Lecture (3) Orthogonal and Transformations Coordinate Systems

Orthogonal Coordinate Systems
1 – 6 – 1 Cartesian Coordinates :

Fig. (1 – 11 ) The Cartesian Coodinates
1 – 6 – 2 Cylindrical Coordinates :

Fig (1 – 12 ) The Cylindrical Coordinates





1 – 6 – 3 Spherical Coordinates

Fig. ( 1 – 13 ) The Spherical Coordinates










1.7







1.8 Line and Surface Integrals
By using eq.(1 – 56 ) ,we can to find :

Fig.( 1 – 14 ) The line Vector


Fig. ( 1 – 15 ) The Surface Vector area
( 1-57)
Fig. ( 1 – 16 ) The Surface Vector for tree areas
1.9 Gradient of a Scalar Field
Let us assume a temperature T as a function of space parameters . Gradient is an extension of the derivative ( dT / dz ) , however , if the T is a function of 3 – D position ( x , y , z ) , then we need to use Gradient to describe the increase if the temperature T as a function of ( x , y , z ).

z

y

x Fig. (1 – 17 ) The Gradient of Scalar Field in Cartesian Coordinates
Del or