1. Lecture 2eee3401 Chapter 2 Coordinate Systems 1)Cartesian (rectangular) 2)Circular cylindrical 3)Spherical 4)Others (elliptic cylindrical, conical,…) A hard problem in one coordinate system may turn out to be easy in another system. Example: Laplace’s equation

2. Lecture 2eee3402 Cartesian coordinates ( x, y, z ) The ranges of the coordinate variables x, y, z are A vector in Cartesian coordinates can be written as

3. Lecture 2eee3403 Circular Cylindrical coordinates ( , , z) The ranges of the variables are A vector in cylindrical coordinates can be written as

4. Lecture 2eee3404 The unit vectors are mutually perpendicular: The relationships between the variables ( x, y, z ) and ( , , z )

5. Lecture 2eee3405 The relations between ( ) and ( ) or

6. Lecture 2eee3406 The relationships between ( ) and ( ) are or

7. Lecture 2eee3407 These can be written in matrix form Example: 1)Convert point P(1,3,5) from Cartesian to cylindrical coordinates. 2)Transform vector to cylindrical coordinates.

8. Lecture 2eee3408 3)Evaluate at P in both coordinate systems. Example: Express the following vector in Cartesian coordinates: Example: At point (1,  /3,0), find

9. Lecture 2eee3409 Spherical coordinates (r, ,  )  is called the colatitude.  is called the azimuthal angle. The ranges of the variables are A vector in spherical coordinates may be written as

10. Lecture 2eee34010 The unit vectors and are related as