x,y)}y'+\underbrace{[x^{4}y]}_{M(x,y)}= -10 $$

Looking at case #1 for the integrating factor we obtain:

\begin{align} \frac{1}{N}\left(N_x - M_y\right) &= -f(x) \qquad \text{replacing values found above}\\ \frac{2}{x^2}\left(x - x^4\right) &= -f(x) \qquad \text{applying knowledge from integrating factor we know}\\ h(x)&=\exp \int^{x}f(s)ds \qquad \text{replacing f(x) into the integral and evaluating it, obtain}\\ h(x) &= \frac{1}{x^2}\exp \left(\frac{2x^3}{3}\right) \end{align} $$

Now we can try the 2nd condition of exactness to see if by using integrating factor we can make this ODE exact

\begin{align} \bar{M}_y &= \bar{N}_x\\ \underbrace{(hM)}_{\bar{M}}dx&=\underbrace{(hN)}_{\bar{N}}dy\qquad \text{calculating the respective values we obtain}\\ \bar{N}_x &=x^2 \exp\left(\frac{2x^3}{3}\right)\\ \bar{M}_y &=x^2 \exp\left(\frac{2x^3}{3}\right) \end{align} $$

Hence the non-homogenous L1_ODE_VC is exact.

 Nice work. --Egm6321.f09.TA 03:14, 28 September 2009 (UTC) =Problem 4=
 * }

Given
An aribitrary 1st order ODE:

 * $$ \left(\frac{1}{3}x^{3}\right)(y^{4})y'+(5x^{3}+2)\left(\frac{1}{5}y^{5}\right)=0$$

Find
Show that the above is non-linear and exact

Solution
So let's determine that the above ODE is non-linear by making use of the $$D(.)\!$$ operator

To be a linear ODE the following must be true:

 * $$D\left(\alpha u + \beta v \right) = D\left(\alpha u \right) + D\left(\beta v \right)$$

Now we will define the $$D(.)\!$$ operator for the above ODE:

 * $$D(.)= \left(\frac{1}{3}x^{3}\right)(\cdot)^{4}\frac{d(\cdot)}{dx}+(5x^{3}+2)\left(\frac{1}{5}(\cdot)^{5}\right)$$

Then let's evaluate the linearity condition to see if it's true:

\begin{align} D\left(\alpha u + \beta v \right) &= \left(\frac{1}{3}x^{3}\right)(\alpha u + \beta v)^{4}\frac{d}{dx}(\alpha u + \beta v)+(5x^{3}+2)\left(\frac{1}{5}(\alpha u + \beta v)^{5}\right)\\ D\left(\alpha u \right) + D\left(\beta v \right) &= \left(\frac{1}{3}x^{3}\right)(\alpha u)^{4}\frac{d(\alpha u)}{dx}+(5x^{3}+2)\left(\frac{1}{5}(\alpha u)^{5}\right) +  \left(\frac{1}{3}x^{3}\right)(\beta v)^{4}\frac{d(\beta v)}{dx}+(5x^{3}+2)\left(\frac{1}{5}(\beta v)^{5}\right) \end{align} $$

Clearly $$D\left(\alpha u + \beta v \right) \neq D\left(\alpha u \right) + D\left(\beta v \right)$$ so the ODE is non-linear

 Nonlinearity can be determined by inspection. This would have sufficed for this problem, although your explanation is very complete. --Egm6321.f09.TA 03:18, 28 September 2009 (UTC) To prove that the ODE is exact, let's first look at the 1st condition of exactness:

 * $$ \underbrace{\left(\frac{1}{3}x^{3}\right)(y^{4})}_{N(x,y)}y'+\underbrace{(5x^{3}+2)\left(\frac{1}{5}y^{5}\right)}_{M(x,y)}=0$$

hence $$N(x,y)y' + M(x,y) = 0\!$$ so 1st condition is met.

Looking at the 2nd condition where $$M_y = N_x\!$$. However, from above we can clearly see that:

 * $$M_y \neq N_x$$

So we will try to find an integrating factor to find if our ODE can be exactly integrable

\begin{align} \left(\frac{1}{3}x^{3}\right)(y^{4})y'+(5x^{3}+2)\left(\frac{1}{5}y^{5}\right) &=0 \qquad \text{let us multiply througout  by} \qquad \frac{3}{x^3y^4}\\ y' +\frac{3}{x^3y^4}(5x^{3}+2)\left(\frac{1}{5}y^{5}\right) &=0\qquad \text{re-writing the equation obtain}\\ \underbrace{1}_{N}\cdot y' + \underbrace{\left(3 + \frac{6}{5x^3}\right)}_{a_0}y &=0 \end{align} $$ throughout

Now we will make use of integrating factor knowledge:

\begin{align} h(x,y) &= \exp\int^{x}a_0(s)ds\qquad \text{replacing the value of} \quad a_0\\ h(x,y) &= \exp\int^{x}\left(3 + \frac{6}{5s^3}\right)ds\qquad \text{evaluating the integral obtain}\\ h(x,y) &= \exp\left(3x - \frac{3}{5x^2}\right) \end{align} $$

Now we will try to evaluate the 2nd condition of exactness which is:

\begin{align} (hM)_{y}&=(hN)_x \qquad \text{the condition says:} \\ \bar{M}_y &= \bar{N}_x \qquad \text{evaluating the derivatives we obtain}\\ \dfrac{6\exp(3x)}{\left(\exp^{\frac{1}{x^2}}\right)^{\frac{3}{5}} x^3} + \dfrac{3\exp(3x)}{\left(\exp^{\frac{1}{x^2}}\right)^{\frac{3}{5}} } & = \dfrac{6\exp(3x)}{\left(\exp^{\frac{1}{x^2}}\right)^{\frac{3}{5}} x^3} + \dfrac{3\exp(3x)}{\left(\exp^{\frac{1}{x^2}}\right)^{\frac{3}{5}}} \end{align} $$

Hence the ODE given is then, exact N1-ODE-VC
 * }

= Problem 7: Deriving First Condition for N2-ODE Exactness Criterion =

Given
A general N2-ODE is given in the form:

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

F(x,y,y',y) = 0 = f(x,y,p)y + g(x,y,p) $$ $$ where
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 1)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

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

g(x,y,p):=\phi_x + \phi_y(x,y,p)p $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 3)
 * }
 * }

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

p:=y'. $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 4)
 * }
 * }

Find
Derive the first exactness condition given by Eq 5.

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

f_{xx} + 2p f_{xy} + p^2 f_{yy} = g_{xp} + p g_{yp} - g_{y} $$ $$
 * $$\displaystyle
 *
$$\displaystyle (Eq. 5)

 * }
 * }

Solution
We know that $$\displaystyle \phi_{xy}=\phi_{yx}$$

where,

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

\phi_{x} = g - p ( g_p - f_x) + p^2 f_y $$ $$
 * $$\displaystyle
 *
$$\displaystyle (Eq. 6)

 * }
 * }

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

\phi_{y} = g_p - f_y p - f_x $$ $$
 * $$\displaystyle
 *
$$\displaystyle (Eq. 7)

 * }
 * }

Taking the partial derivative of (6) with respect to $$\displaystyle y$$ and the partial derivative of (7) with respect to $$\displaystyle x$$ gives

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

\phi_{xy} = g_y - p_y ( g_p - f_x) - p (g_{py} - f_{xy}) + 2 p_y f_y + p^2 f_{yy} $$ $$
 * $$\displaystyle
 *
$$\displaystyle (Eq. 8)

 * }
 * }

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

\phi_{yx} = g_{px} - f_{yx} p - f_y p_x - f_{xx} $$ $$
 * $$\displaystyle
 *
$$\displaystyle (Eq. 9)

 * }
 * }

Since (8) and (9) are equal

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

g_y - \cancelto{0}{p_y} g_p + \cancelto{0}{p_y} f_x - p g_{py} + p f_{xy} + 2 \cancelto{0}{p_y} f_y + p^2 f_{yy} = g_{px} - f_{yx} p - f_y \cancelto{0}{p_x} - f_{xx} $$ $$
 * $$\displaystyle
 *
$$\displaystyle (Eq. 10)
 * }
 * }

Re-arranging terms yields

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

$$\displaystyle f_{xx} + 2 p f_{xy} + p^2 f_{yy}  = g_{xp} + p g_{yp} - g_y $$ $$ = Problem 9: Exactness of N2-ODE=
 * style="width:45%; padding:10px; border:2px solid #8888aa" |
 * style="width:45%; padding:10px; border:2px solid #8888aa" |
 *
$$\displaystyle (Eq. 11)
 * }
 * }

Given
The following N2-ODE,

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

\sqrt{x}y''+2xy'+3y=0 $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 1) )
 * }
 * }

Find
Is this ODE exact?

Solution
The 2 exactness conditions are given by,

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

1: f_{xx} + 2pf_{xy} + p^2f_{yy} = g_{xp} + pg_{yp} - g_{y} $$ $$
 * $$\displaystyle
 *
$$\displaystyle (Eq. 2)

 * }
 * }

and

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

2: f_{xp} + pf_{yp} + 2f_{y} = g_{pp} $$ $$
 * $$\displaystyle
 *
$$\displaystyle (Eq. 3)

 * }
 * }

By substituting $$\displaystyle p=y'$$, into Eq. 1, the result is:

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

(\sqrt{x})y''+(2xp+3y)=0 $$ $$
 * $$\displaystyle
 *
$$\displaystyle (Eq. 4)

 * }
 * }

From Eq. 4 and knowing the form of a N2-ODE (See Problem 7 Eq. 1),

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

f(x,y,p)=\sqrt{x} $$ $$
 * $$\displaystyle
 *
$$\displaystyle (Eq. 5)
 * }
 * }

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

g(x,y,p)=2xp+3y $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 6)
 * }
 * }

Taking the partial derivatives of (5) and (6) respectively yields

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

\begin{array}{*{20}l} {f_x = \frac{x^{-0.5}}{2}} & {f_{xx}  = -\frac{x^{-1.5}}{4}} & {g_x  = 2p} & {g_{xp}  = 2}  \\ {} & {f_{xy} = 0} & {g_y  = 3} & {g_{yp}  = 0}  \\ {} & {f_{xp} = 0 } & {g_p  = 2x} & {g_{pp}  = 0 }  \\ {f_y = 0} & {f_{yy}  = 0} & {} & {}  \\ {} & {f_{yp} = 0} & {} & {}  \\ \end{array} $$
 * $$\displaystyle
 * $$\displaystyle

 * }
 * }

Substituting the elements of Eq. 2 results in

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

(-\frac{x^{-1.5}}{4}) + 2 p (0) + p^2 (0)  = (2) + p (0) - (3) $$
 * $$\displaystyle
 * $$\displaystyle
 * }
 * }

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

 * style="width:30%; padding:10px; border:2px solid #8888aa" |
 * $$ \displaystyle
 * $$ \displaystyle

(-\frac{x^{-1.5}}{4}) = -1 $$ $$
 *
$$\displaystyle (Eq. 7)
 * }
 * }

Obviously, these equations are not equal, therefore given N2-ODE is NOT EXACT.

title: User:Egm6321.f10.team4.Yoon/HW22009


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(== Summary == )

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Laboratory on Mathematics and Mathematics Education/Fermi Questions

Task 1: Characters in your life
Answer the question for yourself: "How many characters have you read in your life?" After 10 minutes, discuss the problem and find a solution as group (think-pair-share, active plenum).

 * Your results: Model of reality

Task 2: Mozambican Fermi questions
Create a list of Fermi questions which are related to Mozambican culture and life.

 * Your results: Fermi questions

Task 3: Think about Fermi questions!
Answer the following questions for yourself:

 * 1) What are the characteristics of Fermi questions?
 * 2) Why should Fermi questions be part of mathematics in school? Find some arguments!

Collect the answers in the group (think-pair-share, active plenum).

 * Your results: arguments pro Fermi questions and contra Fermi questions

Task 4: Cars in Mozambique
Reflect on the mathematical modeling process by answering the Fermi question "How many cars are in Mozambique?". What has to be done in each step of the process?

Task 5: Introducing Fermi questions
When students are not used to Fermi questions, they have problems to solve them. It's the teachers responsibility to help them. How can students be supported when they answer Fermi questions for the first time? Collect your results!

 * Your results

Links and Materials

 * Introduction to Fermi questions
 * Introduction to cognitive apprenticeship
 * Wikipedia article about Enrico Fermi
 * Wikipedia article about Fermi questions
 * Louisiana Lessons Web Activity


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Laboratory on Mathematics and Mathematics Education/Logo

Task 1: Exploring Logo

 * 1) Install the English version of MSW Logo on your computer. (Please use the English version, because the Portuguese version uses other commmands.) If you are not allowed to install software on your computer, I will give you MSW Logo on a flash.
 * 2) Try to create a regular triangle, pentagon, and hexagon by interactively directing the turtle.
 * 3) Teach the turtle a new word "regpolygon" with the number of edges and the length of the sides of the regular polygon as parameters. For example, the command "regpolygon 5 100" should paint a regular pentagon with side length 100.
 * 4) Write a procedure "rectangle :width :height" which paints a rectangle with the given width and height.
 * 5) Paint a circle.

Task 2: Be creative!

 * 1) Teach the turtle a new word "star" which paints a star.
 * 2) Teach the turtle to paint a house.
 * 3) Teach the turtle to paint the skyline of a city. Therefore, use your house command.
 * 4) Teach the turtle to paint flowers.
 * 5) Be creative! Just paint!

Please copy and paste your code snippets into our results page!

Task 3: Why Logo?

 * 1) Find some arguments why Logo should be used in schools. Think about learning objectives and learning philosophies.
 * 2) Collect your arguments in the group (active plenum).

Task 4: Add the images
Add the resulting Logo images to our results page.
 * 1) Save the image as gif file on your hard disk or flash (choose "Bitmap/Save" and then select "gif").
 * 2) Upload the image to wikiversity (use the "Toolbox/Upload file" option on the left side).
 * 3) Put the image link on our results page.

Task 5: Traditional ethnic patterns of Mozambique

 * Write procedures which paint different beautiful traditional ethnic patterns of Mozambique.
 * Copy and paste your code into our results page.
 * Upload the image and make a link on the results page.

Task 6: Introduction to Logo in Schools
How can Logo be introduced in schools, especially to students at very young ages in primary school? Collect your ideas!

 * Your results

Task 7: Logo and EIS

 * 1) Create an idea how Logo can be introduced with regard to Bruner's EIS principle in school (e.g. on grade level... 1!).
 * 2) Present your ideas.

For those who are fast: Think about how the EIS principle can be used in the field of learning to calculate with fractions.

Task 8: Be recursive with numbers!

 * 1) Write a procedure which calculates the factorial of a given natural number.
 * 2) Write a procedure which calculates the n-th Fibonnacci number.
 * 3) Write a procedure which calculates the greatest common divisor of two natural numbers.

Task 9: Be recursive with graphics!
Paint one of the following images:

Task 10: Recursion and EIS
How can the EIS principle be realized within the context of recursion? Collect ideas!

Links and Materials

 * The Logo Philosophy
 * MSW Logo
 * Image of the first turtle robot
 * Logo Philosophy and Implementation - Text about Logo and its implementation in different countries (e.g. Argentinia, Brazil, and Thailand)
 * Videos about Logo: Video 1 Video 2
 * Seymour Papert about teaching thinking
 * Introduction to Bruner's EIS principle


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Laboratory on Mathematics and Mathematics Education/DGS

Task 1: Exploring Dynamic Geometry Systems!

 * 1) Download GeoGebra. If you are not allowed to install software on your system, I will give you GeoGebra on a flash.
 * 2) Try to construct the perpendicular bisector of two points on at least three different ways.
 * 3) Try to create the construction which "proofs" Thales' Theorem.
 * 4) Show that the sum of a triangle's angles is always 180°.
 * 5) Show that in a circle the angle at the center is double of the angle at the circumference.
 * 6) Given a triangle, show that its perpendicular bisectors always intersect in one single point, the circumcenter. Do this also for its median lines  (centroid) and for the heights of its sides (orthocenter). Afterwards, show that these three points always are on one line (Euler line)
 * 7) Construct a regular hexagon.
 * 8) "Proof" some other geometric theorems. If you can't remember one, select on from the following list.

Task 2: Dynamic aspects of functions

 * 1) Invent a bathtube story for a given a "bathtube graph".
 * 2) Create filling graphs for a given jar (and vice versa).
 * 3) How could the EIS principle be realized in this context? Collect ideas!

Task 3: Making functions dynamic!

 * 1) Show how the unit circle is connected to the sinus curve in GeoGebra.
 * 2) Do the same for the graphs of cosine and tangent.
 * 3) Show the effects of functional parameters on graphs of different functions (for example, quadratic functions in different representations, (co)sine, exponential functions, ...). Create dynamic worksheets using sliders!
 * 4) Show that the loci of points which have the same distance from a given point and line are on a parabola. Are all parabolas graphics of a function?

Task 4: Using spreadsheet calculation

 * 1) Create a boxplot from data given in the spreadsheet view. What happens if you change the data? Observe!

Task 5: The Rabbit Problem
You have fence material with the length of 18 m, and you want to build a rectangular enclosure for your rabbit. How do you have to choose the side lengths of the rectangle that the area for your rabbit is maximal?

 * 1) Use a spreadsheet calculation program to try out some different solutions.
 * 2) Solve the problem formally (on a sheet of paper)!
 * 3) Create a dynamic sheet in GeoGebra showing the graph and the enclosure in order to visualize the solution. Be creative!

Links

 * Introduction to DGS
 * Introduction to Action Learning (Principle of operation)
 * Filling Graphs
 * Combination of dynamic geometry, algebra and calculus in the software system GeoGebra (by Hohenwarter & Fuchs)
 * GeoGebra help
 * Geogebra: Dynamic mathematics made easy


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Laboratory on Mathematics and Mathematics Education/Methods

Reflect on our lab methods!

Active Plenum

 * Introduction to the active plenum
 * Erich-Hammer-Video
 * neuron metaphor

Task 1: Active plenum in schools
Watch the Erich-Hammer-Video and discuss: Could the active plenum be also used in Mozambican schools? Find pro and contra arguments.

Wikiversity
We will use wikiversity in the course in order to
 * 1) structure the sessions
 * 2) collect our results and
 * 3) share our ideas with the world

Task 1: Create an account in Wikiversity
Create your own account in wikiversity. You can decide if you want to use your real name or an imaginative name.

Task 2: Create your user page in Wikiversity

 * 1) Write something about you in your user page. Inform people who you are, what your interests are, what you (don't) like to do, ...
 * 2) Add your user page to the list of participants at the top of this page. Just copy and paste the syntax already there and modify it.
 * 3) Read the user pages of the other participants and comment on their user page's discussion board!


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Laboratory on Mathematics and Mathematics Education/Fermi Questions/Scaffolds

Fermi questions: How teachers can help
When students are not used to Fermi questions, they have problems to solve them. It's the teachers responsibility to help them. How can students be supported when they answer Fermi questions for the first time? Collect your results!

Group 1

 * Os estudantes podem ficam asustados quando apresentados as perguntas de fermi, como tambem podem achar que é mera brincadeira e nao levarem a serio a questao apresentada.
 * Perante as perguntas de fermi pode-se notar nos estudantes um sembrante de desespero de espanto ou de brincadeira como que diz que as perguntas nao precisam de respostas.

or The fermi questions create in students cembrant of admiretion, create in mind of students questions for play or for relax.

 * hi group 1. coment of group 7
 * Português
 * o grupo 7 agradece a contribuicao do grupo 1 nesta questao, porem acreditamos que nao apresenta solucoes concretas, apenas o cenario que pode suceder durante a aula, o leva concluir que estao totalmente contra o uso das questoes de Fermi no processo ensino aprendizagem
 * no entanto, sugerimos que o grupo 1 entcontre a solucao do despero dos alunos tomando em conta improtancia destes na construcao do conhecimento ns sala de aula
 * melhores cumprimentos

OuvirLer foneticamente
 * Inglês
 * Group 7 thanks to a contribution of the group this question, but believe it does not present concrete solutions, just the scenario that may happen during class, leads to conclude who are totally against the use of Fermi questions in the learning process
 * However, suggest that group 1 entcontre the solution to the despair of students taking these into account improtancia in the construction of classroom knowledge ns

 * best regard

Group 2

 * A Primeira reaccao dos Alunos, provavelmente, Seria de considerar e Espanto uma Pergunta Absurda , Pelo facto de O PARECER impossivel encontrar UMA Resposta exacta . UMa Vez nao descubrindo uma Resposta , desmotivados FICAM , Pelo Que o professor desen Ajuda - los um trocadilho um pesrpectiva da Questão

 * A seguir, eles apresentam muita exitacao em responder esse tipo de perguntas porque julgam vagas as suas possiveis respostas.

 * We are not agree because: the questions are not absurd or impossible for the student, but he is faced with a difficult question to answer, and structuring and raises a number of assumptions in an attempt to find the answer, ultimately concluding that it is not conclusive issues.

Group 3
When the student is facing Fermi type has the following printing:

 * Are complex,
 * Are non-terminating
 * Do not have a logical reasoning
 * Are difficult to design
 * Are difficult validation

To solve these problems caused by Fermi questions we can:

 * Raise student, showing the relevance of the questions,
 * Demonstrate with the essence of these truthful cases issues, giving an example and solving the problems.
 * Demonstrate that this type of question allows the student to have different ways of solving problems and also allows you to make a good interaction between theory and practice.

Comments about analysis of Group 4:

We agree with reality terrace by Group 4, about Fermi questions, but we have to add that permit the development of student thinking, opens the horizon analysis of the phenomena and the pursuit of various solutions.

Group 4

 * Are difficult questions to answer and structuring

 * Do not have a conclusive answer, are open.

 * Stimulate various research

Comment We agree your position, but we think that the playing caracter of this type stimulates to trian mind. thanks for your comments

Group 5

 * exigem muito esforço...

Group 7

 * Português
 * As questoes de Fermi devem estar ligado o dia a dia do aluno, de modo a ter uma imagem da solucao
 * Definir claramente o objectivo das questoes
 * Orientar o aluno com questoes mais simples que podem conduzir ao resultado problema em causa

 * Inglish
 * The Fermi questions must be connected on the day of the student to take a picture of the solution
 * Clearly define the purpose of the questions
 * To guide students with simple questions that can lead to the outcome problem in question

Ok. Talves questionar da seguinte maneira para melhor entender o vosso raciocinio: -Quando é que o aluno pode ter uma imagem duma soluçao com uma questao que deseja saber o numero de cabelo que ele leva na cabeça, ou seja, que tipo de soluçao ele pode trazer na mente? -Sera que o aluno vai difinir o objectivo da questao de que modo? Por exemplo um professor questiona quantos fios de cabelo tens na cabeça, que objetivo pode surgir. -Que questoes mais cimples, as mesmas de Fermi ou outras seria bom que detalhassem. VALEU!


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Laboratory on Mathematics and Mathematics Education/Logo/Images

Logo results
Make a collection of interesting Logo code! Be careful: You have to embed your code in a "preformatted environment" surrounded by the <pre> and </pre> tags this way:

<pre> to square :side repeat 4 [ fd :side rt 90 ] end </pre>

Square Rose (example)
to square :side repeat 4 [ fd :side rt 90 ] end

to squarerose :side repeat 10 [ square 100 rt 36 ] end

regpolygon
to regpolygon :side :n repeat :n [ fd :side rt 360/:n ] end

grupo 7

rectangle
to rectangle :width :heigth repeat 2 [ fd :width rt 90 fd :heigth rt 90 ] end

grupo 7

BIG STAR
to star :side repeat 8 [ fd :side rt 135 ] end

house
to house :altura :base rectangle :altura :base fd :altura lt 90 fd :base/5 rt 120 triangle :base*7/5 rt 60 fd :base/5 rt 90 fd :altura lt 90 fd :base*2/5 lt 90 rectangle :altura*3/4 :base/4 end

grupo 7


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Laboratory on Mathematics and Mathematics Education/Pictures

Task 1: Walking with open eyes
Let's make a collection of photos showing mathematics in the world!

 * 1) Search for mathematics in the world! While walking, have your eyes open and detect mathematics everywhere! Make a photograph.
 * 2) Upload your photographs to wikiversity.

Links and Materials

 * Image pool created by German students