Ockendon H., Ockendon John R. Waves and Compressible Flow

Springer-Verlag, 2004. — 198 p. — (Texts in Applied Mathematics 47). — ISBN: 0-387-40399-X.Series Preface
Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and teach-ing, has led to the establishment of the series Texts in Applied Mathematics (TAM)
The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and to encourage the teaching of new courses
TAM will publish textbooks suitable for use in advanced undergraduate
and beginning graduate courses, and will complement the Applied Mathe-matical Sciences (AMS) series, which will focus on advanced textbooks and
research-level monographsThe starred sections are self-contained and may be omitted at a first reading
Series Preface.The Equations of Inviscid Compressible Flow
The Field Equations
Initial and Boundary Conditions
Vorticity and Irrotationality
Homentropic Flow
Incompressible Flow
Exercises
Models for Linear Wave Propagation
Acoustics
Surface Gravity Waves in Incompressible Flow
Inertial Waves
Waves in Rotating Incompressible Flows
Isotropic Electromagnetic and Elastic Waves
Exercises
Theories for Linear Waves
Wave Equations and Hyperbolicity
Fourier Series, Eigenvalues, and Resonance
Fourier Integrals and the Method of Stationary Phase
Dispersion and Group Velocity
Dispersion Relations
Other Approaches to Group Velocity
The Frequency Domain
Homogeneous Media
Scattering Problems in Homogeneous Media
Inhomogeneous Media
Stationary Waves
Stationary Surface Waves on a Running Stream
Steady Flow in Slender Nozzles
Compressible Flow past Thin Wings
Compressible Flow past Slender Bodies
High-frequency Waves
The Eikonal Equation
Ray Theory
Dimensionality and the Wave Equation
Exercises
Nonlinear Waves in FluidsModels for Nonlinear Waves
One-dimensional Unsteady Gasdynamics
Two-dimensional Steady Homentropic Gasdynamics
Shallow Water Theory
Nonlinearity and Dispersion
Smooth Solutions for Nonlinear Waves
The Piston Problem for One-dimensional Unsteady Gasdynamics
Prandtl–Meyer Flow
The Dam Break Problem
The Hodograph Transformation
Exercises
Shock Waves
Discontinuous Solutions
Introduction to Weak Solutions
Rankine–Hugoniot Shock Conditions
Shocks in Two-dimensional Steady Flow
Jump Conditions in Shallow Water
Other Flows involving Shock Waves
Shock Tubes
Oblique Shock Interactions
Steady Quasi-one-dimensional Gas Flow
Shock Waves with Chemical Reactions
Open Channel Flow
Further Limitations of Linearized Gasdynamics
Transonic Flow
The Far Field for Flow past a Thin Wing
Non-equilibrium Effects
Hypersonic Flow
Exercises
Epilogue