Symmetry and Integration Methods for Differential Equations

Description

new edition of [Bluman & Kumei (1989)](https://isidore.co/calibre/browse/book/6100) (of the 1st 4 chapters)[Altmetric](https://www.altmetric.com/details/6019777)"REDUCE, MATHEMATICA, MAPLE (which was used for the calculations for the ODE examples in Sections 3.5–3.8)"[MSC classifications](http://ams.rice.edu/mathscinet/search/mscdoc.html?code=22E25,\(22E65,22E70,34-01,34A05,35K05,35L05,35Q20,58F35,58F37,58G37,70H35\))* * *> "The book by Bluman and Anco is an introduction to symmetry-based methods … . The book is written in a clear and straightforward style, using many excellent worked examples … . As someone who teaches an undergraduate course on symmetry methods, I would recommend Bluman and Anco’s book as a good source of examples and supplementary reading. … for anyone wishing to master techniques for obtaining first integrals of ODEs, this book is outstanding."[Peter Hydon, *UK Nonlinear News* , June, 2003](https://www1.maths.leeds.ac.uk/Applied/news.dir/issue32.dir/art/symmetry.html)> "The book under review devoted to symmetry and integration methods for differential equations is a significant update … . The book has a Preface and Introduction well presenting its aim. … Moreover, it has a final section Discussion which puts its contents into perspective by summarizing major results, by referring to related works and by introducing related material. … the book should be particularly suitable for applied mathematicians, physicists and engineers. … the publication of the present book should be highly welcome."*J. Synnatzschke, Zeitschrift für Analysis und ihre Anwendungen, Vol. 22 (1), 2003** * *The book under review is an update of the first four chapters of the book by Bluman and S. Kumei [Symmetries and differential equations, Springer, New York, 1989; [MR1006433](http://www.ams.org/mathscinet/search/publdoc.html?r=1&pg1=MR&s1=1006433&loc=fromrevtext)]. The chapters are (1) Dimensional analysis modeling, and invariance, (2) Lie groups of transformations and infinitesimal transformations, (3) ODE's, (4) PDE's. The emphasis of the text is on infinitesimal methods for scalar equations (both ODE's and PDE's) along with computational methods for these concepts. The majority of differences between this book and the corresponding chapters from the previous version appear in Chapter 3 on ODE's. In particular there are two sections on integrating factors and their relation to symmetries and first integrals. Chapter 3 also addresses how to find contact and higher order (generalized) symmetries for ODE's and how to use them to reduce order as is typically done with point symmetries. [Reviewed by Mark E. Fels](http://www.ams.org/mathscinet-getitem?mr=1914342)