Recent content by sam2

Hi, Has anyone here used the complex C++ class before Header <complex>? I am trying to do something VERY straightforward but there doesn't seem to be any way to do it! Basically, I define a complex, and then want to re-asign its real and imaginary parts: complex<double> A(1,1); //...

Hi, Sorry about the text, but Latex doesn't work. Can anyone please give me an outline for the derivation of the probability function by inverting its Fourier transform, i.e. P(X>x) = \frac{1}{2} + \frac{1}{\pi} \int_{0}^{\infty} Re \bigg[\frac{e^{-i \theta x}f(\theta)}{i \theta} \bigg]...

much appreciated

Hi George, Thanks for the reply but I am still stuck when I use your method. It makes perfect sense but I can't see where I am going wrong. I am doing the integral that I mentioned in my first post; but basically end up with the integral equal to tan^{-1} [ -2x/(1-x^2) ] Sorry, latex doesn't...

Gotcha. Many thanks.

Hi, I'm doing the following as an exercise to try and get my head around complex numbers. Specifically, I need to understand what it means to take the natural log of a complex number and what it involves. Say I wanted to integrate 1/ (1 +x^2) dx I know this is arcTan(x). I can also...

So do I just solve the ODE on the basis of the sign of the real part of the complax coefficient? I.e. I still don't know whether to use a tan or ln solution to the above. My b is indeed positive but I was worried about using a tan substitution because of the 'i'. So you are effectively saying...

Hi, Thanks for the replies. But I am still unsure as to why the solution is a tangent rather than a logarithm. We can rewrite the quadratic term in the ode as the difference of two squares, say: 1/a . df / (F^2 + D^2) = dx If D is positive then I agree that the solution uses a tan...

Hi, I have never had to handle ODEs where the coefficients are complex. Just wondering if solving this is even possible and whether you can point me to any sources/books. Say I had the ODE (df/dx) + a.f^2 + (b+i)f + c = 0 where f(x) is a function of x, a, b and c are constants, and i...

Got it. Many thanks for the replies. Regards, Sam

Hi all, Looking for some help on the following problem. Any replies much appreciated. I have the complex number exp(i.x) If x = - infinity, is this zero?? Is there any intuitive/straightforward value that it should be? I decomposed the expression into cos and sin and it looks like...

Hi, thanks for the replies... Integral I like your intuition... regards

Hi all, Came across this problem, but it has stumped me: Let S denote the unit sphere x^2 + y^2 + z^2 = 1, and let u = x + 2y + 3z be temperature at points everywhere in 3-space. Find the hottest and coldest points on the unit ball x^2 + y^2 + z^2 <= 1 I figured out that...

How about using the Binomial Exapnsion to re-write the expression and then looking at whether you can simplify it when x--> 0?

What about using the Central Limit theorem? X(1) = The outcome from dice number 1, it can be 1,2...6 We want Y = X(1)+X(2)+... X(20). This should be approximately normal in distributoin. Mean = 20 *3.5, variance = 20*2.92. We want P(Y>100) Sam