Dapthar

Glad to help.

Here you go, info from their graduate program web page. http://www.graduate.ucf.edu/currentGradCatalog/content/Degrees/ACAD_PROG_71.cfm

Here's the inverse Laplace transform formula. [math]f(t) = \frac{1}{2\pi j}\int_{\sigma - j\infty}^{\sigma + j\infty}F(s)e^{st}ds[/math], where [math]s = \sigma + j\omega[/math], and [math]F(s)[/math] is the Laplace transform of [math]f(t)[/math]. To evaluate this integral as it stands, one needs to use techniques from complex analysis, specifically, contour integration. It's worth noting that most people never have any use for this formula, since one can basically use lookup tables to compute Laplace transforms, and use the same tables, combined with partial fractions to compute inverse Laplace transforms.

dave's right. In addition, the for definition for: [math]\lim_{x\to a}f(x) = -\infty[/math] is [math]\forall L < 0[/math] [math]\exists \delta > 0[/math] such that [math]|x - a| < \delta \implies f(x) < L[/math]

It's one of the big secrets in Mathematics; formal proofs almost never deal with infinity. Note that the proof mentions "for all M < 0"' date=' i.e., I can choose [b']M[/b] to be -1, -10, or -1 000 000, thus, 'in the limit, we go to negative infinity'. Infinite limits 'basically' follow the same rules as 'regular' limits, that for any error e, we can provide a d such that if |x-a| < d then |f(x) - L| < e, so 'at a, f(x) equals L', except here, our L is negative infinity. We just had to show that 'we can get arbitrarily close to negative infinity'. Thanks.

1:21:49.0909... (Time is in hours:minutes:seconds) Of course, this assumes continuous movement of the minute and hour hands.

Well, if you have any more questions, feel free to ask.

LaTeX is the language used to display mathematical symbols in everything from bulletin boards to research papers. However, I guess it sounds a bit odd when mentioned out of context. You just need to translate 'f is continuous at L' into an epsilon-delta condtion. Whenever anyone says that a function h(x) is continuous at a point b, it is the exact same thing as saying that as x->b, lim h(x) = h(b), i.e., the limit is what you expect it to be.

Yup. Nope. [LeVar Burton Voice] But you don't have to take my word for it! [/LeVar Burton Voice] Source: http://www.newton.dep.anl.gov/askasci/env99/env002.htm

Thanks.

Do you have a specific example in mind? I ask because solving such a problem might be more helpful to you, as opposed to just working out a random epsilon-delta proof.

[ joke ] 5614's probably a CSci Major, so he started at 0, and counted "0, 1, 2, 3, 4, 5", and arrived at 5 threads. [/ joke ]

[math joke] I'm sure Mathematicians will get to that right after they standardize notation. [/math joke]

This makes the scenario even odder, since why would they be willing to pay for an indeterminate amount of tuiton (undergraduate and graduate school), but not a fixed amount (one semester's worth of classes)? Also, on a related note, almost no one directly pays for graduate school (in the sciences) in the US due to the exorbitant cost. At least in Mathematics, a good 80% of students are TAs, 15% are RAs (both of which generally come with a tuition waver, based upon the hours you work) and the remaining 5% are paying via fellowships/private funds. This is because graduate schools rarely accept people that they are not willing to fund. Source: http://www.ams.org/employment/asst.pdf However, there are exceptions, just as in undergraduate admissions, and alumni/family connections combined with the fact one is not seeking financial support can, sadly, be a rather large positive factor when an application is considered. (Case in point, how do you think Bush got into Yale?) In the US, the general path is high school then college. I believe the closest analog to the college you refer to is called junior college here. In the US, the term "high school", generally refers to the institution one attends between the ages of 13 and 17. However, most students have a birthday during the school year, and as a result, most high school students are between 14 and 18.

[tangent] Unless your parents are barely getting by (in the financial sense), they would seem to think that their money is better spent on ventures besides that of furthering your academic knowledge. The inevitable question that arises is, what are they spending it on in lieu of advancing your education? I suggest you ask them. [/tangent]

The person I was referring to was a junior in high school when they took the PSAT, and they were still a junior when they received their results.

If you plan on going to graduate school, you can take solace in the fact that the general GRE has not one, but two required essays. As do I. However, in my experience, I have found them to be rather useless. Thus, I highly recommend going to http://www.collegeboard.org, and getting your information directly from the source. It's not guaranteed, for I know of at least one person who took the PSAT and met the criterion you described above, but received no such scholarship. I believe AP tests are looked upon more favorably than the SAT IIs, but if one doesn't take any AP classes, the SAT IIs are another means by which to improve one's record. Yup. Also, be aware of the difference between early decision and early action. Well, one's most recent score is usually the highest, and I doubt that if one got a lower score on a subsequent testing that it would be considered, unless the admissions officials are comparing the records of two students with very similar credentials. True. I believe one can only suppress all the scores from one's record, or none.

I didn't really notice a question before this point, so could you please clarify what you would like explained in more detail? Without using tools developed in Calculus, it is rather difficult to get anything more than a vague idea of what a rational function looks like without graphing it on a calculator or computer. A brief description of a Calculus based approach is located in the following thread: rational functions. A site with decent introductory material, and a few worked out examples is located here :http://www.scienceforums.net/forums/showthread.php?t=6296.

Crucify? You're kidding, right? 5 months in a minimum security prison, affectionately referred to as "Camp Cupcake", is about as nominal a prison sentence that one can receive. Source: http:// http://216.239.39.104/search?q=cache:tRui1RxrI3sJ:money.canoe.ca/News/MoversShakers/MarthaStewart/2004/03/11/378693.html+camp+cupcake&hl=en&start=2

If you don't know, do you truly believe that an outside observer could define who you are? Because I know I'm not anyone else. I believe that there would have to be a generally agreed upon definition of awareness first. Is it simply recognizing one's image in a mirror? Or something more complex? Sorry to burst your bubble, but philosophical questions rarely have satisfying answers. If you focused your questions on more specific issues, such as "What causes one to recognize a mirror image as a representation of themselves?", then they would most likely fall into a scientific field, such as cognitive neuroscience, and more definite answers could be provided.

I don't think [math]\emptyset[/math] or [math]\varnothing[/math] are supposed to be a [math]\Phi[/math], or a [math]\phi[/math], simply a separate symbol.