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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?

    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...
  4. 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...
  5. 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.
  6. 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
  7. 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...
  8. 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...
  9. 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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