gmalivuk wrote:Does this include the forces caused by rotation?

As far as I know, no it doesn't. This is just the effect of the shape of the GRS80 ellipsoid.

- Wed Oct 21, 2009 3:08 pm UTC
- Forum: Science
- Topic: Gravity question
- Replies:
**56** - Views:
**4468**

gmalivuk wrote:Does this include the forces caused by rotation?

As far as I know, no it doesn't. This is just the effect of the shape of the GRS80 ellipsoid.

- Wed Oct 21, 2009 2:30 pm UTC
- Forum: Science
- Topic: Gravity question
- Replies:
**56** - Views:
**4468**

I would argue that when you do a point particle sum, you would find that for an oblate configuration with z axis symmetry and uniform density, you would find that there is a greater force and potential at the z axis poles and less at the equator since more mass is closer to you at the poles. What w...

- Wed Oct 21, 2009 3:53 am UTC
- Forum: Mathematics
- Topic: PDE Confusion: What to do with boundary condition?
- Replies:
**9** - Views:
**799**

Thanks for the help, Blacksails, Nitrodon, and EduardoLeon! I knew I had to use the x + y = 1 somewhere.

*Puts away this example under "Keep for reference"*

*Puts away this example under "Keep for reference"*

- Tue Oct 20, 2009 2:23 am UTC
- Forum: Mathematics
- Topic: PDE Confusion: What to do with boundary condition?
- Replies:
**9** - Views:
**799**

BlackSails wrote:Do you know euler's formula?

I don't really see any complex exponentials in there...

- Tue Oct 20, 2009 2:11 am UTC
- Forum: Mathematics
- Topic: PDE Confusion: What to do with boundary condition?
- Replies:
**9** - Views:
**799**

Unfortunately, that's the part where I got stuck. I had applied the initial condition to get g(x) , but all I can see to use the other boundary condition is: On x+y=1 , u(x,y)=u(x,1-x)=h(1-x)+g(x)=h(1-x)+\sin{x}=1 \Rightarrow h(1-x)=1-\sin{x} w...

- Tue Oct 20, 2009 1:47 am UTC
- Forum: Science
- Topic: Gravity question
- Replies:
**56** - Views:
**4468**

Except, I thought I remembered reading somewhere that the uneven density as you go toward the core means gravity is actually fairly constant all the way down through the crust. I wouldn't be surprised by that. Like I said, the linear decay of gravity is merely a first-order approximation, assuming ...

- Tue Oct 20, 2009 1:34 am UTC
- Forum: Mathematics
- Topic: PDE Confusion: What to do with boundary condition?
- Replies:
**9** - Views:
**799**

I'm working through an exercise sheet (not for credit, if anybody was wondering) for my partial differential equations course, and I've run into an issue that I can't seem to sort out. The simple PDE is as follows: u_{xy}=0 With the following initial and boundary conditions: u(x,0)=\sin{x} a...

- Mon Oct 19, 2009 9:33 pm UTC
- Forum: Science
- Topic: Gravity question
- Replies:
**56** - Views:
**4468**

Just to summarize: Local gravity is affected by altitude, surrounding structures (such as mountain ranges and valleys), and with the local density of the earth below you. In geophysical gravity surveys, the altitude and environment factors are corrected for, because all the surveyors are (usually) i...

- Thu Oct 15, 2009 9:42 pm UTC
- Forum: Mathematics
- Topic: So, does this work as a prrof that e^pi*i=-1?
- Replies:
**39** - Views:
**2999**

I can It's somewhat intuitive to say that if two functions shared the same 0th to infinityth derivative, they are at least somewhat similar. And in sin(x)'s case...they happen to be identical. If two functions share all the same derivatives, arent they then the same function? Counterexample: f(x) =...

- Fri Jul 24, 2009 5:25 am UTC
- Forum: Food
- Topic: Who else loves Pizza Hut Stuffed Crust?
- Replies:
**28** - Views:
**2906**

So... you made a calzone?

- Sun Jun 28, 2009 5:04 pm UTC
- Forum: Mathematics
- Topic: Natural math versus foreign language aptitude
- Replies:
**13** - Views:
**3430**

I'd say the same thing applies to me as well. I took French through elementary/junior high/high school (being in Canada), and currently my girlfriend is teaching me Spanish. I wouldn't say I can "speak" French (or Spanish; not yet anyway), but I knew enough vocab and verb/conjugation rules...

- Sat May 23, 2009 5:12 am UTC
- Forum: Science
- Topic: Variable acceleration
- Replies:
**28** - Views:
**2001**

Are the point masses the mass of a feather?

- Thu Apr 30, 2009 11:18 pm UTC
- Forum: Mathematics
- Topic: Residue Calculus Problem
- Replies:
**16** - Views:
**1771**

Thanks for the help guys. I just realized that this same issue tripped me up on the problem I mentioned in the OP. D'oh! I guess now I'll remember this for good.

- Wed Apr 29, 2009 6:40 pm UTC
- Forum: Mathematics
- Topic: Ver' confused
- Replies:
**2** - Views:
**511**

You could always find the roots of a power series.

- Tue Apr 28, 2009 1:13 am UTC
- Forum: Mathematics
- Topic: Residue Calculus Problem
- Replies:
**16** - Views:
**1771**

I just took the final exam today, and it went well except for one snag I caught when trying to find the following integral: \int_{-\infty}^{\infty} \frac{x\sin{kx}}{x^2+1} \,dx. I calculated the residues correctly, but when it came to using Cauchy's integral formula, I couldn't find a contour that c...

- Sat Apr 25, 2009 4:00 am UTC
- Forum: Mathematics
- Topic: Residue Calculus Problem
- Replies:
**16** - Views:
**1771**

The first thing to realize is that the ellipses don't represent the same terms in both places. I'm assuming that for the rest of the problem, it didn't really matter what the ellipses were, and just having the z2 term is enough? I realize that. I interpreted the first series to be the series for si...

- Fri Apr 24, 2009 10:50 pm UTC
- Forum: Mathematics
- Topic: Residue Calculus Problem
- Replies:
**16** - Views:
**1771**

I'm working on the final review assignment for this same course and I'm trying to figure out what my prof did in the following steps: Find the residue at z=0 of f(z)=\frac{1}{z^2\sinh{z}} Solution: Since \sinh{z}=z+\frac{z^3}{3!}+\frac{z^5}{5!}+\cdots it follows that \frac{1}{z^2\sinh{z}}=\f...

- Tue Apr 21, 2009 1:27 pm UTC
- Forum: Site/Forum issues
- Topic: Add comic image title attribute as image caption too
- Replies:
**10** - Views:
**1896**

I'm guessing the OP thinks that none (or at least a small minority) of the readers actually know there is an alt-text to each comic, so by "making it more interesting" he means "give everyone the benefit of reading this title text" and by "feel like an asshole" he means...

- Mon Apr 13, 2009 2:57 pm UTC
- Forum: Mathematics
- Topic: Inverse Laplace transforms and partial fractions
- Replies:
**5** - Views:
**801**

Maybe it would help to take a look at this example: http://en.wikipedia.org/wiki/Partial_fraction#An_irreducible_quadratic_factor_in_the_denominator Thanks, that was the ticket. The inverse Laplace Transform of \frac{1}{s^2+a^2} has an elementary solution that you can easily look up in a table. The...

- Mon Apr 13, 2009 2:54 pm UTC
- Forum: Site/Forum issues
- Topic: Math markup
- Replies:
**77** - Views:
**23500**

I fixed what the problem was. I had to go into the Greasemonkey options and add some inclusions/exclusions to the webpages. I just copied the same inclusions/exclusions as the forums.xkcd.tld/* entries, but used the echochamber domain instead of the forums.xkcd domain. All the scaling works properly...

- Mon Apr 13, 2009 2:43 pm UTC
- Forum: Mathematics
- Topic: Inverse Laplace transforms and partial fractions
- Replies:
**5** - Views:
**801**

The inverse Laplace Transform of [imath]\frac{1}{s^2+a^2}[/imath] has an elementary solution that you can easily look up in a table. There's no need to decompose it further.

- Sat Apr 11, 2009 8:55 pm UTC
- Forum: Mathematics
- Topic: Z-Transforms and their Properties
- Replies:
**4** - Views:
**578**

Thank you kindly, folks. I probably should have thought of starting from the definition to begin with, but getting insight from others never hurts. :) What tends to be the best way to find the inverse Z-Transform anyway? I understand that you can use the direct method of finding residues, but is it ...

- Sat Apr 11, 2009 5:16 am UTC
- Forum: Site/Forum issues
- Topic: Math markup
- Replies:
**77** - Views:
**23500**

So this Echochamber thing has borked the math fonts so that I can't scale them to be bigger, and it makes them somewhat difficult to read. Did/does anybody else have this problem, and can it be fixed? Have you tried going to options and then picking a scaling factor like 150%? I just did that and i...

- Sat Apr 11, 2009 4:31 am UTC
- Forum: Site/Forum issues
- Topic: Math markup
- Replies:
**77** - Views:
**23500**

So this Echochamber thing has borked the math fonts so that I can't scale them to be bigger, and it makes them somewhat difficult to read. Did/does anybody else have this problem, and can it be fixed?

- Fri Apr 10, 2009 10:49 pm UTC
- Forum: Mathematics
- Topic: Z-Transforms and their Properties
- Replies:
**4** - Views:
**578**

Yet another homework assignment issue, but this time the issue is with the teaching of the material. We were introduced to Z-Transforms the other day and we were given a homework assignment dealing with them, but unfortunately we were not actually taught *how* to use these things. I've taken a DE co...

- Fri Apr 10, 2009 2:16 am UTC
- Forum: Mathematics
- Topic: On the periodic caffeine content in a ceramic enclosure
- Replies:
**1** - Views:
**498**

It should just be

[math]y(x)=y_0{r}^x[/math]

Where [imath]y_0[/imath] is the initial amount of caffeine in the bag, and [imath]r[/imath] is the percentage of caffeine drawn out every cup. Since [imath]r[/imath] is less than 1, this is simply going to be an exponential decay curve, and would in fact be "curved".

[math]y(x)=y_0{r}^x[/math]

Where [imath]y_0[/imath] is the initial amount of caffeine in the bag, and [imath]r[/imath] is the percentage of caffeine drawn out every cup. Since [imath]r[/imath] is less than 1, this is simply going to be an exponential decay curve, and would in fact be "curved".

- Sat Apr 04, 2009 6:25 pm UTC
- Forum: Mathematics
- Topic: Help with a tricky Fourier series, perhaps?
- Replies:
**8** - Views:
**847**

You'd need to manually define the value for the jump-discontinuity. Okay, so it's not like a removable discontinuity where you can set the value equal to the limit of the function as it approaches that discontinuity, since the limits aren't equal. Makes perfect sense. And this whole thing with the ...

- Sat Apr 04, 2009 1:07 am UTC
- Forum: Mathematics
- Topic: Help with a tricky Fourier series, perhaps?
- Replies:
**8** - Views:
**847**

Would I take the value of f(\pi) to be equal to \pi/2 instead of \pi ? Yes this. Recall that in general the Fourier series agrees with the original function where it is defined, in this case (-pi, pi), and is periodic over the real line with the discontinuities filled in by the average of t...

- Sat Apr 04, 2009 12:51 am UTC
- Forum: Mathematics
- Topic: Help with a tricky Fourier series, perhaps?
- Replies:
**8** - Views:
**847**

Hint: you're evaluating it at a jump-discontinuity. There's a useful property of Fourier series at such points. Oh, that the value of the function at the jump is the average of the jump? I thought of that, but I'm not sure how I would apply that in the a_k and b_k integrals. Would the integral from...

- Sat Apr 04, 2009 12:40 am UTC
- Forum: Mathematics
- Topic: Help with a tricky Fourier series, perhaps?
- Replies:
**8** - Views:
**847**

Hey guys, I'm trying to tackle this homework problem, and I seem to keep getting tripped up despite my best efforts to check and double check my work. The question is this: a.) Find the Fourier series expansion of the function f(x) = \left\{ \begin{array}{ll} 0 & \mbox{if $-\pi<x\leq 0$}...

- Wed Apr 01, 2009 6:12 pm UTC
- Forum: Mathematics
- Topic: Cardinalities of "Non-Standard" Sets
- Replies:
**10** - Views:
**825**

Wow, thanks guys. I'm impressed by the amount of response this is getting. It's probably going to take me a day or two to wade through all of this. I'll definitely get back to you guys about what you've brought up.

Thanks again!

Thanks again!

- Wed Apr 01, 2009 3:46 pm UTC
- Forum: Mathematics
- Topic: Substitution by Intergration Help
- Replies:
**12** - Views:
**1130**

I don't think substitution would be the ideal choice here. Have you tried integration by parts?

- Wed Apr 01, 2009 5:32 am UTC
- Forum: Mathematics
- Topic: Cardinalities of "Non-Standard" Sets
- Replies:
**10** - Views:
**825**

The set of all series has cardinality c (the same as the reals). When you say "all series", are you talking about finite series as well? I'm specifically asking about infinite series. The only familiarity I have with determining cardinalities of sets is by trying to form a bijection with ...

- Wed Apr 01, 2009 4:29 am UTC
- Forum: Mathematics
- Topic: Cardinalities of "Non-Standard" Sets
- Replies:
**10** - Views:
**825**

Okay, I'm not quite sure how to explain exactly what I mean, so I'll tell you what I'm trying to figure out and maybe some of you can shed some light on it for me. Are there more divergent infinite series than convergent series? If you have an infinite sum of random (uniformly distributed) numbers g...

- Tue Mar 31, 2009 2:41 pm UTC
- Forum: Mathematics
- Topic: Capacitor Diff. EQ
- Replies:
**4** - Views:
**763**

Well, you probably shouldn't use [imath]C[/imath] as your constant.

- Wed Mar 25, 2009 5:00 am UTC
- Forum: Mathematics
- Topic: a problems been bugging me
- Replies:
**26** - Views:
**1895**

All you need to do is find the minimums of the three functions in the square roots, and evaluate the whole expression at each of the minimums to find the absolute minimum of the function. The middle function is a bit tricky, but it can be done if you know how to find the minimum of a multivariate f...

- Tue Mar 24, 2009 11:39 pm UTC
- Forum: Mathematics
- Topic: a problems been bugging me
- Replies:
**26** - Views:
**1895**

All you need to do is find the minimums of the three functions in the square roots, and evaluate the whole expression at each of the minimums to find the absolute minimum of the function. The middle function is a bit tricky, but it can be done if you know how to find the minimum of a multivariate f...

- Tue Mar 24, 2009 11:20 pm UTC
- Forum: Mathematics
- Topic: Integrating e^(- sqrt(x))
- Replies:
**3** - Views:
**2110**

Try letting [imath]u=-\sqrt{x}[/imath].

- Tue Mar 24, 2009 10:34 pm UTC
- Forum: Mathematics
- Topic: a problems been bugging me
- Replies:
**26** - Views:
**1895**

I can also tell you that the second question has an answer of 13 (and no I haven't tried anything, everytime I do I get nowhere) Is it *exactly* 13? Because I'm getting a value of 13.76 (rounded to the nearest hundredth). EDIT: Never mind, I got 13 as an answer as well. All you need to do is find t...

- Thu Mar 19, 2009 4:39 pm UTC
- Forum: Mathematics
- Topic: Unrolling Toilet Paper - Just a fun brain teaser
- Replies:
**9** - Views:
**2829**

Which is exactly what I derived I can never decide how I feel when that happens. A bit clever, because I correctly solved an interesting problem, and a bit annoyed because I could've just googled it. Meh, it wasn't difficult to get that expression, so it wasn't any more annoying than doing a 2 minu...