This is an introductory book on Lie group analysis, intended for advanced undergraduate and beginning graduate students, as well as for scientists wishing to learn how to use symmetry methods in solving differential equations.
The content of the book is as follows: the Introduction is followed by Chapter 2 on ordinary differential equations (ODEs) which explains how symmetries are constructed and exploited for ODEs. The focus is on first-order ODEs such as linear, Bernoulli, homogeneous, exact, and Riccati equations. However, higher order and systems of ODEs are considered as well.
In Chapter 3, the symmetry analysis of partial differential equations (PDEs) is presented. It starts with first-order PDEs and then follows with the second-order PDEs, including heat equation with a source term, Burgers’, and Laplace’s equations. Further, higher-order and systems of PDEs are studied. Chapter 4 is devoted to extensions of Lie’s classical method.
The book suits perfectly for a university course on symmetry analysis, it contains many examples on different levels. More advanced examples are labeled by a special mark. The book has been a basis for a course given at the University of Central Arkansas by the author. As the author suggests: “The methods presented in this book are very algorithmic in nature, and the author encourages the reader to become familiar with one of the computer algebra packages, sich as Maple or Mathematica”.