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1. Differential Equations: I hate them.

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.
2. Differential Equations: I hate them.

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...
3. Next Number in the Sequence.

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...
4. Next Number in the Sequence.

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...
5. Next Number in the Sequence.

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...
6. Next Number in the Sequence.

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.
7. Utilitarianism-john stuart mills

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...
8. Testing GRE Physics Prep Courses

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...
9. Home Haircuts

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...
10. Name for programming functions , i think

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...
11. Name for programming functions , i think

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...
12. Calc Formulas

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...
13. Directed study in real analysis

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...
14. Supplement to spivak's calc on manifolds

yeah, right after i posted that, i started up at the beginning. i think I'm good to give it a go, but, it looks like it's going to be a bit tough.
15. Supplement to spivak's calc on manifolds

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...
16. Max/Min problem I'm fundamentally flawed in my understanding I think

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...
17. 1997 Calculus AB AP Test Answers NEEDED

were there any answers you were unsure about? i mean, you ought to know whether you got something correct or you think it may be wrong.
18. Gradient vector over an area of a surface

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...
19. Calculus DVD's would you recommend these?

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...
20. Gradient vector over an area of a surface

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...
21. Another Line Integral Problem

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...
22. Evaluation of an integral

that's like the classic example of something that has no elementary solution...
23. Line Integrals

oh, indeed, it is a dx. ecks, ess, they sound so similar in my noisy head...
24. Line Integrals

\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...
25. Limit change on triple integral

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?
26. Limit change on triple integral

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...
27. Limit change on triple integral

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...
28. Limit change on triple integral

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...
29. Limit change on triple integral

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)...
30. Limit change on triple integral

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...
31. My bicycle tire pressure

these tires are typically run between 90 and 120psi. yeah, anyways, I've got it figured out, thanks
32. My bicycle tire pressure

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...
33. Calculus is boring

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...
34. Calculus is boring

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...
35. Who's done the most homework in shortest amount of time?

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...
36. Implicit diff (2 var), error or what?

thank you, jameson
37. Implicit diff (2 var), error or what?

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...
38. Implicit diff (2 var), error or what?

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...
39. Implicit diff (2 var), error or what?

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...
40. Spherical geometry, some simple things

Thanks you very much :-) though i don't get the satisfaction of having done it myself now, but, at least i get it...
41. Trig function products

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 :-)
42. Trig function products

yes, i'd imagine it is a bit more ambiguous than I had supposed... I'm working on this https://www.physicsforums.com/showthread.php?t=57665
43. Trig function products

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...
44. Spherical geometry, some simple things

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...
45. Quick question about Michael Spivak's Calculus

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...
46. Quick question about Michael Spivak's Calculus

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...
47. Proofs in sequences and series

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...
48. Research topic

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...
49. Question - is it impossible for nothing to exist?

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...
50. Calculus Help

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...