What did you do last night?

[t i c a l]

I went bar hopping in another city with my girl, my two roommates, and a few friends of theirs. My girl and I finished half a 5th of Captain on the way thereand one of the bars had unlimited Coronas for a dollar. Now, I consider myself a beer connoisseur and I usually only drink dark beer, but dollar Coronas? Iwas all over that *%## and had two in my hands at all times. Then at another bar some chick was having a bachelorette party there for some reason and wascarrying around a male blow up doll which I thought was pretty weird, but I was so drunk by that point I was just dancing my #$% off in the middle of the emptydance floor to some bad techno that the DJ absolutely sucked at mixing. Ended up getting home around 4 and feasted upon everything in my apartment.

My girl and I...

My roommates...

Dollar Coronas FTW!

Gone...

I had a good time overall, post pictures of your evening if you have any...

- Tical.

 

[ninjallamafromhell]

http://en.wikipedia.org/wiki/Laplace_transform#External_links
http://
[h2][edit] History[/h2]
The Laplace transform is named in honor of mathematician and astronomer Pierre-Simon Laplace, who used the transform in his work on probability theory.

From 1744, Leonhard Euler investigated integrals of the form:

- as solutions of differential equations but did not pursue the matter very far.[sup][2][/sup]Joseph Louis Lagrange was an admirer of Euler and, in his work onintegrating probability density functions,investigated expressions of the form:

- which some modern historians have interpreted within modern Laplace transform theory.[sup][3][/sup][sup][4][/sup]

These types of integrals seem first to have attracted Laplace's attention in 1782 where he was following in the spirit of Euler in using the integralsthemselves as solutions of equations.[sup][5][/sup] However, in 1785, Laplace took the critical step forward when, rather than just look for a solution in the form ofan integral, he started to apply the transforms in the sense that was later to become popular. He used an integral of the form:

- akin to a Mellin transform, to transform the whole of a difference equation, in order to look for solutions ofthe transformed equation. He then went on to apply the Laplace transform in the same way and started to derive some of its properties, beginning to appreciateits potential power.[sup][6][/sup]

Laplace also recognised that Joseph Fourier's method of Fourier series for solving the diffusion equation could only apply to a limited region of space as thesolutions were periodic. In 1809, Laplace applied his transform to find solutions that diffused indefinitely in space.[sup][7][/sup]

http://
[h2][edit] Formal definition[/h2]
The Laplace transform of a functionf(t), defined for all real numbers t ≥ 0, is the functionF(s), defined by:

The lower limit of 0[sup]−[/sup] is short notation to mean

and assures the inclusion of the entire Dirac delta functionδ(t) at 0 if there is such an impulse in f(t) at 0.

The parameter s is in general complex:

This integral transform has a number of properties that make ituseful for analyzing linear dynamic systems. The mostsignificant advantage is that differentiation and integration become multiplication and division, respectively, by s. (This is similar tothe way that logarithms change an operation of multiplication of numbers to addition oftheir logarithms.) This changes integral equations and differential equations to polynomial equations, which are much easier to solve.Once solved, use of the inverse Laplace transform reverts back to the time domain.

http://
[h3][edit] Bilateral Laplace transform[/h3]
Main article: Two-sided Laplace transform

When one says "the Laplace transform" without qualification, the unilateral or one-sided transform is normally intended. The Laplace transform canbe alternatively defined as the bilateral Laplace transform or two-sided Laplace transform by extending the limits of integration to be the entire real axis. If that is done the commonunilateral transform simply becomes a special case of the bilateral transform where the definition of the function being transformed is multiplied by theHeaviside step function.

The bilateral Laplace transform is defined as follows:

http://
[h3][edit] Inverse Laplace transform[/h3]
For more details on this topic, see Inverse Laplace transform.

The inverse Laplace transform is given by thefollowing complex integral, which is known by various names (theBromwich integral, the Fourier-Mellin integral, and Mellin's inverse formula):

where γ is a real number so that the contour path of integration is in the region of convergence of F(s)normally requiring γ > Re(s[sub]p[/sub]) for every singularity s[sub]p[/sub] of F(s) and i[sup]2[/sup] = −1. If all singularities are inthe left half-plane, that is Re(s[sub]p[/sub]) < 0 for every s[sub]p[/sub], then γ can be set to zero and theabove inverse integral formula becomes identical to the inverse Fouriertransform.

An alternative formula for the inverse Laplace transform is given by Post's inversion formula.

http://
[h2][edit] Region of convergence[/h2]
The Laplace transform F(s) typically exists for all complex numbers such that Re{s} > a, where a is a realconstant which depends on the growth behavior of f(t), whereas the two-sided transform is defined in a range a < Re{s}< b. The subset of values of s for which the Laplace transform exists is called the region of convergence (ROC) or the domain of convergence. In the two-sided case, it issometimes called the strip of convergence.

The integral defining the Laplace transform of a function may fail to exist for various reasons. For example, when the function has infinite discontinuitiesin the interval of integration, or when it increases so rapidly that e [sup]− pt[/sup] cannot damp itsufficiently for convergence on the interval to take place. There are no specific conditions that one can check a function against to know in all cases if itsLaplace transform can be taken,[sup][citationneeded][/sup] other than to say the defining integral converges. It is however possible to give theorems on cases where it may or may not betaken.

http://
[h2][edit] Properties and theorems[/h2]
Given the functions f(t) and g(t), and their respective Laplace transforms F(s) andG(s):

the following table is a list of properties of unilateral Laplace transform:
[table] Properties of the unilateral Laplace transform [tr][th=""]
[/th] [th=""]Time domain[/th] [th=""]Frequency domain[/th] [th=""]Comment[/th] [/tr][tr][th=""]Linearity[/th] [td]

[/td] [td]

[/td] [td]Can be proved using basic rules of integration.[/td] [/tr][tr][th=""]Frequency differentiation[/th] [td]

[/td] [td]

[/td] [td]F' is the first derivative of F.[/td] [/tr][tr][th=""]Frequency differentiation[/th] [td]

[/td] [td]

[/td] [td]More general form, (n)th derivative of F(s).[/td] [/tr][tr][th=""]Differentiation[/th] [td]

[/td] [td]

[/td] [td]Obtained by integration by parts[/td] [/tr][tr][th=""]Second Differentiation[/th] [td]

[/td] [td]

[/td] [td]Apply the Differentiation property to f'(t).[/td] [/tr][tr][th=""]General Differentiation[/th] [td]

[/td] [td]

[/td] [td]Follow the process briefed for the Second Differentiation.[/td] [/tr][tr][th=""]Frequency integration[/th] [td]

[/td] [td]

[/td] [td]
[/td] [/tr][tr][th=""]Integration[/th] [td]

[/td] [td]

[/td] [td]u(t) is the Heaviside step function. Note (u * f)(t) is the convolution of u(t) and f(t); it does not denote multiplication.[/td] [/tr][tr][th=""]Scaling[/th] [td]

[/td] [td]

[/td] [td]
[/td] [/tr][tr][th=""]Frequency shifting[/th] [td]

[/td] [td]

[/td] [td]
[/td] [/tr][tr][th=""]Time shifting[/th] [td]

[/td] [td]

[/td] [td]u(t) is the Heaviside step function[/td] [/tr][tr][th=""]Convolution[/th] [td]

[/td] [td]

[/td] [td]
[/td] [/tr][tr][th=""]Periodic Function[/th] [td]

[/td] [td]

[/td] [td]f(t) is a periodic function of period T so that

. This is the result of the time shifting property and the geometric series.[/td] [/tr][/table]

 

[jpthe3]

nosy tical.

 

[i dont pass]

Damn I aint see this dude in a good minute

 

[forty 1]

Went over to the usual spot, (nice little bar) then to a friends house. got home at about 2:30am Highlight? I met a chick at the bar, cute redhead. : )
Tonight I'll be going to a party. If i can get enough work done so as not to feel guilty that is.

 

[mjsaver]

lol

i smoked out & watched the lakers win.

 

[ev209]

work for me...
made caramel fraps with extra caramel all night long to all the asian kids that watched fast and the furious in the movies right next to my store
line stayed busy all night and ended up getting of at 130am when i was supposed to be out by midnight
not to mention all i heard was the roaring engines and lame burnouts everyone tried to do

well.... back to work at 6 to do it all over again

 

[jumpmanjunkie]

- pregame at 730
- laser tag at 830
- apartment party at 1030
- party in my friends dorm

 

[akajae]

Lamb of God show...

madness lol.

 

[ajchick23]

drinking the same thing you were.
Coronas all night with my buddies.

 

[milestailsprowe]

Played Lord of teh rings online MMO all night long DAMN I it was a boring night

 

[23kidd]

Wow looks like yu had fun bro...how's the hangover?? Haha ..I just chilled and watched some dvd's with the wifey the whole night at her crib.

 

[trapmuzik617]

went out to a sigma party... got super drunk

after the party

messed up my green beans

layed on the floor for like 2 hours

 

[ducktailsxaintxi]

went to a BBQ had pizza, drank crown/beer/vodka ate oysters (I was with a bunch of red vietnamese)

came home had the girl come over, watched a movie, ordered takeout relaxed. but tonight it goes down!

 

[ballinamillion1]

this a pyp in disguise now???

^^^ host those aint nobody going to copy and paste those lol

 

[travman24]

-Played basketball at 24hr Fitness, beasted.

-30mins on the treadmill.

-Few situps bout 50

-Played a game of 2k9 (LAKERS vs celtics typical) lost a close game.

-Laid in the bed an dwelled on how much my life sucks righ now.
(Broke/alone)

-Sleep

 

[t i c a l]

Originally Posted by 23kidd

Wow looks like yu had fun bro...how's the hangover??

I felt like hell this morning but I'm good to go now. I took 4 extra strength tylenol before I went to sleep so that took care of the headache.

- Tical.

 

[queencitysneakerqueen]

Nothing

 

[miketysonthekiller]

Haven't seen Tical in a long minute. lol. As far as what I did last night, nothing just saw I love you man with my brother.

 

[youngflykidchris]

Originally Posted by travman24

-Played basketball at 24hr Fitness, beasted.

-30mins on the treadmill.

-Few situps bout 50

-Played a game of 2k9 (LAKERS vs celtics typical) lost a close game.

-Laid in the bed an dwelled on how much my life sucks righ now.
(Broke/alone)

-Sleep

fyl.


























jk

 

[jpioneer]

Your girl is fine

I just drove around the city with my friends...

 

[sohi 23]

Uh,

and watched Taken.
Then I went home at like 12 and fell asleep for like 12 hours

 

[antonlavey]

I was just talking about you yesterday Tical, where in the hell have you been


Last night i went to see Mstrkrfts at Webster Hall in NYC.....it was madness.

Tonite....one of my best friends bday/going away party

. Top shelf openbar+bros, should be shambles.

Expect a drunken post at the end of the night.

 

[10508 cardo jr ln]

I wish I took the cam wit me last night..
Some lame tried to style on me in the club cause my swag (for lack of better term) in the club was on a hundred thousand zillion
Puttin his chain up in the air like he copped from IF & Co. when he got it out the middle of the mall
Pullin out his lil money
The worst part was, his pendant was a big ol' "L" with glass stones in it.. I'm like G, 1 of my stones is 10x your whole setup, why you keeplookin at me for?
First time I ever thought to myself somewhere in the real world.. "

this is a NT thread/ take the L and keep movin gif" waitin to happen

but yea, no pics so story sucks.. had to be there i guess

 

[kiddin like jason]

Adventureland.