TABLE OF CONTENTS Physical laws, if they are to be valid, must be independent of the choice of the coordinate system used to describe them mathematically. This is possible by tensors, since the properties of tensors are independent of the choice of the co-ordinate system used to describe them. Mainly due to this reason, Einstein s theory of relativity and gravitational theory are expressed in the language of tensors. This tempts us to ask : what is a tensor ?
The quantities which are associated with two or more directions are called tensors. For example, the stress at a point of an elastic solid which depends upon two directions one normal to the area and other that of the force on it is a tensor. Tensors are generally defined in terms of their ranks and components.
In this chapter we study briefly the subject of tensor analysis which is of great use in differential geometry, mechanics, electromagnetic theory and numerous other fields of science and engineering.
In two-dimensional geometry ( x, y) ( r, ?) are co-ordinates of a point in rectangular and polar coordinate systems. In three-dimensional space ( x, y, z), ( r, ?, z), ( r, ?, 
) are coordinates of a point in rectangular, cylindrical and spherical coordinate systems. In N-dimensional space ( x 1, x 2, , x n) [where 1, 2,
