Description

December 2nd 1974 | Paperback | PDF, EPUB, FB2, DjVu, talking book, mp3, ZIP | 333 pages | ISBN: 9780387901077 | 4.28 Mb

The aim of this book is to provide a systematic and practical account of methods of integration of ordinary and partial differential equations based on invariance under continuous (Lie) groups of trans formations. The goal of these methods is theMoreThe aim of this book is to provide a systematic and practical account of methods of integration of ordinary and partial differential equations based on invariance under continuous (Lie) groups of trans formations.

The goal of these methods is the expression of a solution in terms of quadrature in the case of ordinary differential equations of first order and a reduction in order for higher order equations. For partial differential equations at least a reduction in the number of independent variables is sought and in favorable cases a reduction to ordinary differential equations with special solutions or quadrature. In the last century, approximately one hundred years ago, Sophus Lie tried to construct a general integration theory, in the above sense, for ordinary differential equations.

Following Abels approach for algebraic equations he studied the invariance of ordinary differential equations under transformations. In particular, Lie introduced the study of continuous groups of transformations of ordinary differential equations, based on the infinitesimal properties of the group. In a sense the theory was completely successful. It was shown how for a first-order differential equation the knowledge of a group leads immediately to quadrature, and for a higher order equation (or system) to a reduction in order.

In another sense this theory is somewhat disappointing in that for a first-order differ ential equation essentially no systematic way can be given for finding the groups or showing that they do not exist for a first-order differential equation.

Related Archive Books

Related Books

- Twisted Sanction
- 16.01.2012Mafia Don
- 15.10.2013Trial
- 25.08.2012Astronaut for A Day
- 25.02.2013The Stronghold of Jezebel: A True Story of a Man S Journey
- 05.02.2014年下彼氏の恋愛管理癖 2 [Toshishita Kareshi no Renai Kanriguse 2]
- 19.05.2015Platos Meno: A Philosophy of Man as Acquisitive
- 03.02.2012Eating
- 04.12.2014Time Math
- 30.07.2011Blue

Comments

Recommendations

- Design That Cares: Planning Health Facilities for Patients and Visitors
- Online Dating Boxed Set: The Fast Track To Love and Happiness
- Human Interactive Proofs: Second International Workshop, HIP 2005, Bethlehem, PA, USA, May 19-20, 2005, Proceedings (Lecture Notes in Computer Science / Security and Cryptology)
- Star Woman: We Are Made From Stars And To The Stars We Must Return
- In Vivo Neuromethods. Neuromethods, Volume 32.
- Thunder Canyon