type COMPLEX C NZ - Number of underflows set to zero C NZ0 Normal return. Systems of ordinary differential equations is something that comes up a lot in physics, and it will be crucial to be able to solve such equations in this course. PROLOGUE CBESK CPURPOSE Compute a sequence of the Bessel functions K(a. This is provided in the standard library of some programming languages like modern C++ and Python, but if its not provided in the language you use we have some notes on how you can compute it yourself if you cannot find a good library for this. The only special (non-standard) function we need is the spherical Bessel function. A good ODE solver and a way of interpolating functions of one and two variables is basically all we need and we will briefly talk about the theory behind these below. We need surprisingly few numerical methods to be able to compute the CMB power-spectrum. 1.7 Generating a CMB map (not in the curriculum).

1.6 Generating a gaussian random field (not in the curriculum).

NAG FORTRAN Library Manual Mark 7, the Numerical Algorithms Group (1978) Oxford. MacMillan, London, New York (1922) Google Scholar.

1.5 External codes: Einstein-Boltzmann solvers Intel Fortran Compiler Classic and Intel Fortran Compiler Developer Guide and Reference. So as an assignment I was given the task to write a function that when given an x, calculates the corresponding first order Bessel function from it. A fortran subroutine for the bessel function J n (x) of order 0 to 10.1.4 External codes: Recombination solvers.

Fortran zeros of bessel function