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  1. J

    Totally ordered partition of a set

    If I have a totally ordered set and then create a noncrossing partition of that set it seems intuitively obvious that each block of the partition would be totally ordered as well. Can I assume this inheritance or do I need to prove each block is totally ordered? How would one go about proving...
  2. J

    General Relationship Between Area & Perimeter

    This is kind of a vague question but does anybody know if there is a more general relationship between the area and perimeter of plane figures. For example circles, squares, rectangles triangles any regular polygon really, the area can be written in terms of the perimeter. Is there anything...
  3. J

    Series Name?

    Kaisxuans - I had no plan to jump into the dificult Zeta Function but it's one of the few things related to my problem that I can search for. Other than that I don't know what to look for. Dodo - Thanks for the link. This first part about wether Zeta(3) is a rational multiple of pi^3 is...
  4. J

    Series Name?

    I'm interested in the problem: \sum_{n=1}^{ \infty} \frac{1}{n^3} and would like to know more about what attempts have been made at it and any insights into it but I am unable to find much because I don't know the name of this series or if it even has one. I have learned what little...
  5. J

    What is wrong with my logic?

    Whoops, sorry :blushing:
  6. J

    What is wrong with my logic?

    I thought if ab=0 then you could have two solutions a = 0 and b = 0?
  7. J

    What is wrong with my logic?

    if e^{\pi\imath}=-1 then: -e^{\pi\imath}=1 and, e^{2\pi\imath}=1 then: -e^{\pi\imath}=e^{2\pi\imath} \rightarrow e^{2\pi\imath}+e^{\pi\imath}=0 \rightarrow (e^{\pi\imath})^2+e^{\pi\imath}=0 \rightarrow (e^{\pi\imath}+1)e^{\pi\imath}=0 then: e^{\pi\imath}=0 and...
  8. J

    Impossible problem? [Varibles ONLY]

    Any statics problem should begin with a free body diagram. Once that is done the solution usually comes easily. If you have done one you can post it for comments.
  9. J

    Is this possible to integrate?

    You are wrong on both counts, the dv is supposed to be dx :biggrin:
  10. J

    Is this possible to integrate?

    Please help me integrate the following: \int_0^x \frac{1}{\sqrt{(A+Bx^2+Cx^3+Dx^4)}} \,dx I have no idea where to start or if this is even possible.
  11. J

    Is this possible to integrate?

    Sorry, I should have said x and r are real non-negative constants..
  12. J

    Is this possible to integrate?

    Does anybody have any suggestions on how to go about integrating this.... ? Or maybe explain why mathcad isn't able to integrate this..
  13. J

    Is this possible to integrate?

    I haven't had any luck with mathcad and was wondering if this was possible to integrate... \int_{0}^{2\pi} \frac {x+r*cos(\theta)}{(x^2+2r*x*cos(\theta)+r^2)^\frac {3}{2}} d\theta
  14. J

    Second Order Nonhomogeneous

    Okay guys I got it, thanks for your help. And yes k_{3} = 8
  15. J

    Second Order Nonhomogeneous

    The following equation was derived from a RLC circuit: \frac{d^2}{dt^2} (V(t)) + 6 \frac{d}{dt} (V(t)) + 5V(t) = 40 Setting up the equation: s^2 +6s + 5 = 0 yields s = -1 and s = -5 Giving me the general equation: V(t) = k_{1}e^{-t} + k_{2}e^{-5t} But the general equation...
  16. J

    Why Sound Doesnt Travel Through A Vacuum

    The animation of the longitudinal wave on http://www.kettering.edu/~drussell/Demos/waves/wavemotion.html [Broken] is a good example of sound waves. If those were molecules of air they would continute bouncing like that until they hit your ear drum and then you would hear sound. Without those...
  17. J

    Differential Equation: Frobenius

    Yeah, I also set a_1 to 0 I noted this on the work I turned in. Thank you for helping me.
  18. J

    Differential Equation: Frobenius

    Haha, yeah I have finished the semester and while I never want to see one of these again this question is nagging me. I just came back from class so I'll go ahead and show you what I turned in. After going back and cleaning my notation up I got the same initial answer for y...
  19. J

    Help with frobenius

    Using the reduction formula I came up with this solution: y2=y1*integral(x*(y1)^(-2)*dx) I don't know how to write math symbols in here so I attached a picture that is easier to understand. does this seem like the correct solution? I'm also concerned about my answer for y1. The index...
  20. J

    Differential Equation: Frobenius

    Using the reduction formula I came up with this solution: y2=y1*integral(x*(y1)^(-2)*dx) I don't know how to write math symbols in here so I attached a picture that is easier to understand. does this seem like the correct solution? I'm also concerned about my answer for y1. The index...
  21. J

    Differential Equation: Frobenius

    My problem: find the first solution and use it to find the second solution for x^2*y"-x*y'+(x^2+1)y=0 assuming y=summation from n=0 to infinity for An*x^n+r substituting and solving gives me r=1 and a general equation: An=A(n-2)/((n+r)*(n+r-2)+1) for n >= 2 plugging r into my...
  22. J

    Help with frobenius

    Somebody please help, I'm not sure I know what is going on with this. My problem: find the first solution and use it to find the second solution for x^2*y"-x*y'+(x^2+1)y=0 assuming y=summation from n=0 to infinity for An*x^n+r substituting and solving gives me r=1 and a general...
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