Due Jan. 18.
General guidelines:
- Label plot appropriately, including axes, units, curve
parameters, and other plot parameters.
- Always carry out analytic checks, and present them.
- Think about the physical meaning of the results -- do the
numbers produced by the program seem reasonable.
- Understand the point and meaning of the numerical procedures.
- Comment your code!
- Write a program to perform Romberg extrapolation of Simpson's
rule for an arbitrary function.
- Apply the program to calculate the cosmological lookback time as
a function of redshift for a cosmological model with arbitrary regular
matter (
) and cosmological constant (
):
for the models
.
Hint: Test your program against the analytic result for the
(1,0) model.
- Use the results to make tables of the values of redshift
vs. time over the range
. Write a program to linearly
interpolate on these tables to return the lookback time given the
redshift. Plot the table values as points for each of the models, and
the linear interpolations as curves.
- Integrate to infinity to get the age of the Universe (in units
of
) for each of
the models. Be careful in considering how to properly treat the upper
limit at infinity.
This document was generated using the
LaTeX2HTML translator Version 99.2beta8 (1.43)
Copyright © 1993, 1994, 1995, 1996,
Nikos Drakos,
Computer Based Learning Unit, University of Leeds.
Copyright © 1997, 1998, 1999,
Ross Moore,
Mathematics Department, Macquarie University, Sydney.
The command line arguments were:
latex2html -split 0 hw1.tex
The translation was initiated by Tom Quinn on 2001-02-07
Tom Quinn
2001-02-07
![\begin{displaymath}
H_0 t(z) = \int_1^{1+z} dy\ y^{-1} \left[ \Omega_m y^3 + (1 - \Omega_m
- \Omega_\Lambda) y^2 + \Omega_\Lambda \right]^{-1/2}
\end{displaymath}](img3.png){kind=small}