Introduction to Symmetry Analysis

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Overview

This text offers a broad, self-contained, introduction to the basic concepts of symmetry analysis and is intended primarily for first and second year graduate students in science, engineering and applied mathematics. Mathematica-based software for finding the Lie point symmetries and Lie-Bäcklund symmetries of differential equations is included on a CD along with more than forty sample notebooks illustrating applications ranging from simple, low order, ordinary differential equations to complex systems of partial differential equations. The software requires Mathematica 2.2 or higher. MathReader 4.0 is included to permit the user without access to Mathematica to read the sample notebooks and follow the procedure used to find symmetries.

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Editorial Reviews

From The Critics
This graduate textbook introduces the methods of symmetry analysis based on Lie groups and how to express the symmetry properties of ordinary and partial differential equations. Sample applications in heat conduction, fluid mechanics, and nonlinear wave propagation are provided. The included CD-ROM contains Mathematica functions for finding the invariant groups of a differential equation and 60 sample notebooks. Annotation c. Book News, Inc., Portland, OR
From the Publisher
'... an easy to read informal introduction to symmetry methods for ordinary and partial differential equations.' Monatshefte für Mathematik

'Overall, this was an enjoyable book to read, which I could recommend to someone to tackle as background reading. ... if one's interest is in the application of symmetry analysis to problems arising in fluids, then this book discusses 'how' in detail.' Peter Clarkson, University of Kent

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Product Details

  • ISBN-13: 9780521777407
  • Publisher: Cambridge University Press
  • Publication date: 9/28/2002
  • Series: Texts in Applied Mathematics Series , #29
  • Edition description: BK&CD-ROM
  • Pages: 654
  • Sales rank: 1,164,844
  • Product dimensions: 6.97 (w) x 9.96 (h) x 1.34 (d)

Table of Contents

Author's Preface
Historical Preface
1 Introduction to Symmetry 1
2 Dimensional Analysis 33
3 Systems of ODEs and First-Order PDEs; State-Space Analysis 55
4 Classical Dynamics 96
5 Introduction to One-Parameter Lie Groups 121
6 First-Order Ordinary Differential Equations 149
7 Differential Functions and Notation 178
8 Ordinary Differential Equations 191
9 Partial Differential Equations 237
10 Laminar Boundary Layers 277
11 Incompressible Flow 318
12 Compressible Flow 364
13 Similarity Rules for Turbulent Shear Flows 395
14 Lie-Backlund Transformations 446
15 Variational Symmetries and Conservation Laws 498
16 Backlund Transformations and Nonlocal Groups 515
App. 1 Review of Calculus and the Theory of Contact 552
App. 2 Invariance of the Contact Conditions under Lie Point Transformation Groups 558
App. 3 Infinite-Order Structure of Lie-Backlund Transformations 569
App. 4 Symmetry Analysis Software 584
Author Index 601
Subject Index 604
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