Preface Part I Local Transformation Groups 1 Preliminaries 1.1 Changes of frames of reference and point transformations 1.1.1 Translations 1.1.2 Rotations 1.1.3 Galilean transformation 1.2 Introduction of transformation groups 1.2.1 Definitions and examples 1.2.2 Different types of groups 1.3 Some useful groups 1.3.1 Finite continuous groups on the straight line 1.3.2 Groups on the plane 1.3.3 Groups in IRn Exercises to Chapter 1 2 One-parameter groups and their invariants 2.1 Local groups of transformations 2.1.1 Notation and definition 2.1.2 Groups written in a canonical parameter 2.1.3 Infinitesimal transformations and generators 2.1.4 Lie equations 2.1.5 Exponential map 2.1.6 Determination of a canonical parameter ……
