Might do that.
I do see that there is some beauty underlying all of this, but when you're given a DE and told "solve", it is just an ugly process. clever, but ugly.
Yep. Taking the course now, and out of all my math courses (calc 1-3, matrix theory&linear algebra , abstract algebra I & II, linear programming, and real analysis) I'd have to say that it's the worst. Not because it's difficult, but because it's so boring.
It seems to me, and this probably...
Wow. That is just a bit too complicated. It also doesn't work. Sorry, but 10 is not in the sequence as I stated in my last post, but it's understandable that you didn't want to read down since you were solving the puzzle. With 10 in the sequence, it's something radically different, so your...
AKG, I feel like a total ass. 10 is not in the sequence. I noticed that today while going over this again, and immediately thought of what you said, and wondered if 10 was the number. Sure enough. I should have taken note of that and checked 10. Flagrant mistake on my part.
I would...
AKG: That is the first direction I headed with this as well, and really couldn't find any patterns right off having to do with primes. I have a good feeling that primes are somehow involved in the solution.
Also, this is a non-trivial problem. There is something interesting actually going on...
You know the routine, what is the next number in this sequence.
4, 8, 9, 10, 12, 16, 18, 20, 24, 25, 27, 28, ...
I think that I would rate this as difficult.
What exactly do you mean by 'satisfied'? I do believe that Socrates (as he is typically portrayed) was immune to dissatisfaction. I do believe he even said this himself by way of "you cannot harm a virtuous man".
In the pig's case (I take it that you mean a glutton), I would argue that...
Well, it's my last semester at my university (and next fall i will hopefully be doing math in moscow, which will be my last for my bachelor in math). so far I've done the calc series, matrix theory and linear algebra. I'm currently enrolled in abstract algebra and I'm doing a directed study in...
We live nowadays in a pluralistic world, one that has many different creatures/cultures, each with their own outlook on life.
This sort of reminds me of the something-or-other written, i forgeth where and when. The gist is, this king wants to find out some sort of moral truth, etc. The...
If my problem were to be solved using a computer, it wouldn't even be a problem, simply an exercise. nope, this needs to be the good ol' f(n) form.
oh, and I've managed to simplify it, i no longer need to cycle 1 and 2 or get only odds, but, I've still got more complicated stuff than that...
name for "programming functions", i think...
I'm looking for the name of the class of techniques you use to get functions to do what you want. for example, if you wanted to cycle between odd and even, you would use -1^n . In particular, I want to cycle between 1 and 2, and also be able to...
agreed. a bit part of calculus is learning how to think for yourself. given a problem, methodically going from point to point to figure out a solution. the only "formulas" that i think are worth having, is a sheet with a bunch of integrals on it, since some of them are a pain to figure out or...
Well, this semester I'm in my first directed study in real analysis. I'm on my own. sort of worried about doing it, just got the book, and it looks kinda tough. I'm going to have to rethink how i go about classwork. i won't be rushing to get anything done before it's due or anything like...
so i checked out Spivak's calculus on manifolds today, to work on while I'm in colorado this summer. i just finished up this semester with calc3 (multivariable), and I've take matrix theory and linear algebra as well. should I be good to go on this book at this point? I'd like to know since...
don't worry, if you pay attention, you will see that people make this mistake all the time. pretty much any news article you read that converts units^2 does it incorrectly.
to make things worse even, in my 300 level geography class a few weeks ago, the instructor was saying something about...
nope, not really what i was going at at all.
state differently, perhaps more simply, is I want to know how to find the equivalent of a gradient vector of a surface f(x,y) over an arbitrary area, not just a specific point.
now that i think of it a little more, this seems a bit absurd. an...
i don't recommend them. nobody can teach you calculus. you cannot learn it by watching, no matter how many times you watch. you just have to do the problems. i think that getting the n-1 edition of a textbook (so that it's super cheap) is the way to go, if you just want to learn it on your...
what follows is a question I asked myself, the answer I figured out, and the new question that arose as a result.
I was thinking about the gradient vector on a 3d surface, and how it shows the direction of the max rate of change at a point. the 2 directions perpendicular to it are tangent to...
physicsmajor, what you've done on this probllem, with yoru parametricization, is turned your path from a helix into a straight line. you should be computing along the helix.
now, if your vector field is conservative, you can do that, the straight line approach, which makes things much...
\int_c f(x,y,z) ds = \int_a^b f(x(t), y(t), z(t)) \sqrt { \left( \frac{dx}{dt} \right)^2 + \left( \frac{dy}{dt} \right)^2 + \left( \frac{dz}{dt} \right)^2 }
so, you need to parametricize your line in space. par exemple:
\begin{align*}
x=2 + 2t \\
y=1 - t \\
z=2t \\
0<t<1...
don't get me wrong, maple is totally sweet, but, as the adage goes, only trust it as far as you can throw it.
speaking of which, anyone have a really cool trick they can make maple do, like your favourite graph or anything else really interesting?
computers are notorious for that sort of thing. I'm terrible careful using maple, and generally use it just for graphing things. i'd never even dream of using it for something like integration.
thanks, both of you, for checking my work though, I'm glad to see that it was confirmed correct...
well, i solved this. it was problematic, and so, i graphed this thing in maple, so i could spin around a lot more easily, and see what it was i was doing. i am really glad maple exists, or it may have taken me a little longer and a lot more drawing to get it right... to anyone who may care...
i've just left the integrand as the constant "1", and all my correct answers came out as 32/3. i have been beginning to suspect this is not possible to keep it as a single triple integral. i have tried, serioulsy, every possibly combination of things, i must have done a dozen integrals in all...
i'm pretty familiar with those things, I've done this on others, and i just cannot figure out what is sticking me on this particular problem. I've tried what i *thought* was all possible ways (for dy anyhow). let's see, the region is z=y^2, x=y^3, 0<y<2 (those are "...or equal to" sings)...
ok, so I've got this triple integral: \int_{0}^{2} \int_{0}^{y^3} \int_{0}^{y^2} f(x,y,z) dz\, dx\, dy\
what i want to do is get the other five integrals that are equivalen. I've got correctly 3 of them, but, for the life of me, cannot get dy dz dx and dy dx dz to work out.
i've...
i have a small hand pump, that i can set on a block of wood and put all of my weight against to get some pretty high pressures. i dont' have a good gauge so I'm not really sure what i can do with it, other than get tires pretty high pressure (if i had to guess, at the least 75psi).
i...
I disagree. mathematics can and is a creative art as much as a science, at least, i feel as though that is the case. it's beautiful. I'm just, i guess sick of going through the motions. i was really good at first of building it up by hand, knowing all the proofs, or, at the least, where...
In cacl I, it was really fun. Quite mind blowing when I was first exposed to it a little over a year ago. I decided I wanted to major in mathematics. I took calc 2 concurrently with "matrix theory and linear algebra". calc 2 was boring, just techniques of integration, highly mechanical...
i know what you mean about the writeups. 5 minutes a problem, and a good hour writing it up after that so it looks all pretty and professional, like a mathematician :-)
i don't think I've set any records, but, i have spent long periods of time (8 solid hours, without even peeing) doing a...
looking at the graph is what caused me to realize the point isn't on there. it's not even close. now, as x approches 0 from the left, y approaches 2pi. the slope would also be increasing without bound. but that's for 2pi, which has no bearing on my problem.
it's becoming obvious to me...
um, point slope form looks messy, but that's besides the point. perhaps this wasn't clear enough. the point (0, \pi) doesn't exist in the original equation. not on the graph. sin(-\pi) does not equal 4. that's the crux of my problem.
IF the point was on the original graph, no...
i am working on a homework assignment. it's easy, or, so i think...
Given.
3x^2 - xy^3 + sin(x^3 - y) = 4
Find \frac{dy}{dx}
not a problem. i ended up with
\frac{dy}{dx} = \frac {6x - y^3 + 3x^2 cos(x^3 - y)}{3xy^2 + cos(x^3 - y)}
using implicit differention.
now...
that's what i missed. i (embarrassingly) just didn't think of trig identities. btw, i posted this thread before you had replied to my problem. i do thank you for your well given response, all is understood now :-)
what exactly does \cos \theta_1 \cos \theta_2 represent, in relation to the angles? is this a dot product? i have played, and don't really see what this product is supposed to represent.
EDIT: you know, i may have just answered my own question with a mere trig identity... perhaps i will...
So, I'm working my way through "Geometry from a Differentiable viewpoint" (or, trying to get through section 1.1, anyways).
right now, it's spherical geometry. so far, a great circle has been defined as the set of points on the sphere that intersect with a plane that intersects the origin of...
i guess i didn't say what i meant very clearly. work on it over break, see what's up, and then work on it all of next semester, hopefully garnering some indedpendent study credit along the way.
oh yeah, i found it online only 2 places. amazon, new, for 70, but it won't ship for 3-4 weeks...
after reading about this, i think I'm going ot order it online as well, work on it over christmas break. maybe i could even weasel out some independent study credit for it...
my calc 2 professor today was just discussing putting proofs on the board today (and we are doing stuff with series, so a double coincidence). we are going through the different tests for convergence/divergence, and he finally got to the point where he said "do you really want me ot put the...
Well, I will certainly keep an eye our for those calc texts. perhaps over break i can do that, though the books i have now are going to keep me busy for the next 6 weeks.
As for Ann Arbor, yes, I've looked into transferring in general, and in fact, moved to flagstaff, arizona, 3 years ago...
a void is only something when compared to something.
that sounds incredibly cryptic and has no basis in meaning.
this reminds me of godel's theorem, or of something said that led to godel's theorem coming about. I forget who said this "it occurred to me that sometimes sets are are a member of...
this really belongs in the calculus forum.
for the first problem, you can simplify it by looking at only the section of a circle in the first quadrant of the coordinate plane. then look to maximize the area of a rectangle inscribed within the area of the 1/4 circle.
the second problem...