ABSTRACT
This chapter introduces two basic tools required for the understanding and interpretation of different field phenomena: coordinate systems and vector algebra. The chapter first discusses the meaning and essence of coordinate systems, enlists various types of coordinates, and explains the meaning of the orthogonal and right- and left-handed coordinate systems. This briefly describes Cartesian, cylindrical, and spherical systems with necessary illustrations. This includes the expressions for the elemental volumes and illustrations of the shapes of constant coordinate surfaces in the three orthogonal coordinate systems. Lastly the applications of these are also noted. The vector algebra part begins with vector representation and briefly describes the general form of vector addition, vector subtraction, scalar product, and the vector product. Later it describes the treatment of vectors in Cartesian, cylindrical, and spherical coordinates systems, and coordinate transformation between Cartesian and cylindrical systems and Cartesian and spherical systems. There are field problems which involve complex geometries and cannot be accommodated in any of the conventional coordinate systems. This briefly indicates the way to deal with such cases. These include the division of configuration into regions and simultaneous use of more than one coordinate system.
