| Preface | p. v |
| Basic Fluid Equations | p. 1 |
| The Material Derivative | p. 2 |
| The Continuity Equation | p. 3 |
| The Momentum Equation | p. 3 |
| Newtonian Gravity | p. 6 |
| The Mechanical and Thermal Energy Equations | p. 7 |
| A Little More Thermodynamics | p. 9 |
| Perfect Gases | p. 11 |
| The Virial Theorem | p. 12 |
| Vorticity | p. 14 |
| Simple Models of Astrophysical Fluids and Their Motions | p. 19 |
| Hydrostatic Equilibrium for a Self-gravitating Body | p. 20 |
| Spherically symmetric case | p. 20 |
| Plane-parallel layer under constant gravity | p. 22 |
| Equations of Stellar Structure | p. 23 |
| Small Perturbations about Equilibrium | p. 25 |
| Isothermal fluctuations | p. 26 |
| Adiabatic fluctuations | p. 27 |
| Lagrangian Perturbations | p. 28 |
| Sound Waves | p. 28 |
| Surface Gravity Waves | p. 30 |
| Phase Speed and Group Velocity | p. 32 |
| Order-of-magnitude Estimates for Astrophysical Fluids | p. 33 |
| Typical scales | p. 33 |
| Importance of viscosity | p. 33 |
| The adiabatic approximation | p. 35 |
| The approximation of incompressibility | p. 35 |
| Theory of Rotating Bodies | p. 37 |
| Equation of Motion in a Rotating Frame | p. 38 |
| Equilibrium Equations for a Slowly Rotating Body | p. 38 |
| The Roche Model | p. 40 |
| Chandrasekhar-Milne Expansion | p. 41 |
| Dynamics of Rotating Stellar Models | p. 45 |
| Solar Rotation | p. 46 |
| Binary Stars | p. 50 |
| Fluid Dynamical Instabilities | p. 55 |
| Convective Instability | p. 55 |
| The Schwarzschild criterion | p. 55 |
| Effects of dissipation | p. 60 |
| Modelling convection: the Boussinesq approximation | p. 61 |
| The Rayleigh-Taylor Instability | p. 62 |
| Rotational Instability | p. 63 |
| Shear and the Kelvin-Helmholtz Instability | p. 64 |
| The Kelvin-Helmholtz instability | p. 64 |
| Critical Richardson and Reynolds numbers | p. 67 |
| Turbulence and the Kolmogorov spectrum | p. 68 |
| Magnetohydro dynamics | p. 71 |
| Maxwell's Equations and the MHD Approximation | p. 71 |
| MHD Waves | p. 74 |
| Some MHD Applications | p. 76 |
| Solar prominences | p. 76 |
| Dynamo theory | p. 78 |
| Coronal heating | p. 81 |
| MHD Instabilities | p. 82 |
| Numerical Computations | p. 85 |
| The Formulation of Finite Differences | p. 86 |
| The von Neumann Stability Analysis | p. 87 |
| Various Finite-difference Schemes | p. 89 |
| The Lax method | p. 89 |
| Upwind differencing | p. 89 |
| The staggered leapfrog method | p. 90 |
| The Lax-Wendroff method | p. 90 |
| Implicit schemes: the Crank-Nicholson method | p. 91 |
| Considerations for More Complex Systems | p. 92 |
| Operator Splitting | p. 93 |
| Examples of Implementations | p. 95 |
| 1-D Lagrangian scheme with artificial viscosity | p. 95 |
| 2-D scheme using operator splitting | p. 98 |
| Codes for computing astrophysical flows | p. 100 |
| Smoothed Particle Hydrodynamics | p. 101 |
| Planetary Atmosphere Dynamics | p. 107 |
| The Importance of Rotation: the Rossby Number | p. 107 |
| Relative and Absolute Vorticity | p. 108 |
| Potential Vorticity | p. 110 |
| Baroclinicity and the Thermal Wind Equation | p. 110 |
| Geostrophic Motion | p. 112 |
| Some Approximate Models | p. 116 |
| The shallow-water model | p. 117 |
| f-plane and ?-plane models | p. 119 |
| Waves | p. 120 |
| Ekman Layers | p. 122 |
| Accretion, Winds and Shocks | p. 127 |
| Bernoulli's Theorem | p. 128 |
| The de Laval Nozzle | p. 129 |
| The Bondi Problem | p. 130 |
| The Parker Solar-Wind Solution | p. 134 |
| Nonlinear Acoustic Waves | p. 134 |
| Shock Waves | p. 139 |
| Blast Wave from a Supernova | p. 140 |
| Viscous Accretion Disks | p. 143 |
| Role of Angular Momentum and Energetics of Accretion | p. 143 |
| Thin Accretion Disks | p. 145 |
| Diffusion Equation for Surface Density | p. 147 |
| Steady Disks | p. 150 |
| The Need for Anomalous Viscosity | p. 153 |
| Jeans Instability and Star Formation | p. 155 |
| Links to Observations | p. 156 |
| Jeans Instability | p. 156 |
| Jeans Instability with Rotation | p. 158 |
| Jeans instability for a rotating system | p. 159 |
| Ambipolar Diffusion | p. 161 |
| Fragmentation | p. 162 |
| Some Comments on Star Formation | p. 163 |
| Radial Oscillations of Stars | p. 165 |
| Linear Adiabatic Wave Equation for Radial Oscillations | p. 165 |
| Boundary conditions | p. 168 |
| Eigenvalue nature of the problem | p. 169 |
| Self-adjointness of the problem | p. 170 |
| A lower bound on the fundamental frequency | p. 172 |
| Homology scaling for the fundamental frequency of stars | p. 172 |
| Non-adiabatic Radial Oscillations | p. 173 |
| Physical discussion of driving and damping | p. 176 |
| The Quasi-adiabatic Approximation | p. 178 |
| Nonradial Oscillations and Helioseismology | p. 181 |
| Nonradial Modes of Oscillation of a Star | p. 181 |
| Mode Classification | p. 185 |
| The Cowling Approximation | p. 186 |
| A Simplified Discussion of Nonradial Oscillations | p. 187 |
| A More General Asymptotic Expression | p. 190 |
| Helioseismology: The Duvall Law | p. 193 |
| Tassoul's Formula | p. 196 |
| Asymptotics of g Modes | p. 198 |
| Probing the Sun's Internal Rotation | p. 199 |
| Useful Constants and Quantities | p. 205 |
| Fundamental Physical Constants | p. 205 |
| Astronomical Quantities | p. 205 |
| Cartesian Tensors: Index Notation and Summation Convention | p. 206 |
| Vector Calculus in Spherical and Cylindrical Polar Coordinates | p. 207 |
| Cylindrical Polar Coordinates (¿,ø,z) | p. 207 |
| Spherical Polar Coordinates (r,&theda;,ø) | p. 208 |
| Self-adjoint Eigenvalue Problems | p. 209 |
| Reality of Eigenvalues | p. 209 |
| Orthogonality of Eigenfunctions | p. 210 |
| Eigenhmction Expansions | p. 210 |
| Variational Principle | p. 211 |
| The JWKB Method | p. 213 |
| Bibliography | p. 217 |
| Index | p. 223 |
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