Written by an engineer and sharply focused on practical matters, this text explores the application of Lie groups to solving ordinary differential equations (ODEs). Although the mathematical proofs and derivations in are de-emphasized in favor of problem solving, the author retains the conceptual basis of continuous groups and relates the theory to problems in engineering and the sciences.
The author has developed a number of new techniques that are published here for the first time, including the important and useful enlargement procedure. The author also introduces a new way of organizing tables reminiscent of that used for integral tables. These new methods and the unique organizational scheme allow a significant increase in the number of ODEs amenable to group-theory solution.
Solution of Ordinary Differential Equations by Continuous Groups offers a self-contained treatment that presumes only a rudimentary exposure to ordinary differential equations. Replete with fully worked examples, it is the ideal self-study vehicle for upper division and graduate students and professionals in applied mathematics, engineering, and the sciences.
Continuous One-Parameter Group-I
Global Group Equations
Method of Characteristics
Continuous One-Parameter Group-II
The Once-Extended Group
Higher-Order Extended Groups
ORDINARY DIFFERENTIAL EQUATIONS
Invariance Under a One-Paramter Group
Finding the Groups
System of First-Order ODEs
Classification of Two-Parameter Groups
Invariance and Canonical Coordinates
Bibilography and References
The Rotation Group
Answers to Selected Problems