difference equations?

- anonymous

difference equations?

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- anonymous

amistre...hi

- anonymous

Step 1: What you want to do is drop the constant, the same as simply making
the constant zero to get the homogeneous difference equation. Then you get
a general solution to that homogenous difference equation.
Step 2: Then go back and come up with a trial solution to the non-homogenous
difference equation, the style of the trial solution being based on the kind
of terms that are creating the non-homogeneous part (this will probably be
the hardest part, so read that section of material carefully). Then put in
particular values that you know solve the difference equation, specific
values you got from working with the difference equation such as what xo
is, what x1 is, allowing you to determine what the constants in your trial
solution need to be. This gives you your particular solution.
Step 3: As the last step you combine your general solution and your
particular solution to get your complete solution for this specific
problems, and of course verify that when applied it creates the correct
values for x0, x1, .... xn.
Overall you will have started with a "difference equation" expressing how to
get x n+1 if you know x n, and you are ending with a formula that will
calculate any x n by just knowing n. The formula allows you to calculate
any x n term without working out all of the terms ahead of it.

- anonymous

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- amistre64

isnt this from yesterday :)

- anonymous

yes need clear understanding for solutions starting with 2b

- anonymous

I have 0,0 1, -1 2, -1.5 , 3 -1.75 4 -1.875, 5 -1.9375 6, -1.96875 for a

- amistre64

this is on 2a right?

- anonymous

yes

- anonymous

you need to track these as community service hours ; )

- anonymous

add to resume

- amistre64

lol.... the problem or this session ;)

- anonymous

all of your time in OS

- anonymous

lol

- anonymous

just realized that was a joke, lol

- amistre64

homo diff is dropping the constant... :)

- amistre64

what does dropping the constant do for us?

- anonymous

gives us xsubn?

- amistre64

the good computers are all locked away today; this one hates openstudy. small font, no formating..... just awful

- amistre64

might go to McDs later and use the wifi.... if it aint busy/closed

- anonymous

yeah my laptop will not let me do anything in os anymore so have to sit at desktop

- anonymous

are you in school

- amistre64

so if we strip the constant; we are just left with:
Xn+1 = (1/2)Xn which always equals itself, so I dont quite know why wed do that....

- amistre64

yeah, in the computer lab downstairs....

- anonymous

are you a student

- amistre64

yup

- anonymous

me to and unemployed since move

- anonymous

taught 8th grade Algebra back in SC

- amistre64

i cant get work since I hurt my back.

- amistre64

ima "liability"

- anonymous

oh no sorry to hear that...ever thought about starting online tutoring business..I can help you out

- amistre64

i thought about trying to do something like that; id be nice to have some sort of income other than PELL grant...

- anonymous

I'm studying off loans for now ; ( that is why I have to take this extra module that has nothing to do with my program of study...technically

- anonymous

send me your email address and I can send you a presentation I'm actually presenting on Tues. and the link to my website...I just started in March and have
3 students now but hope to advertise some more this summer...brishundra@yahoo.com

- amistre64

So the complete solution is jsut finding an equation that will sum up all the nth terms....

- anonymous

I have xn=(0.5)raised to n *C

- anonymous

keep looking back at table in a and messing me up bc different ?

- amistre64

couldnt we just solve for "Xn" and plug it in? maybe?...

- amistre64

y = .5(0) - 1 + .5(1) - 1 +.5(2)-1 + .5(3) -1 seems to be what they are getting at.

- amistre64

we can rearrange our equation to see it better:
y - .5(0) + .5(1) + .5(n) - 1 - 1 - 1 - 1

- amistre64

we need ".5(n)" for any given interation of n right?

- anonymous

yes

- amistre64

and we need -(1n) for every iteration of n right?

- amistre64

whatis:
.5(n) - (n) = ?

- anonymous

the constant

- amistre64

at =1 we get -1.5 right?

- amistre64

at n=2 we get:
.5(2) - (2) = -2.5 right?

- amistre64

-1.5 maybe, gonna have to see this on a calculator.... terrible font

- anonymous

ok

- amistre64

whats yout table in a look like?

- anonymous

0,0 1, -1, 2, -1.5 3, -1.75...

- anonymous

4 -1.875 5 -1.9375 6 -1.96875

- amistre64

i get from teh original stuff, not my stuff:
0; -1; -1.5; -1.75; -1.875...

- anonymous

I had that when I first started this , lol

- anonymous

but looked at xo=0 and thought I was wrong

- amistre64

your "key returns" arent formating; they look like this:

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- amistre64

the value of X0 = 0 then it iterates from there

- anonymous

ok so 6 -1.984375

- amistre64

we get add ons of 1/2; 3/4; 7/8; 15/16; 31/32; 63/64; 127/128; 511/512

- amistre64

(2^n)-1
------
2^n

- amistre64

[(2^n)-1]
-1 - -------- = y
2^n

- amistre64

thats our formula/equation for this bit lol

- amistre64

n=[1,inf]

- amistre64

it fits right?

- amistre64

the bottom of the fractions ar plugging away at 2^n; and the tops are following one step behind at (2^n)-1

- amistre64

X{n+1} = (1/2) X{n}
2X{x+1} = X{n} I got no idea how they supposed to do this and come up with that lol

- amistre64

X{n+1} 1
----- = ---
X{n} 2 <-- 2^n ? if we borrow that "n"

- amistre64

any ideas?

- anonymous

lost...trying something

- amistre64

I got the right equation; just dont know how to get it from their stuff....

- anonymous

is that for c

- amistre64

thats for ..... D i think

- amistre64

you got a link to the "look over this material" part of it?

- amistre64

The style of the trial solution being based on the kind of terms that are creating the non-homogeneous part (this will probably be the hardest part, so read that section of material carefully).

- amistre64

got 10 minutes til the college closes....

- amistre64

and StLeo is a catholic college so that ones closed for today as well; my internets are getting scarce :)

- amistre64

email me the "material" section: tony031172@gmail.com

- anonymous

ok THANKS a bunch!

- anonymous

http://www.aw-bc.com/ggts/

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