Mathematical Methods and Fluid Mechanics: Block 1

This book contains 4 units of study that form the foundation of mathematical methods and fluid mechanics.Unit 1 Properties of a fluid introduces the continuum model and many of the properties of a fluid, such as density, pressure and viscosity. The basic equation of fluid statics is formulated and used to find the pressure distribution in a liquid and to provide a model for the atmosphere.Unit 2 Ordinary differential equations starts by showing how changes of variables (involving use of the Chain Rule) can be applied to solve certain non-constant-coefficient differential equations, and leads on to the topics of boundary-value and eigenvalue problems. It concludes with an introduction to the method of power-series for solving initial-value problems.Unit 3 First-order partial differential equations extends the earlier version of the Chain Rule to cover a change of variables for functions of two variables, and shows how this leads to the method of characteristics for solving first-order partial differential equations.Unit 4 Vector field theory relates line, surface and volume integrals through two important theorems - Gauss' theorem and Stokes' theorem - and formulates the equation of mass continuity for a fluid in motion.Please note this book refers to the use of other materials, therefore you are advised that you may also need to purchase the Audio CD Pack (order code MST326/CDAPACK)