Lie Groups, Infinitesimal Generators and Lie Algebras

In this Chapter, the basics of the Lie groups and the corresponding infinitesimal generators, invariance of a curve, multi-parameter Lie group of transformations and the corresponding Lie algebra will be discussed. The ideas about special groups given in Chapter 2 will be generalized in this section.  
3.1. LIE GROUPS OF TRANSFORMATIONS 
A one parameter Lie group of transformation for two variables with 
may be written in the general form