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.