A presentation of some of the basic ideas of fluid mechanics in a mathematically attractive manner. The text illustrates the physical background and motivation for some constructions used in recent mathematical and numerical work on the Navier- Stokes equations and on hyperbolic systems, so as to interest students in this at once beautiful and difficult subject. This third edition incorporates a number of updates and revisions, while retaining the spirit and scope of the original book.

1. The Equations of Motion: 1.1. Euler's Equations. 1.2. Rotation and Vorticity. 1.3. The Navier-Stokes Equations. 2. Potential Flow and Slightly Viscous Flow 2.1. Potential Flow. 2.2. Boundary Layers. 2.3. Vortex Sheets. 2.4. Remarks on Stability and Bifurcation. 3. Gas Flow in One Dimension: 3.1. Characteristics. 3.2. Shocks. 3.3. The Riemann Problem. 3.4. Combustion Waves.

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