adding the tutorials.

tutorials/Lab.tex

+\documentclass[prd,preprintnumbers,eqsecnum,floatfix,a4paper,nofootinbib]{revtex4}
+\usepackage{color}
+\usepackage{url}
+\usepackage{calc}
+\usepackage{amsmath,amssymb,graphicx}
+\usepackage{amssymb,amsmath}
+\usepackage{tensor}
+\usepackage{bm}
+\usepackage{times}
+\usepackage[varg]{txfonts}
+\usepackage[colorlinks, pdfborder={0 0 0}]{hyperref}
+\definecolor{LinkColor}{rgb}{0.75, 0, 0}
+\definecolor{CiteColor}{rgb}{0, 0.5, 0.5}
+\definecolor{UrlColor}{rgb}{0, 0, 0.75}
+\hypersetup{linkcolor=LinkColor}
+\hypersetup{citecolor=CiteColor}
+\hypersetup{urlcolor=UrlColor}
+\maxdeadcycles=1000
+\allowdisplaybreaks
+\newcommand{\comment}[1]{\textcolor{red}{\textit{#1}}}
+\newcommand{\checkthis}{\textcolor{magenta}{(CHECKTHIS)}}
+
+\newcommand{\bx}{\mathbf{x}}
+\newcommand{\boldeta}{\bm{\eta}}
+
+\begin{document}
+
+\newcommand{\be}{\begin{equation}}
+\newcommand{\ee}{\end{equation}}
+\newcommand{\ber}{\begin{eqnarray}}
+\newcommand{\eer}{\end{eqnarray}}
+\def\bea{\begin{eqnarray}}
+\def\eea{\end{eqnarray}}
+\newcommand{\etal}{\emph{et al.}}
+
+\newcommand{\Sl}{S_\ell}
+\newcommand{\Sigmal}{\Sigma_\ell}
+\newcommand{\Flux}{\mathcal{F}}
+\newcommand{\LNh}{\hat{\mathbf{L}}_N}
+\newcommand{\LN}{\mathbf{L}_N}
+\newcommand{\bS}{\mathbf{S}}
+\newcommand{\bJ}{\mathbf{J}}
+\newcommand{\e}{\mathrm{e}}
+\newcommand{\rmi}{\mathrm{i}}
+\newcommand{\flow}{f_\mathrm{low}}
+\newcommand{\fcut}{f_\mathrm{cut}}
+
+\newcommand{\bchi}{\bm{\chi}}
+\newcommand{\blambda}{\bm{\lambda}}
+\newcommand{\bLambda}{\bm{\Lambda}}
+\newcommand{\bchia}{\bm{\chi}_a}
+\newcommand{\bchis}{\bm{\chi}_s}
+\newcommand{\chis}{\chi_s}
+\newcommand{\chia}{\chi_a}
+\newcommand{\chiadL}{\bchia \cdot \LNh}
+\newcommand{\chisdL}{\bchis \cdot \LNh}
+\newcommand{\chisSqr}{\bchis^2}
+\newcommand{\chiaSqr}{\bchia^2}
+\newcommand{\chisDchia}{\bchis \cdot \bchia}
+\newcommand{\cA}{\mathcal{A}}
+\newcommand{\cB}{\mathcal{B}}
+\newcommand{\cC}{\mathcal{C}}
+\newcommand{\cP}{\mathcal{P}}
+
+
+\title{ICTS Graduate Course: Tools of Astrophysics (PHY410.5)}
+\author{Parameswaran~Ajith}\email{ajith@icts.res.in}
+\author{Rajaram Nityananda} \email{rajaram.nityananda@icts.res.in}
+\affiliation{International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India.}
+\author{Muhammed Irshad (tutor)}\email{muhammed.irshad@icts.res.in}
+\affiliation{International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India.}
+\bigskip
+\date{\today}
+\maketitle
+
+\section{Astrophysics across scales}
+\input{astro_scale.tex}
+
+% 
+
+\bibliography{Lab}
+\end{document}

tutorials/Makefile

+#
+# $Header: /numrelcvs/NumrelGWDA/docs/TemplBank/Makefile,v 1.4 2007/09/23 10:57:22 ajith Exp $
+#
+
+DOCS = Lab.pdf
+
+BYPROD = Lab.ps Lab.blg
+
+TEXS = Lab.tex 
+
+FIGS = 
+
+default: ${DOCS}
+
+#Lab.pdf: Lab.ps
+#	ps2pdf Lab.ps Lab.pdf
+
+#Lab.ps: Lab.dvi ${FIGS}
+#	dvips -t a4 -P pdf -o Lab.ps Lab.dvi
+
+Lab.pdf: Lab.tex ${FIGS} ${TEXS}
+#	latex Lab && latex Lab && latex Lab && bibtex Lab
+	pdflatex Lab  && bibtex Lab && bibtex Lab && pdflatex Lab && pdflatex Lab 
+
+Lab.ps: Lab.pdf ${FIGS}
+	pdftops Lab.pdf
+
+%.pdf: %.eps
+	epstopdf --outfile=$@ ${@:.pdf=.eps}
+
+clean:
+	rm -f *.aux *.log *.out *.dvi *~ ${DOCS} ${BYPROD}
+
+copy:
+	cp Lab.pdf /Users/pajith/Sites/ICTS/P._Ajiths_Homepage/Teaching_files
+publish: 
+	/Users/pajith/Sites/ICTS/P._Ajiths_Homepage/updateweb.sh

tutorials/astro_scale.tex

+
+\subsection{Virial Equilibrium}
+
+As we discussed in the class, the {virial theorem} provides a unifying description of equilibrium configurations across a wide range of astrophysical systems. You are encouraged to make {order-of-magnitude estimates}, clearly state assumptions, and focus on physical scalings rather than numerical prefactors. Unless stated otherwise, assume spherical symmetry and equilibrium. The virial theorem may be written schematically as
+\begin{equation}
+K  = -\frac{1}{2} U ,
+\end{equation}
+where $K$ is the total kinetic (or pressure-support) energy and $ U$ is the potential (binding) energy. We disscussed in the class that, in different systems, the pressure support is provided by different effects: 1) random motions of dark matter particles in dark matter halos, 2) thermal pressure of the gas in molecular clouds, 3) Coulomb energy of the protons in a cold planet, 4) degeneracy pressure of electrons in a white dwarf. 
+
+\subsubsection{Problems}
+
+\begin{enumerate}
+
+\item Consider a virialized dark matter halo of total mass $M$ and radius $R$. The halo is supported by random motions characterized by a circular velocity $v_c$.
+
+\begin{enumerate}
+\item[(a)] Using the virial theorem, estimate the relation between $M$, $R$, and $v_c$.
+
+\item[(b)] Assume the halo virializes at redshift $z$, with mean density
+$ \rho_{\rm vir} \simeq 200 \rho_c(z)$, where $\rho_c(z) = \frac{3H^2(z)}{8\pi G}. $
+Express the characteristic halo mass in terms of $v_c$ and the Hubble parameter $H(z)$.
+
+\item[(c)] Estimate the halo mass for the following representative values: $v_c \sim 200 ~ \mathrm{km ~s^{-1}}$ ~ $H_0 \sim 70 ~ \mathrm{km,s^{-1} ~Mpc^{-1}}$.
+
+\item Why does the characteristic mass of a virialized dark matter halo depend on the Hubble parameter at the epoch of collapse?
+
+\end{enumerate}
+
+
+\item A molecular cloud of mass $M$, radius $R$, and temperature $T$ is supported by thermal pressure.
+
+\begin{enumerate}
+\item[(a)] Use the virial theorem to estimate $M$ in terms of $T$ and $R$.
+
+\item[(b)] Using the sound speed $c_s$ and a characteristic size $R \sim c_s/\sqrt{G\rho}$, derive the scaling of the Jeans mass with $c_s$ and the density $\rho$.
+
+\item[(c)] Estimate the Jeans mass for a typical molecular cloud with: $T = 10,\mathrm{K}$, number density $n = 100,\mathrm{cm^{-3}}$ and mean molecular weight $\mu = 2.3$.
+
+\item Why does increasing the temperature of a molecular cloud tend to suppress gravitational collapse?
+
+\end{enumerate}
+
+\item Consider a cold, solid planet composed of atoms with atomic number $Z$ and mass number $A$. The planet has mass $M$ and radius $R$.
+
+\begin{enumerate}
+\item[(a)] Estimate the gravitational binding energy. Assume the typical Coulomb (electrostatic) energy per atom is $E_C \sim \frac{Z^2 e^2}{a}$, where $a$ is the characteristic interatomic spacing. Estimate the total Coulomb energy of the planet in terms of $M$ and $R$.
+
+\item[(b)] Using virial balance between gravity and Coulomb energy, estimate the maximum mass of a stable planet.
+
+\item[(c)] Using representative rocky material parameters $Z \sim 10$ $A \sim 20$ estimate the maximum planetary mass and compare it to the mass of Jupiter.
+
+\item Why does electron degeneracy pressure not play an important role in setting the mass scale of ordinary planets?
+
+\end{enumerate}
+
+\item A white dwarf is supported against gravitational collapse by electron degeneracy pressure.
+
+\begin{enumerate}
+\item[(a)] Estimate the gravitational energy. For relativistic degenerate electrons, assume the characteristic kinetic energy is
+$K \sim N_e p_F c,$ where $p_F \sim \hbar n_e^{1/3}$ is the Fermi momentum and $n_e$ is the electron number density.
+
+\item[(b)] Express the total degeneracy energy in terms of $M$ and $R$, assuming $N_e \sim M/m_p$.
+
+\item[(c)] Using the virial theorem, estimate the maximum mass of a white dwarf supported by electron degeneracy pressure.
+
+\item Why does the maximum mass of a white dwarf depend only on fundamental constants and not on its radius?
+
+\end{enumerate}
+
+\end{enumerate}