TABLE OF CONTENTS The object of this appendix is to provide the reader with a short presentation of the major concepts and results concerning vector and tensor calculus, which are necessary for the applications discussed in this book.
First, it is recalled that physical entities depending on the position within a continuous medium are categorized, either as scalar, vector, or tensor fields. To identify them independently of the coordinate system used to describe their components, a symbolic notation is used. The notation is not uniform; in this book a quantity denoted q is a scalar, 
is a vector and 
is a tensor. Symbolic notation is useful to write out the physical laws in an intrinsic form, that is independent from the coordinate system. For instance, the dynamic equilibrium equation,
where 
is the position vector, holds in any coordinate system, Cartesian or not. ?( ) is a scalar field, 
and 
are fluctuating (time varying) vector fields and 
( ; t) is a fluctuating tensor field.
If calculus is performed using symbolic notation, operations such as addition, product, differentiation etc. have to be made according to distinct rules depending on the nature of the quantities involved. Moreover, symbolic notation provides only abstract results not suited to produce numerical results. For this last purpose, it is necessary to describe the physical entities by their components in a specific coordinate system which, in...
