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...
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...
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...
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
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...
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...
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...