Search found 2028 matches

by Mathmagic
Wed Oct 21, 2009 3:08 pm UTC
Forum: Science
Topic: Gravity question
Replies: 56
Views: 4472

Re: Gravity question

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.
by Mathmagic
Wed Oct 21, 2009 2:30 pm UTC
Forum: Science
Topic: Gravity question
Replies: 56
Views: 4472

Re: Gravity question

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

Re: PDE Confusion: What to do with boundary condition?

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

Re: PDE Confusion: What to do with boundary condition?

BlackSails wrote:Do you know euler's formula?

I don't really see any complex exponentials in there...
by Mathmagic
Tue Oct 20, 2009 2:11 am UTC
Forum: Mathematics
Topic: PDE Confusion: What to do with boundary condition?
Replies: 9
Views: 799

Re: PDE Confusion: What to do with boundary condition?

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...
by Mathmagic
Tue Oct 20, 2009 1:47 am UTC
Forum: Science
Topic: Gravity question
Replies: 56
Views: 4472

Re: Gravity question

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

PDE Confusion: What to do with boundary condition?

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...
by Mathmagic
Mon Oct 19, 2009 9:33 pm UTC
Forum: Science
Topic: Gravity question
Replies: 56
Views: 4472

Re: Gravity question

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...
by Mathmagic
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

Re: So, does this work as a prrof that e^pi*i=-1?

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) =...
by Mathmagic
Fri Jul 24, 2009 5:25 am UTC
Forum: Food
Topic: Who else loves Pizza Hut Stuffed Crust?
Replies: 28
Views: 2906

Re: Who else loves Pizza Hut Stuffed Crust?

So... you made a calzone?
by Mathmagic
Sun Jun 28, 2009 5:04 pm UTC
Forum: Mathematics
Topic: Natural math versus foreign language aptitude
Replies: 13
Views: 3430

Re: Natural math versus foreign language aptitude

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...
by Mathmagic
Sat May 23, 2009 5:12 am UTC
Forum: Science
Topic: Variable acceleration
Replies: 28
Views: 2001

Re: Variable acceleration

Are the point masses the mass of a feather?
by Mathmagic
Thu Apr 30, 2009 11:18 pm UTC
Forum: Mathematics
Topic: Residue Calculus Problem
Replies: 16
Views: 1773

Re: Residue Calculus Problem

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.
by Mathmagic
Wed Apr 29, 2009 6:40 pm UTC
Forum: Mathematics
Topic: Ver' confused
Replies: 2
Views: 512

Re: Ver' confused

You could always find the roots of a power series. ;)
by Mathmagic
Tue Apr 28, 2009 1:13 am UTC
Forum: Mathematics
Topic: Residue Calculus Problem
Replies: 16
Views: 1773

Re: Residue Calculus Problem

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...
by Mathmagic
Sat Apr 25, 2009 4:00 am UTC
Forum: Mathematics
Topic: Residue Calculus Problem
Replies: 16
Views: 1773

Re: Residue Calculus Problem

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...
by Mathmagic
Fri Apr 24, 2009 10:50 pm UTC
Forum: Mathematics
Topic: Residue Calculus Problem
Replies: 16
Views: 1773

Re: Residue Calculus Problem

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...
by Mathmagic
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: 1898

Re: Add comic image title attribute as image caption too

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...
by Mathmagic
Mon Apr 13, 2009 2:57 pm UTC
Forum: Mathematics
Topic: Inverse Laplace transforms and partial fractions
Replies: 5
Views: 805

Re: Inverse Laplace transforms and partial fractions

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...
by Mathmagic
Mon Apr 13, 2009 2:54 pm UTC
Forum: Site/Forum issues
Topic: Math markup
Replies: 77
Views: 23504

Re: Math markup

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...
by Mathmagic
Mon Apr 13, 2009 2:43 pm UTC
Forum: Mathematics
Topic: Inverse Laplace transforms and partial fractions
Replies: 5
Views: 805

Re: Inverse Laplace transforms and partial fractions

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

Re: Z-Transforms and their Properties

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 ...
by Mathmagic
Sat Apr 11, 2009 5:16 am UTC
Forum: Site/Forum issues
Topic: Math markup
Replies: 77
Views: 23504

Re: Math markup

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...
by Mathmagic
Sat Apr 11, 2009 4:31 am UTC
Forum: Site/Forum issues
Topic: Math markup
Replies: 77
Views: 23504

Re: Math markup

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

Z-Transforms and their Properties

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

Re: On the periodic caffeine content in a ceramic enclosure

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".
by Mathmagic
Sat Apr 04, 2009 6:25 pm UTC
Forum: Mathematics
Topic: Help with a tricky Fourier series, perhaps?
Replies: 8
Views: 848

Re: Help with a tricky Fourier series, perhaps?

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 ...
by Mathmagic
Sat Apr 04, 2009 1:07 am UTC
Forum: Mathematics
Topic: Help with a tricky Fourier series, perhaps?
Replies: 8
Views: 848

Re: Help with a tricky Fourier series, perhaps?

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...
by Mathmagic
Sat Apr 04, 2009 12:51 am UTC
Forum: Mathematics
Topic: Help with a tricky Fourier series, perhaps?
Replies: 8
Views: 848

Re: Help with a tricky Fourier series, perhaps?

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...
by Mathmagic
Sat Apr 04, 2009 12:40 am UTC
Forum: Mathematics
Topic: Help with a tricky Fourier series, perhaps?
Replies: 8
Views: 848

Help with a tricky Fourier series, perhaps?

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 $-\pi<x\leq 0$}...
by Mathmagic
Wed Apr 01, 2009 6:12 pm UTC
Forum: Mathematics
Topic: Cardinalities of "Non-Standard" Sets
Replies: 10
Views: 828

Re: Cardinalities of "Non-Standard" Sets

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

Re: Substitution by Intergration Help

I don't think substitution would be the ideal choice here. Have you tried integration by parts?
by Mathmagic
Wed Apr 01, 2009 5:32 am UTC
Forum: Mathematics
Topic: Cardinalities of "Non-Standard" Sets
Replies: 10
Views: 828

Re: Cardinalities of "Non-Standard" Sets

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 ...
by Mathmagic
Wed Apr 01, 2009 4:29 am UTC
Forum: Mathematics
Topic: Cardinalities of "Non-Standard" Sets
Replies: 10
Views: 828

Cardinalities of "Non-Standard" Sets

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...
by Mathmagic
Tue Mar 31, 2009 2:41 pm UTC
Forum: Mathematics
Topic: Capacitor Diff. EQ
Replies: 4
Views: 764

Re: Capacitor Diff. EQ

Well, you probably shouldn't use [imath]C[/imath] as your constant. ;)
by Mathmagic
Wed Mar 25, 2009 5:00 am UTC
Forum: Mathematics
Topic: a problems been bugging me
Replies: 26
Views: 1897

Re: a problems been bugging me

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...
by Mathmagic
Tue Mar 24, 2009 11:39 pm UTC
Forum: Mathematics
Topic: a problems been bugging me
Replies: 26
Views: 1897

Re: a problems been bugging me

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

Re: Integrating e^(- sqrt(x))

Try letting [imath]u=-\sqrt{x}[/imath].
by Mathmagic
Tue Mar 24, 2009 10:34 pm UTC
Forum: Mathematics
Topic: a problems been bugging me
Replies: 26
Views: 1897

Re: a problems been bugging me

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...
by Mathmagic
Thu Mar 19, 2009 4:39 pm UTC
Forum: Mathematics
Topic: Unrolling Toilet Paper - Just a fun brain teaser
Replies: 9
Views: 2834

Re: Unrolling Toilet Paper - Just a fun brain teaser

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...

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