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Post by Helena Ravenclaw Tue Sep 25, 2012 1:15 am

Press ctrl + v, posting the last thing that you copied
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Post by Helena Ravenclaw Tue Sep 25, 2012 1:15 am

So if you love me, let me go.
And run away before I know.
My heart is just too dark to care.
I can't destroy what isn't there.
Deliver me into my fate -
If I'm alone I cannot hate
I don't deserve to have you...
My smile was taken long ago
If I can change I hope I never know
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Post by Admin Jigglypuffy Thu Oct 04, 2012 6:45 pm

KAty Perry

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Post by Helena Ravenclaw Mon Oct 15, 2012 8:22 pm

Manganese(III) acetate dihydrate
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Post by Madam Triwizard Tue Oct 16, 2012 3:40 am

Tonks was nervous, and it wasn't her normal nerves about a mission going wrong either. She was going to be walking down the aisle in just a few hours, hopefully to meet the man of her dreams and marry him, but after so much trouble to convince him to accept being with her she wasn't sure he would turn up. 'He asked you." She thought to herself as she pulled on the cream dress which looked like it as from the fifties, with a knee length skirt and a black sash, trying to still her nerves.
'It was his choice, and he loves you.' Tonks muttered as Mrs Weasley helped to style her hair.
"Tonks, Dear, are you getting nervous that he won't show?" Molly asked after hearing Tonks mutter for the fifth time something confirming to herself that Remus would be there.
Tonks had to fight jumping at the question so her hair didn't get messed up. "Just a little bit Molly. I mean he was so reluctant to date me in the first place so now I feel like he'll call it off at any minute or just fail to turn up." Tonks replied quickly, her nervesmaking her words indistinguishable almost.
Molly finished her hair before speaking again. "You have no need to worry Tonks, we all know he was ony reluctant to date ou because he thought you deserved someone better than him. We have him convinced that he is what you want and deserve now so he isn't going anywhere. Plus he's seen me when I'm mad and doesn't want to face that any time soon. Come on, we need to head to the church now."
Molly and Tonks stood slowly, knowing they'd managed to be five minutes late apparating as had been planned between them. "Let's go and find the groom." Tonks smiled.
***
Remus stood at the front of the make-shift church, trying his hardest not to pace the aisle. "Moony, sit down, or at least relax. She'll be here soon." Sirius tried to calm the groom, but it was getting harder.
Mr Weasley was waiting outside, keeping an eye out for the slightly late bride and bridesmaid. There were ony 5 of them there for the wedding, as well as Dumbledore who had agreed to perform the ceremony and Tonk's parents who had turned their front room into the church for the day.
A crack signalled the arrival of Molly and Tonks, already stood like they were walking down the aisle once Ted Tonks had pulled his daughters arm through his own. "Ready to get married?" Ted asked his daughter.
"Yes, ready to give me away?" Tonks replied.
"I guess I must be." Ted smiled as they reached Remus and he handed Nymphadora's hand to Remus in the traditional way.
The service was simple and short, as they recited their vows from Dumbledore after each other. The amusement came when they needed to say their 'I do's'.
"Remus Lupin, Do you take Nymphadora Tonks..." Dumbledore started, only to be interrupted by everyone. "DON'T CALL HER NYMPHADORA!"
"... to be your lawful wedded wife?"
Laughing Remus only just managed to say "I Do!" as he watched his wife's hair calm to an amused light pink at everyone's response to the use of her name.
"Nymphadora Tonks..." Dumbledore began again.
"WE SAID DON'T CALL HER THAT!" The rest of the group shouted again, laughing at Dumbledore's insistance of using her first name.
"...do you take Remus Lupin as your lawful wedded husband?"
Tonks grinned and replied, "I do, but stop calling me Nymphadora, Dumbledore. It seems they don't like it." She laughed, her eyes twinkling as everyone else laughed with her.
"Then I pronounce you man and wife. You may kiss the bride." Dumbledore finished the ceremony, joining in the laughter that delayed the kiss for a moment or two more.
When everyone had calmed down Remus pulled Tonks into a close hug, and kissed her softly on the lips to confirm their marriage.
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Copy and Paste Empty Degree Maths homework answers ;) it didn't like the equations though ;)

Post by Helena Ravenclaw Fri Oct 19, 2012 2:37 am

Question 1: Score 50/50

Consider the PDE

(a)


Classify the PDE as being hyperbolic, parabolic or elliptic:


Correct
Your Answer:

parabolic
Comment:

. Thus, the PDE is parabolic.
(b)


Given that the two new variables can be used to reduce the given PDE to canonical form, find the value of and enter your answer in the Equation Editor window below. Note that if for instance your answer is , you simply enter .


Correct
Your Answer: 5
Comment:

The single characteristic equation is given by

Thus, we may take

(c)


Define , where and are defined in the previous item. Express in terms of derivatives of with respect to and , and enter the coefficients of and in the box below. If, e.g., , then enter 4, 5, 7 in the box below (brackets or semi-colons are not allowed).


Correct
Your Answer: 25, 0, 0
(d)


Express in terms of derivatives of with respect to and , and enter the coefficients of , and in the box below.. If, e.g., , then enter 4, 5, 7 in the box below.


Correct
Your Answer: 5, 5, 0
(e)


Express in terms of derivatives of with respect to and , and enter the coefficients of , and in the box below. If, e.g., , then enter 4, 5, 7 in the box below.


Correct
Your Answer: 1, 2, 1
(f)


By reducing the PDE to the canonical form, find its general solution


Correct
Your Answer:
Comment:

Write . Then

On substituting these expressions into the original PDE, we obtain the canonical form

or

which can be integrated to obtain

and hence

(g)


Find the unique solution that satisfies the the conditions



Correct
Your Answer:
Comment:

From the boundary conditions we obtain

Thus, , and the solution is

Comments:

Question 2: Score 50/50

Consider the PDE

(a)


Classify the PDE as being hyperbolic, parabolic or elliptic:


Correct
Your Answer:

hyperbolic
Comment:

. Thus, the PDE is hyperbolic except for .
(b)


Given that the two new variables can be used to reduce the given PDE to canonical form, find the value of and enter your answer in the Equation Editor window below:


Correct
Your Answer: 5
Comment:

The characteristic equations are

Thus, the characteristic curves are and . Thus, we may take

(c)


Define , where and are defined in the previous item. Express in terms of derivatives of with respect to and , and enter the coefficients of and in the box below. If, e.g., , then enter xˆ(11), x*yˆ5, yˆ(15) in the box below.


Correct
Your Answer: 25*x^(Cool*y^(2), 0, 0
(d)


Express in terms of derivatives of with respect to and , and enter the coefficients of , and in the box below. If, e.g., , then enter xˆ(11), x*yˆ5, yˆ(15) in the box below.


Correct
Your Answer: 5*x^(9)*y, 5*x^(4)*y, 0
(e)


Express in terms of derivatives of with respect to and , and enter the coefficients of , and in the box below. If, e.g., , then enter xˆ(11), x*yˆ5, yˆ(15) in the box below.


Correct
Your Answer: x^(10), 2*x^(5), 1
(f)


Reduce the given PDE to canonical form and hence find its general solution


Correct
Your Answer:
Comment:

Define through

Then,

On substituting these expressions into the original PDE, we obtain . It then follows that the general solution is given by

where and are arbitrary functions of their arguments.
(g)


Find the unique solution that satisfies the conditions



Correct
Your Answer:
Comment:

On substituting the general solution into the boundary conditions, we obtain

Writing in the second equation, we obtain

where is an arbitrary constant. The first boundary condition then gives

Therefore, the solution is given by
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