Idiot Cube

Scumbag Cube But, seriously...I think all the big ones have been covered already.

Needs more integrals.

I DON'T HAVE A PROBLEM!!! There's an unusual right around the corner, I can FEEL it!

Something along the lines of "Hey, guys! I just found this neat Goggles thing! Let's vandalize the main page!"

We should change his title to "Admeuniskator!"

Welcome to our humble batcave, weary Goggle travelers! I see you are hard at work defiling our home page, but I hope you will take a moment out of your busy schedule to join in our discussion of ponies, furries, and higher mathematics. Today I will be discussing Laplace transforms. The Laplace transform is a widely used integral transform with many applications in physics and engineering. Denoted , it is a linear operator of a function f(t) with a real argument t (t ≥ 0) that transforms it to a function F(s) with a complex argument s. This transformation is essentially bijective for the majority of practical uses; the respective pairs of f(t) and F(s) are matched in tables. The Laplace transform has the useful property that many relationships and operations over the originals f(t) correspond to simpler relationships and operations over the images F(s). It is named after Pierre-Simon Laplace, who introduced the transform in his work on probability theory. The Laplace transform is related to the Fourier transform, but whereas the Fourier transform expresses a function or signal as a series of modes of vibration (frequencies), the Laplace transform resolves a function into its moments. Like the Fourier transform, the Laplace transform is used for solving differential and integral equations. In physics and engineering it is used for analysis of linear time-invariant systems such as electrical circuits, harmonic oscillators, optical devices, and mechanical systems. In such analyses, the Laplace transform is often interpreted as a transformation from the time-domain, in which inputs and outputs are functions of time, to the frequency-domain, where the same inputs and outputs are functions of complex angular frequency, in radians per unit time. Given a simple mathematical or functional description of an input or output to a system, the Laplace transform provides an alternative functional description that often simplifies the process of analyzing the behavior of the system, or in synthesizing a new system based on a set of specifications. The Laplace transform is named after mathematician and astronomer Pierre-Simon Laplace, who used a similar transform (now called z transform) in his work on probability theory. The current widespread use of the transform came about soon after World War II although it had been used in the 19th century by Abel, Lerch, Heaviside and Bromwich. The older history of similar transforms is as follows. From 1744, Leonhard Euler investigated integrals of the form as solutions of differential equations but did not pursue the matter very far. Joseph Louis Lagrange was an admirer of Euler and, in his work on integrating probability density functions, investigated expressions of the form which some modern historians have interpreted within modern Laplace transform theory. 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 integrals themselves as solutions of equations. However, in 1785, Laplace took the critical step forward when, rather than just looking for a solution in the form of an 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 of the 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 appreciate its potential power. 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 the solutions were periodic. In 1809, Laplace applied his transform to find solutions that diffused indefinitely in space. The Laplace transform of a function f(t), defined for all real numbers t ≥ 0, is the function F(s), defined by: The parameter s is a complex number: with real numbers σ and ω. The meaning of the integral depends on types of functions of interest. A necessary condition for existence of the integral is that ƒ must be locally integrable on [0,∞). For locally integrable functions that decay at infinity or are of exponential type, the integral can be understood as a (proper) Lebesgue integral. However, for many applications it is necessary to regard it as a conditionally convergent improper integral at ∞. Still more generally, the integral can be understood in a weak sense, and this is dealt with below. One can define the Laplace transform of a finite Borel measure μ by the Lebesgue integral An important special case is where μ is a probability measure or, even more specifically, the Dirac delta function. In operational calculus, the Laplace transform of a measure is often treated as though the measure came from a distribution function ƒ. In that case, to avoid potential confusion, one often writes [stolen word-for-word from the Wikipedia page.] At this time I will open the thread to discussion. As always, your input on the subject is greatly appreciated. If you do not wish to discuss Laplace transforms, I suggest you leave SPUFpowered immediately, and never return.

And my calculus lecture.

No matter. The important thing is that they leave SPUFpowered.

And that's 5 too many.

*puffs cigarette* How was it for you, Buddha?

Lololololol...Uh...apparently, all of the threads link to the same page of graffiti. This considerably limits my options for vandalism.

How Strange.

Hopefully it'll be active in time for Gigolo and NinjaWombat's next slapfight.

Judging by all the unnecessarily huge chambers I've played, I think the height limit is plenty big.

http://steamcommunity.com/sharedfiles/filedetails/?id=68553095It's my first chamber! Yay!Basically, the idea I had with this chamber is that you have to make your way across a massive pool of goo, with only your faithful companion cube to keep you company.It's got buttons, a little light-bridging, moving platforms, and a faith plate to carry you right to the exit!Oh, and you're a pirate. The cube is your first mate. Have fun!

You must spread some rep around before yeah, yeah, yeah...

This thread is now about our college workloads.I don't have finals till the end of May. I'll have plenty of time to study. Right now, I have more important things to think about.

I hate it when people pander to such low forms of humor.

Ever heard of prerecorded messages?Also, Aperture now has access to alternate realities. All arguments about the timeline are now and forevermore invalid.

Hey! This thread is bone-dry when there's two new videos out? UNACCEPTABLE!!! :rage:This one showcases the editor: And this one showcases the Workshop interface. There's also some spicy new in-game Cave Johnson lines. So, um...spoilers.

I'm down.

Charizard.

Late to the party, as always!