Description

This book provides a concise introduction to continuum mechanics, with a particular emphasis on fluid dynamics, suitable for upper undergraduate students in applied mathematics and related subjects. Starting with a preliminary chapter on tensors, the main topic of the book begins in earnest with the chapters on continuum kinematics and dynamics. Following chapters cover linear elasticity and both incompressible and compressible fluids. Special topics of note include nonlinear acoustics and the theory of motion of viscous thermal conducting compressible fluids. Based on an undergraduate course taught for over a decade, this textbook assumes only familiarity with multivariate calculus and linear algebra. It includes many exercises with solutions and can serve as textbook for lecture courses at the undergraduate and masters level. Michael S. Ruderman is Professor of Applied Mathematics at the School of Mathematics and Statistics of the University of Sheffield. His main scientific interest is in hydrodynamic and hydromagnetic wave propagation in the solar and stellar atmospheres. His main achievements are in the field of linear and nonlinear hydromagnetic wave propagation in ionised gases. 1 Introduction.- 2 Mathematical Preliminaries.- 3 Continuum Kinematics.- 4 Continuum Dynamics.- 5 Ideal Incompressible Fluids.- 6 Linear Elasticity.- 7 Viscous Incompressible Fluids.- 8 Ideal Barotropic Fluids.- 9 Non-ideal Compressible Fluids.- A Solutions to Problems.- Index