Recent content by ayae

Thanks that really made sense. :approve: One thing; does it not half the angles? e^{i\theta}\rightarrow e^{2i\theta} http://www.wolframalpha.com/input/?i={Re[%28x%2Biy%29]%3D0%2C+Im[%28x%2Biy%29]%3D0} http://www.wolframalpha.com/input/?i={Re[%28x%2Biy%29^2]%3D0%2C+Im[%28x%2Biy%29^2]%3D0}

Recently I have been self teaching myself complex analysis. I am interested in the conformal mapping property of holomorphic functions and why and how it breaks down at stationary points. Could anyone suggest further reading for this or shed some light on the subject. Many thanks, Ayae

Hey guys, if the function f(x) has a special property that; f'(x) = f(x) g(x) Whats the easiest way to find the nth derivative of f(x) in terms of f(x), g(x) and g'(x)'s derivatives? The same problem rephrased is if q(x) is the logarithmic derivative of f(x), then what's the nth derivative...

Thankyou, that looks very promising.

Would it be scientifically sound to conclude with the use of shell theorem that; if the radius is considerablly large compared to the thickness of the torus that the torus can be considered a cross section of a sphere and if we consider that this cross section is the middle of the sphere then...

If I can't find a gaussian surface for a which passes through the center strip what can I do? How would I do this using superposition? Can I not utilize the property of the torus being rotationally symetrical around z? :( Thanks for the help so far.

This is what I feared, I didn't know whether it was symmetrical enough. Thanks for clearing it up. You're going to have to forgive my scientific illilteracy, but I don't understand this. All I need to know is the gravitational acceleration at the very centre edge of the torus. So is it safe...

When you say profitable, do you mean possible or worth while doing? Because I really had my mind set on using Gauss' law for this example, is there no way of numerically calculating it?

I know that but I cannot simplify it to produce a workable result.

I'm a little stuck, how can I go about calculating the gravitational field on the surface of a mass in the shape of a torus using Gauss' Law.

Well c(x, Δx) is 1/2 Csc(x) Csc(x + Δx) s(x) s(x + Δx) Sin(Δx) (Formula for the area of a triangle where Csc(x) s(x) are the length sides. Where s(x) is the solution for z of f(z) == z Cot(x). Where f(z) is the function I want to integrate. (I don't want to just integrate it f(z) dz)

If I have a function c(x,Δx) that gives the area between x and x + Δx of a function. The area under the function can be given by: Sum from j = 0 to n-1 of c(b/n j,c/b) As n tends to infinity and b is the upper limit of integration. How can I convert this from a sum into a integral? I'm not...

I'll make this quick guys: a = e^-t t^x This equation should have 2 solutions real between 0 and e^-x x^x I've found one solution to the equation: t = -x ProductLog[-(a^((1/x))/x)] But I can't find the other :(. Please can you give me a hand finding the other solution.

bump, I only need it solved in 1, 2 or 3 dimensions. Anyone please?

Nevermind found it, if anybody else was interested the solution is here: http://www.bruce-shapiro.com/pair/ElementConversionRecipes.pdf